AI Tools For Ecommerce

AI Tools For Ecommerce — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • MSpy

    MSpy

    mSpy is a brand of mobile and computer parental control monitoring software for iOS, Android, Windows, and macOS. The app monitors and logs user activity on the client device and sends the data to a personalized dashboard. Data the users can monitor includes text messages, calls, GPS locations, social media chats, and more. It is owned by Virtuoso Holding. == History == mSpy was launched as a product for mobile monitoring by Altercon Group in 2010. In 2012, the application allowed parents to monitor not only smartphones but also computers running Windows and macOS. In 2013, mSpy became TopTenReviews cell phone monitoring software award winner. By 2014, the business grew nearly 400%, and the app's user numbers exceeded 1 million. In 2015, mSpy received the Parents Tested Parents Approved (PTPA) Winner’s Seal of Approval in the United States. In 2015 and 2018, mSpy was the victim of data breaches which released user data. In 2016, mLite, a light version of mSpy, became available from Google Play. The same year, it was awarded the kidSAFE Certified Seal in the United States. In 2017, mSpy collaborated with YouTuber and journalist Coby Persin to conduct a social experiment on the dangers of social media and online predators. A social experiment, conducted with parental consent, involved Coby Persin to befriend three children—aged 12, 13, and 14—via Snapchat and then invite them to meet personally. Each of the participants agreed to the meeting and arrived at the designated location. The video of the experiment received widespread attention and helped to raise awareness about the importance of online security and parental controls. In early 2021, mSpy released a new feature - Screenrecorder. The feature allows parents to take screenshots of the kid's screen when they are browsing certain apps. In 2024, mSpy's Zendesk was compromised by an unknown threat actor, revealing their customer list. As of 2025, mSpy is compatible with Android, iPhone, and iPad devices. It provides access to various types of data stored on the device, including contact information, calendar entries, emails, SMS messages, browser history, photos, videos, and installed applications. Functions also include GPS tracking, geofencing, keyword alerts etc. == Reception == It was noted that since MSpy runs inconspicuously, there is risk of the software being used illegally. mSpy was called "terrifying" by The Next Web and was featured in NPR coverage of spyware used against victims of stalking and other domestic violence. In response mSpy released security updates aimed at reducing the risk of misuse and stated that it "uses encryption protocols to protect user data and that access is restricted to the account holder". In May 2015, Brian Krebs reported that mSpy was hacked, leaking personal data for hundreds of thousands of users of devices with mSpy installed. mSpy claimed that there was no data leak, but that instead, it was the victim of blackmailers. In September 2018, Krebs claimed and demonstrated that anyone could easily gain access to the mSpy database containing data for millions of users. The company responded by stating that the exposed data consisted primarily of error logs and incorrect login attempts. Following the incident, mSpy implemented new security measures, changed encryption keys, and reset passwords for affected accounts. A 2024 Sky News story characterised mSpy as "stalkerware". Leaked customer support messages from mSpy reveal misuse of its app for illegally monitoring partners and children.

    Read more →
  • Agentic commerce

    Agentic commerce

    Agentic commerce (also referred to as agent-based commerce) describes an emerging form of e-commerce in which autonomous artificial intelligence (AI) agents independently execute purchasing and payment processes on behalf of users or organizations. Unlike conventional digital commerce systems, which require direct human interaction at key decision points, agentic commerce systems are designed to search for products or services, evaluate options, make purchasing decisions, and complete payments without real-time human involvement. An emerging development within the broader fields of e-commerce, fintech, and artificial intelligence; agentic commerce combines advances in generative AI, autonomous agents, application programming interfaces (APIs), and digital payment infrastructures to direct transactions with no direct human interaction. == Characteristics == A defining feature of agentic commerce is the delegation of end-to-end commercial activities to software agents. These agents typically operate according to predefined user preferences, rules, or constraints, such as price limits, quality criteria, delivery times, or preferred payment methods. Based on these parameters, an agent can autonomously perform tasks including product discovery, price comparison, contract selection, order placement, and payment execution. In contrast to decision-support systems, which provide recommendations to human users, agentic commerce systems are designed to act independently. Human involvement may be limited to initial configuration, periodic supervision, or exception handling. == Comparison with traditional and AI-assisted commerce == Traditional e-commerce requires users to manually browse products, select offers, and authorize payments. Generative AI systems used in commerce commonly assist users by answering questions or suggesting options, and do not complete transactions autonomously. Agentic commerce differs in that decision-making authority is partially or fully transferred to AI agents. As a result, the conventional customer journey, characterized by conscious decision points, may be replaced by continuous, automated micro-decisions performed by software. == Applications and business use cases == Potential applications of agentic commerce include recurring purchases, subscription management, business-to-business procurement, inventory replenishment, and price monitoring. In such contexts, transactions are often predictable and standardized, making them suitable for automation. From a business perspective, agentic commerce systems may be used to optimize supply chains, manage inventory levels, negotiate prices algorithmically, or execute transactions across multiple platforms. Enterprises adopting the new technology include retailers Walmart, Home Depot, Wayfair and Urban Outfitters, and ad tech DSPs, including Google Ads, Amazon, and Yahoo. Chinese tech firms are using apps to provide full-service shopping and payment tools. These includes Alibaba, Tencent, and ByteDance who are currently developing AI powered shopping apps. The Qwen AI chatbot allows users to complete transactions directly within its interface. US firms are still leading in developing AI models but integration is slower due to privacy restrictions. == Payments and technical infrastructure == Agentic commerce relies on digital payment systems capable of supporting automated, machine-initiated transactions, including API-based payment processing, tokenization, real-time authorization, and continuous risk monitoring. Typical user interfaces, such as shopping carts, may be replaced by backend integrations between AI agents, merchants, and payment service providers. For example, Iike 2025, Alibaba launched Alipay AI Pay, which grew and began operating as an application for different retailers. In December 2025, Alipay teamed up with Rokid to enable developers to integrate AI payments into AI agents on Rokid's Lingzhu platform. In January 2025, Alipay unveiled the Agentic Commerce Trust Protocol in partnership with Alibaba's consumer AI applications, such as the Qwen App and Taobao Instant Commerce. Qwen adopted the platform first, connecting it to Taobao Instant Commerce and Alipay AI Pay. Users could use Qwen's agentic feature to place food and drink orders within the application instead of having to click outside to an external browser. For merchants, participation in agentic commerce may require products and services to be presented in structured, machine-readable formats to ensure discoverability and interoperability with autonomous agents. == Universal Commerce Protocol (UCP) == In January 2026, Google announced the Universal Commerce Protocol (UCP), an open-source web standard intended to enable interoperability between AI agents and retail systems across the shopping journey, from discovery and checkout to post-purchase support. UCP makes use of REST, JSON-RPC transports, and support for Agent Payments Protocol (AP2), Agent2Agent (A2A), and Model Context Protocol (MCP). == Legal, regulatory, and security considerations == The use of autonomous agents in commerce raises legal and regulatory questions, particularly regarding authorization, liability, consumer protection, and fraud prevention. Existing payment and contract frameworks are generally based on human decision-makers, and their applicability to autonomous agents remains an area of active discussion. Open issues include responsibility for unauthorized or erroneous transactions, mechanisms for dispute resolution, standards for agent authentication, and compliance with data protection and financial regulations. Continuous, automated transaction patterns may also require new approaches to security and risk assessment. Traditional fraud models centered on identity verification may be insufficient for agentic commerce, and that merchants may need intent-based detection methods using machine learning and behavioral analysis to distinguish legitimate AI agents from malicious automation. === Governance frameworks === The deployment of autonomous AI agents in commercial environments has prompted the development of dedicated governance frameworks. These aim to define operational boundaries, decision authority, oversight mechanisms, and accountability structures for agentic systems. The Agentic Commerce Framework (ACF), created in 2025 by Vincent Dorange, is a governance standard that structures the deployment of autonomous AI agents around four founding principles (Decision Sovereignty, Governance by Design, Ultimate Human Control, Traceable Accountability), four operational layers, and 18 governance KPIs. In January 2026, Singapore's Infocomm Media Development Authority (IMDA) published the Model AI Governance Framework for Agentic AI, extending its existing AI governance guidelines to address agent-specific risks including delegation chains and multi-agent coordination. The Cloud Security Alliance (CSA) has also proposed an Agentic Trust Framework applying zero-trust principles to AI agent governance. == Ecosystem and implementation == The adoption of agentic commerce typically requires changes in commerce architecture, data modeling, identity and permissions, and API-based orchestration of checkout and post-purchase workflows. Management consultancies have identified agentic commerce as a structural evolution of digital commerce, emphasizing the role of AI-driven agents in automating discovery, decision-making, and transaction processes across commerce systems. McKinsey & Company has described agentic commerce as a significant shift in how consumers interact with brands and how enterprises design their commerce operating models. In Europe, this ecosystem also includes digital commerce consultancies specializing in the adoption of agentic commerce. Consulting firms such as Horrea support brands in understanding and implementing the technological and organizational shifts associated with agentic commerce. == Market development and outlook == Agentic commerce is generally regarded as an early-stage development. Industry analysts have projected that AI-driven agents could account for a small but growing share of digital payment transactions within the coming years. Due to the scale of global digital commerce, even limited adoption could represent substantial transaction volumes. Analysts expect that by 2029, AI agents could handle between 1% and 4% of all digital payment transactions. With a projected total transaction volume of over $36 trillion a year, even a small share translates into a market worth up to $1.47 trillion. According to a McKinsey study from October 2025, agentic commerce projects that by 2030, the U.S. business-to-consumer retail market alone could see up to $1 trillion in revenue orchestrated through agentic commerce. On a global scale, the opportunity could range from $3 trillion to $5 trillion. Early experiments and pilot projects have demonstrated both the potential and current limitations of the

    Read more →
  • Artisto

    Artisto

    Artisto is a video processing application with art and movie effects filters based on neural network algorithms created in 2016 by Mail.ru Group machine learning specialists. At the moment the application can process videos up to 10 seconds long and offers users 21 filters, including those based on the works of famous artists (e.g. Blue Dream — Pablo Picasso), theme-based (Rio-2016 — related to the 2016 Summer Olympics in Rio de Janeiro) and others. The app works with both pre-recorded videos and videos recorded with the application. == History == Information on the application first appeared on Mail.ru Group Vice President Anna Artamonova's FB page on July 29, 2016. At the moment of posting there was only an Android version available. According to Anna, the application's first version only took eight days to develop. On July 31, the application was added to the AppStore for free download. From this moment and continuing into the present, Artisto has been the world's first app that uses neural networks for editing short videos, processing them in the style of famous artworks or any other source image. Prisma (app) application developers promise to deliver similar functionality at any moment. The application soon won recognition and started to attract the attention of both international brands (e.g. Korean auto manufacturer Kia Motors) and popular singers and musicians. According to the independent App Annie analysis system, within the first two weeks on the market the application made it onto the TOP download lists in nine countries. == Technology == The idea of transferring styles from works of famous artists to images was first mentioned in September 2015 after the publication of Leon Gatys's article "A Neural Algorithm of Artistic Style", where he described the algorithm in detail. The major shortcoming of this algorithm is its slow performance, which is up to dozens of seconds depending on the algorithm's settings. In March 2016, Russian researcher Dmitry Ulyanov's article was published, where he invented a way to improve the generation of stylized pictures using additional neuron generator network training. With this approach, stylized images can be generated within just dozens of milliseconds. Seventeen days after Ulyanov's article, Justin Johnson published an article containing an identical idea, the only difference being the structure of the generator network. The Artisto application was developed using these open-source technologies, which Mail.ru Group's machine learning specialists improved for faster video processing and better quality.

    Read more →
  • AVT Statistical filtering algorithm

    AVT Statistical filtering algorithm

    AVT Statistical filtering algorithm is an approach to improving quality of raw data collected from various sources. It is most effective in cases when there is inband noise present. In those cases AVT is better at filtering data then, band-pass filter or any digital filtering based on variation of. Conventional filtering is useful when signal/data has different frequency than noise and signal/data is separated/filtered by frequency discrimination of noise. Frequency discrimination filtering is done using Low Pass, High Pass and Band Pass filtering which refers to relative frequency filtering criteria target for such configuration. Those filters are created using passive and active components and sometimes are implemented using software algorithms based on Fast Fourier transform (FFT). AVT filtering is implemented in software and its inner working is based on statistical analysis of raw data. When signal frequency/(useful data distribution frequency) coincides with noise frequency/(noisy data distribution frequency) we have inband noise. In this situations frequency discrimination filtering does not work since the noise and useful signal are indistinguishable and where AVT excels. To achieve filtering in such conditions there are several methods/algorithms available which are briefly described below. == Averaging algorithm == Collect n samples of data Calculate average value of collected data Present/record result as actual data == Median algorithm == Collect n samples of data Sort the data in ascending or descending order. Note that order does not matter Select the data that happen to be in n/2 position and present/record it as final result representing data sample == AVT algorithm == AVT algorithm stands for Antonyan Vardan Transform and its implementation explained below. Collect n samples of data Calculate the standard deviation and average value Drop any data that is greater or less than average ± one standard deviation Calculate average value of remaining data Present/record result as actual value representing data sample This algorithm is based on amplitude discrimination and can easily reject any noise that is not like actual signal, otherwise statistically different than 1 standard deviation of the signal. Note that this type of filtering can be used in situations where the actual environmental noise is not known in advance. Notice that it is preferable to use the median in above steps than average. Originally the AVT algorithm used average value to compare it with results of median on the data window. == Filtering algorithms comparison == Using a system that has signal value of 1 and has noise added at 0.1% and 1% levels will simplify quantification of algorithm performance. The R script is used to create pseudo random noise added to signal and analyze the results of filtering using several algorithms. Please refer to "Reduce Inband Noise with the AVT Algorithm" article for details. This graphs show that AVT algorithm provides best results compared with Median and Averaging algorithms while using data sample size of 32, 64 and 128 values. Note that this graph was created by analyzing random data array of 10000 values. Sample of this data is graphically represented below. From this graph it is apparent that AVT outperforms other filtering algorithms by providing 5% to 10% more accurate data when analyzing same datasets. Considering random nature of noise used in this numerical experiment that borderlines worst case situation where actual signal level is below ambient noise the precision improvements of processing data with AVT algorithm are significant. == AVT algorithm variations == === Cascaded AVT === In some situations better results can be obtained by cascading several stages of AVT filtering. This will produce singular constant value which can be used for equipment that has known stable characteristics like thermometers, thermistors and other slow acting sensors. === Reverse AVT === Collect n samples of data Calculate the standard deviation and average value Drop any data that is within one standard deviation ± average band Calculate average value of remaining data Present/record result as actual data This is useful for detecting minute signals that are close to background noise level. == Possible applications and uses == Use to filter data that is near or below noise level Used in planet detection to filter out raw data from the Kepler space telescope Filter out noise from sound sources where all other filtering methods (Low-pass filter, High-pass filter, Band-pass filter, Digital filter) fail. Pre-process scientific data for data analysis (Smoothness) before plotting see (Plot (graphics)) Used in SETI (Search for extraterrestrial intelligence) for detecting/distinguishing extraterrestrial signals from cosmic background Use AVT as image filtering algorithm to detect altered images. This image of Jupiter generated from this program, detecting alterations in original picture that was modified to be visually appealing by applying filters. Another version of this comparison is the Reverse AVT filter applied to the same original Jupiter Image, where we only see that altered portion as Noise that was eliminated by AVT algorithm. Use AVT as image filtering algorithm to estimate data density from images. Picture of Pillars of Creation Nebula shows data density in filtered images from Hubble and Webb. Note that image on the left has big patches of missing data marked with simpler color patterns.

    Read more →
  • Macromedia FreeHand

    Macromedia FreeHand

    Macromedia FreeHand (formerly Aldus FreeHand) is a discontinued computer application for creating two-dimensional vector graphics oriented primarily to professional illustration, desktop publishing and content creation for the Web. FreeHand was similar in scope, intended market, and functionality to Adobe Illustrator, CorelDRAW and Xara Designer Pro. Because of FreeHand's dedicated page layout and text control features, it also compares to Adobe InDesign and QuarkXPress. Professions using FreeHand include graphic design, illustration, cartography, fashion and textile design, product design, architects, scientific research, and multimedia production. FreeHand was created by Altsys Corporation in 1988 and licensed to Aldus Corporation, which released versions 1 through 4. In 1994, Aldus merged with Adobe Systems and because of the overlapping market with Adobe Illustrator, FreeHand was returned to Altsys by order of the Federal Trade Commission. Altsys was later bought by Macromedia, which released FreeHand versions 5 through 11 (FreeHand MX). In 2005, Adobe Systems acquired Macromedia and its product line which included FreeHand MX, under whose ownership it presently resides. Since 2003, FreeHand development has been discontinued; in the Adobe Systems catalog, FreeHand has been replaced by Adobe Illustrator. FreeHand MX continues to run under Windows 11 and under Mac OS X 10.6 (Snow Leopard) within Rosetta, a PowerPC code emulator, and requires a registration patch supplied by Adobe. FreeHand 10 runs without problems on Mac OS X Snow Leopard with Rosetta enabled, and does not require a registration patch. Later versions of macOS can use a Mac OS X Snow Leopard Server virtual machine to emulate the required PowerPC support. == History == === Altsys and Aldus FreeHand === In 1984, James R. Von Ehr founded Altsys Corporation to develop graphics applications for personal computers. Based in Plano, Texas, the company initially produced font editing and conversion software; Fontastic Plus, Metamorphosis, and the Art Importer. Their premier PostScript font-design package, Fontographer, was released in 1986 and was the first such program on the market. With the PostScript background having been established by Fontographer, Altsys also developed FreeHand (originally called Masterpiece) as a Macintosh Postscript-based illustration program that used Bézier curves for drawing and was similar to Adobe Illustrator. FreeHand was announced as "... a Macintosh graphics program described as having all the features of Adobe's Illustrator plus drawing tools such as those in Mac Paint and Mac Draft and special effects similar to those in Cricket Draw." Seattle's Aldus Corporation acquired a licensing agreement with Altsys Corporation to release FreeHand along with their flagship product, Pagemaker, and Aldus FreeHand 1.0 was released in 1988. FreeHand's product name used intercaps; the F and H were capitalized. The partnership between the two companies continued with Altsys developing FreeHand and with Aldus controlling marketing and sales. After 1988, a competitive exchange between Aldus FreeHand and Adobe Illustrator ensued on the Macintosh platform with each software advancing new tools, achieving better speed, and matching significant features. Windows PC development also allowed Illustrator 2 (aka, Illustrator 88 on the Mac) and FreeHand 3 to release Windows versions to the graphics market. FreeHand 1.0 sold for $495 in 1988. It included the standard drawing tools and features as other draw programs including special effects in fills and screens, text manipulation tools, and full support for CMYK color printing. It was also possible to create and insert PostScript routines anywhere within the program. FreeHand performed in preview mode instead of keyline mode but performance was slower. FreeHand 2.0 sold for $495 in 1989. Besides improving on the features of FreeHand 1.0, FreeHand 2 added faster operation, Pantone colors, stroked text, flexible fill patterns and automatically import graphic assets from other programs. It added accurate control over a color monitor screen display, limited only by its resolution. FreeHand 3.0 sold for $595 in 1991. New features included resizable color, style, and layer panels including an Attributes menu. Also tighter precision of both the existing tools and aligning of objects. FH3 created compound Paths. Text could be converted to paths, applied to an ellipse, or made vertical. Carried over from version 1.0, FreeHand 3 suffered by having text entered into a dialog box instead of directly to the page. In October 1991, a 3.1 upgrade made FreeHand work with System 7 but additionally, it supported pressure-sensitive drawing which offered varying line widths with a users stroke. It improved element manipulation and added more import/export options. FreeHand 4.0 sold for $595 in 1994. Altsys ported FreeHand 3.0 to the NeXT system creating a new program named Virtuoso. Virtuoso continued its development at Altsys and version 2.0 of Virtuoso was feature-equivalent to FreeHand 4 (with the addition of NeXT-specific features such as Services and Display PostScript) and file compatible, with Virtuoso 2 able to open FreeHand 4 files and vice versa. A prominent feature of this version was the ability to type directly into the page and wrap inside or outside any shape. It also included drag-and-drop color imaging, a larger pasteboard, and a user interface that featured floating, rollup panels. The colors palette included a color mixer for adding new colors to the swatch list. Speed increases were made. In the same year of FreeHand 4 release, Adobe Systems announced merger plans with Aldus Corporation for $525 million. Fear about the end of competition between these two leading applications was reported in the media and expressed by customers (Illustrator versus FreeHand and Adobe Photoshop versus Aldus PhotoStyler.) Because of this overlapping of the market, Altsys stepped in by suing Aldus, saying that the merger deal was "a prima facie violation of a non-compete clause within the FreeHand licensing agreement." Altsys CEO Jim Von Ehr explained, "No one loves FreeHand more than we do. We will do whatever it takes to see it survive." The Federal Trade Commission issued a complaint against Adobe Systems on October 18, 1994, ordering a divestiture of FreeHand to "remedy the lessening of competition resulting from the acquisition as alleged in the Commission's complaint," and further, the FTC ordering, "That for a period of ten (10) years from the date on which this order becomes final, respondents shall not, without the prior approval of the Commission, directly or indirectly, through subsidiaries, partnerships, or otherwise .. Acquire any Professional Illustration Software or acquire or enter into any exclusive license to Professional Illustration Software;" (referring to FreeHand.) FreeHand was returned to Altsys with all licensing and marketing rights as well as Aldus FreeHand's customer list. === Macromedia Freehand === By late 1994, Altsys still retained all rights to FreeHand. Despite brief plans to keep it in-house to sell it along with Fontographer and Virtuoso, Altsys reached an agreement with the multimedia software company, Macromedia, to be acquired. This mutual agreement provided FreeHand and Fontographer a new home with ample resources for marketing, sales, and competition against the newly merged Adobe-Aldus company. Altsys would remain in Richardson, Texas, but would be renamed as the Digital Arts Group of Macromedia and was responsible for the continued development of FreeHand. Macromedia received FreeHand's 200,000 customers and expanded its traditional product line of multimedia graphics software to illustration and design graphics software. CEO James Von Ehr became a Macromedia vice-president until 1997 when he left to start another venture. FreeHand 5.0 sold for $595 in 1995. This version featured a more customizable and expanded workspace, multiple views, stronger design and editing tools, a report generator, spell check, paragraph styles, multicolor gradient fills up to 64 colors, speed improvements, and it accepted Illustrator plugins. In September 1995, a 5.5 upgrade added Photoshop plug-in support, PDF import capabilities, the Extract feature, inline graphics to text, improved auto-expanding text containers, the Crop feature, and the Create PICT Image feature. A FreeHand 5.5 upgrade was part of the FreeHand Graphics Studio (a suite that included Fontographer, Macromedia xRes image editing application, and Extreme 3D animation and modeling application). FreeHand 6.0 in 1996. This version only existed in beta. Some Freehand 7 prerelease versions were released under the Freehand 6 tag. FreeHand 7.0 sold for $399 in 1996, or $449 as part of the FreeHand Graphics Studio (see above.) Features included a redesigned user interface that allowed recombining Inspectors, Panel Tabs, Dockable Panels, Smart Cursors,

    Read more →
  • Recommender system

    Recommender system

    A recommender system, also called a recommendation algorithm, recommendation engine, or recommendation platform, is a type of information filtering system that suggests items most relevant to a particular user. The value of these systems becomes particularly evident in scenarios where users must select from a large number of options, such as products, media, or content. Major social media platforms and streaming services rely on recommender systems that employ machine learning to analyze user behavior and preferences, thereby enabling personalized content feeds. Typically, the suggestions refer to a variety decision-making processes, including the selection of a product, musical selection, or online news source to read. The implementation of recommender systems is pervasive, with commonly recognised examples including the generation of playlist for video and music services, the provision of product recommendations for e-commerce platforms, and the recommendation of content on social media platforms and the open web. These systems can operate using a single type of input, such as music, or multiple inputs from diverse platforms, including news, books and search queries. Additionally, popular recommender systems have been developed for specific topics, such as restaurants and online dating services. Recommender systems have also been developed to explore research articles and experts, collaborators, and financial services. A content discovery platform is a software recommendation platform that employs recommender system tools. It utilizes user metadata in order to identify and suggest relevant content, whilst reducing ongoing maintenance and development costs. A content discovery platform delivers personalized content to websites, mobile devices, and set-top boxes. A large range of content discovery platforms currently exist for various forms of content ranging from news articles and academic journal articles to television. As operators compete to serve as the gateway to home entertainment, personalized television emerges as a key service differentiator. Academic content discovery has recently become another area of interest, the emergence of numerous companies dedicated to assisting academic researchers in keeping up to date with relevant academic content and facilitating serendipitous discovery of new content. == Overview == Recommender systems usually make use of either or both collaborative filtering and content-based filtering, as well as other systems such as knowledge-based systems. Collaborative filtering approaches build a model from a user's past behavior (e.g., items previously purchased or selected and/or numerical ratings given to those items) as well as similar decisions made by other users. This model is then used to predict items (or ratings for items) that the user may have an interest in. Content-based filtering approaches utilize a series of discrete, pre-tagged characteristics of an item in order to recommend additional items with similar properties. === Example === The differences between collaborative and content-based filtering can be demonstrated by comparing two early music recommender systems, Last.fm and Pandora Radio. We can also look at how these methods are applied in e-commerce, for example, on platforms like Amazon. Last.fm creates a "station" of recommended songs by observing what bands and individual tracks the user has listened to on a regular basis and comparing those against the listening behavior of other users. Last.fm will play tracks that do not appear in the user's library, but are often played by other users with similar interests. As this approach leverages the behavior of users, it is an example of a collaborative filtering technique. Pandora uses the properties of a song or artist (a subset of the 450 attributes provided by the Music Genome Project) to seed a "station" that plays music with similar properties. User feedback is used to refine the station's results, deemphasizing certain attributes when a user "dislikes" a particular song and emphasizing other attributes when a user "likes" a song. This is an example of a content-based approach. In e-commerce, Amazon's well-known "customers who bought X also bought Y" feature is a prime example of collaborative filtering. It also uses content-based filtering when it recommends a book by the same author you've previously read or a pair of shoes in a similar style to ones you've viewed. Each type of system has its strengths and weaknesses. In the above example, Last.fm requires a large amount of information about a user to make accurate recommendations. This is an example of the cold start problem, and is common in collaborative filtering systems. Whereas Pandora needs very little information to start, it is far more limited in scope (for example, it can only make recommendations that are similar to the original seed). === Alternative implementations === Recommender systems are a useful alternative to search algorithms since they help users discover items they might not have found otherwise. Of note, recommender systems are often implemented using search engines indexing non-traditional data. In some cases, like in the Gonzalez v. Google Supreme Court case, may argue that search and recommendation algorithms are different technologies. Recommender systems have been the focus of several granted patents, and there are more than 50 software libraries that support the development of recommender systems including LensKit, RecBole, ReChorus and RecPack. == History == Elaine Rich created the first recommender system in 1979, called Grundy. She looked for a way to recommend users books they might like. Her idea was to create a system that asks users specific questions and classifies them into classes of preferences, or "stereotypes", depending on their answers. Depending on users' stereotype membership, they would then get recommendations for books they might like. Another early recommender system, called a "digital bookshelf", was described in a 1990 technical report by Jussi Karlgren at Columbia University, and implemented at scale and worked through in technical reports and publications from 1994 onwards by Jussi Karlgren, then at SICS, and research groups led by Pattie Maes at MIT, Will Hill at Bellcore, and Paul Resnick, also at MIT, whose work with GroupLens was awarded the 2010 ACM Software Systems Award. Montaner provided the first overview of recommender systems from an intelligent agent perspective. Adomavicius provided a new, alternate overview of recommender systems. Herlocker provides an additional overview of evaluation techniques for recommender systems, and Beel et al. discussed the problems of offline evaluations. Beel et al. have also provided literature surveys on available research paper recommender systems and existing challenges. == Approaches == === Collaborative filtering === One approach to the design of recommender systems that has wide use is collaborative filtering. Collaborative filtering is based on the assumption that people who agreed in the past will agree in the future, and that they will like similar kinds of items as they liked in the past. The system generates recommendations using only information about rating profiles for different users or items. By locating peer users/items with a rating history similar to the current user or item, they generate recommendations using this neighborhood. This approach is a cornerstone for e-commerce sites that analyze the purchasing patterns of thousands of users to suggest what you might like. Collaborative filtering methods are classified as memory-based and model-based. A well-known example of memory-based approaches is the user-based algorithm, while that of model-based approaches is matrix factorization (recommender systems). A key advantage of the collaborative filtering approach is that it does not rely on machine analyzable content and therefore it is capable of accurately recommending complex items such as movies without requiring an "understanding" of the item itself. Many algorithms have been used in measuring user similarity or item similarity in recommender systems. For example, the k-nearest neighbor (k-NN) approach and the Pearson Correlation as first implemented by Allen. When building a model from a user's behavior, a distinction is often made between explicit and implicit forms of data collection. Examples of explicit data collection include the following: Asking a user to rate an item on a sliding scale. Asking a user to search. Asking a user to rank a collection of items from favorite to least favorite. Presenting two items to a user and asking him/her to choose the better one of them. Asking a user to create a list of items that he/she likes (see Rocchio classification or other similar techniques). Examples of implicit data collection include the following: Observing the items that a user views in an online store, media library, or other repository of med

    Read more →
  • Discoverability

    Discoverability

    Discoverability is the degree to which something, especially a piece of content or information, can be found in a search of a file, database, or other information system. Discoverability is a concern in library and information science, many aspects of digital media, software and web development, and in marketing, since products and services cannot be used if people cannot find it or do not understand what it can be used for. In human-computer interaction the term is further used to describe the discoverability of interactions, features and interactive systems overall . Metadata, or "information about information", such as a book's title, a product's description, or a website's keywords, affects how discoverable something is on a database or online. Adding metadata to a product that is available online can make it easier for end users to find the product. For example, if a song file is made available online, making the title, band name, genre, year of release, and other pertinent information available in connection with this song means the file can be retrieved more easily. The organization of information through the implementation of alphabetical structures or the integration of content into search engines exemplifies strategies employed to enhance the discoverability of information. The concept of discoverability, while related to but distinct from accessibility and usability, which are other qualities that affect the usefulness of a piece of information, is a critical aspect of information retrieval. == Etymology == The concept of "discoverability" in an information science and online context is a loose borrowing from the concept of the similar name in the legal profession. In law, "discovery" is a pre-trial procedure in a lawsuit in which each party, through the law of civil procedure, can obtain evidence from the other party or parties by means of discovery devices such as a request for answers to interrogatories, request for production of documents, request for admissions and depositions. Discovery can be obtained from non-parties using subpoenas. When a discovery request is objected to, the requesting party may seek the assistance of the court by filing a motion to compel discovery. == Purpose == The usability of any piece of information directly relates to how discoverable it is, either in a "walled garden" database or on the open Internet. The quality of information available on this database or on the Internet depends upon the quality of the meta-information about each item, product, or service. In the case of a service, because of the emphasis placed on service reusability, opportunities should exist for reuse of this service. However, reuse is only possible if information is discoverable in the first place. To make items, products, and services discoverable, the process is as follows: Document the information about the item, product or service (the metadata) in a consistent manner. Store the documented information (metadata) in a searchable repository. while technically a human-searchable repository, such as a printed paper list would qualify, "searchable repository" is usually taken to mean a computer-searchable repository, such as a database that a human user can search using some type of search engine or "find" feature. Enable search for the documented information in an efficient manner. supports number 2, because while reading through a printed paper list by hand might be feasible in a theoretical sense, it is not time and cost-efficient in comparison with computer-based searching. Apart from increasing the reuse potential of the services, discoverability is also required to avoid development of solution logic that is already contained in an existing service. To design services that are not only discoverable but also provide interpretable information about their capabilities, the service discoverability principle provides guidelines that could be applied during the service-oriented analysis phase of the service delivery process. === Specific to digital media === In relation to audiovisual content, according to the meaning given by the Canadian Radio-television and Telecommunications Commission (CRTC) for the purpose of its 2016 Discoverability Summit, discoverability can be summed up to the intrinsic ability of given content to "stand out of the lot", or to position itself so as to be easily found and discovered. A piece of audiovisual content can be a movie, a TV series, music, a book (eBook), an audio book or podcast. When audiovisual content such as a digital file for a TV show, movie, or song, is made available online, if the content is "tagged" with identifying information such as the names of the key artists (e.g., actors, directors and screenwriters for TV shows and movies; singers, musicians and record producers for songs) and the genres (for movies genres, music genres, etc.). When users interact with online content, algorithms typically determine what types of content the user is interested in, and then a computer program suggests "more like this", which is other content that the user may be interested in. Different websites and systems have different algorithms, but one approach, used by Amazon (company) for its online store, is to indicate to a user: "customers who bought x also bought y" (affinity analysis, collaborative filtering). This example is oriented around online purchasing behaviour, but an algorithm could also be programmed to provide suggestions based on other factors (e.g., searching, viewing, etc.). Discoverability is typically referred to in connection with search engines. A highly "discoverable" piece of content would appear at the top, or near the top of a user's search results. A related concept is the role of "recommendation engines", which give a user recommendations based on his/her previous online activity. Discoverability applies to computers and devices that can access the Internet, including various console video game systems and mobile devices such as tablets and smartphones. When producers make an effort to promote content (e.g., a TV show, film, song, or video game), they can use traditional marketing (billboards, TV ads, radio ads) and digital ads (pop-up ads, pre-roll ads, etc.), or a mix of traditional and digital marketing. Even before the user's intervention by searching for a certain content or type of content, discoverability is the prime factor which contributes to whether a piece of audiovisual content will be likely to be found in the various digital modes of content consumption. As of 2017, modes of searching include looking on Netflix for movies, Spotify for music, Audible for audio books, etc., although the concept can also more generally be applied to content found on Twitter, Tumblr, Instagram, and other websites. It involves more than a content's mere presence on a given platform; it can involve associating this content with "keywords" (tags), search algorithms, positioning within different categories, metadata, etc. Thus, discoverability enables as much as it promotes. For audiovisual content broadcast or streamed on digital media using the Internet, discoverability includes the underlying concepts of information science and programming architecture, which are at the very foundation of the search for a specific product, information or content. === Human-Computer Interaction === In human–computer interaction (HCI), discoverability refers to the ability of users to perceive and comprehend a system, function, or input method upon encountering it, despite a lack of prior awareness or knowledge, whether through intentional effort or serendipitously . The concept was popularised by Don Norman, who framed it around whether users can determine what actions are possible and how to perform them . Discoverability is considered a precondition for learnability, though the two concepts are frequently conflated in the literature . == Applications == === Within a webpage === Within a specific webpage or software application ("app"), the discoverability of a feature, content or link depends on a range of factors, including the size, colour, highlighting features, and position within the page. When colour is used to communicate the importance of a feature or link, designers typically use other elements as well, such as shadows or bolding, for individuals, who cannot see certain colours. Just as traditional paper printing created other physical locations that stood out, such as being "above the fold" of a newspaper versus "below the fold", a web page or app's screenview may have certain locations that give features additional visibility to users, such as being right at the bottom of the web page or screen. The positional advantages or disadvantages of various locations depend on different cultures and languages (e.g., left to right vs. right to left). Some locations have become established, such as having toolbars at the top of a screen or webpage. Some designers have argued t

    Read more →
  • Project workforce management

    Project workforce management

    Project workforce management is the practice of combining the coordination of all logistic elements of a project through a single software application (or workflow engine). This includes planning and tracking of schedules and mileposts, cost and revenue, resource allocation, as well as overall management of these project elements. Efficiency is improved by eliminating manual processes, like spreadsheet tracking to monitor project progress. It also allows for at-a-glance status updates and ideally integrates with existing legacy applications in order to unify ongoing projects, enterprise resource planning (ERP) and broader organizational goals. There are a lot of logistic elements in a project. Different team members are responsible for managing each element and often, the organisation may have a mechanism to manage some logistic areas as well. By coordinating these various components of project management, workforce management and financials through a single solution, the process of configuring and changing project and workforce details is simplified. == Introduction == A project workforce management system defines project tasks, project positions, and assigns personnel to the project positions. The project tasks and positions are correlated to assign a responsible project position or even multiple positions to complete each project task. Because each project position may be assigned to a specific person, the qualifications and availabilities of that person can be taken into account when determining the assignment. By associating project tasks and project positions, a manager can better control the assignment of the workforce and complete the project more efficiently. When it comes to project workforce management, it is all about managing all the logistic aspects of a project or an organisation through a software application. Usually, this software has a workflow engine defined. Therefore, all the logistic processes take place in the workflow engine. == About == === Technical field === This invention relates to project management systems and methods, more particularly to a software-based system and method for project and workforce management. === Software usage === Due to the software usage, all the project workflow management tasks can be fully automated without leaving many tasks for the project managers. This returns high efficiency to the project management when it comes to project tracking proposes. In addition to different tracking mechanisms, project workforce management software also offer a dashboard for the project team. Through the dashboard, the project team has a glance view of the overall progress of the project elements. Most of the times, project workforce management software can work with the existing legacy software systems such as ERP (enterprise resource planning) systems. This easy integration allows the organisation to use a combination of software systems for management purposes. === Background === Good project management is an important factor for the success of a project. A project may be thought of as a collection of activities and tasks designed to achieve a specific goal of the organisation, with specific performance or quality requirements while meeting any subject time and cost constraints. Project management refers to managing the activities that lead to the successful completion of a project. Furthermore, it focuses on finite deadlines and objectives. A number of tools may be used to assist with this as well as with assessment. Project management may be used when planning personnel resources and capabilities. The project may be linked to the objects in a professional services life cycle and may accompany the objects from the opportunity over quotation, contract, time and expense recording, billing, period-end-activities to the final reporting. Naturally the project gets even more detailed when moving through this cycle. For any given project, several project tasks should be defined. Project tasks describe the activities and phases that have to be performed in the project such as writing of layouts, customising, testing. What is needed is a system that allows project positions to be correlated with project tasks. Project positions describe project roles like project manager, consultant, tester, etc. Project-positions are typically arranged linearly within the project. By correlating project tasks with project positions, the qualifications and availability of personnel assigned to the project positions may be considered. == Benefits of project management == Good project management should: Reduce the chance of a project failing Ensure a minimum level of quality and that results meet requirements and expectations Free up other staff members to get on with their area of work and increase efficiency both on the project and within the business Make things simpler and easier for staff with a single point of contact running the overall project Encourage consistent communications amongst staff and suppliers Keep costs, timeframes and resources to budget == Workflow engine == When it comes to project workforce management, it is all about managing all the logistic aspects of a project or an organisation through a software application. Usually, this software has a workflow engine defined in them. So, all the logistic processes take place in the workflow engine. The regular and most common types of tasks handled by project workforce management software or a similar workflow engine are: === Planning and monitoring project schedules and milestones === Regularly monitoring your project's schedule performance can provide early indications of possible activity-coordination problems, resource conflicts, and possible cost overruns. To monitor schedule performance. Collecting information and evaluating it ensure a project accuracy. The project schedule outlines the intended result of the project and what's required to bring it to completion. In the schedule, we need to include all the resources involved and cost and time constraints through a work breakdown structure (WBS). The WBS outlines all the tasks and breaks them down into specific deliverables. === Tracking the cost and revenue aspects of projects === The importance of tracking actual costs and resource usage in projects depends upon the project situation. Tracking actual costs and resource usage is an essential aspect of the project control function. === Resource utilisation and monitoring === Organisational profitability is directly connected to project management efficiency and optimal resource utilisation. To sum up, organisations that struggle with either or both of these core competencies typically experience cost overruns, schedule delays and unhappy customers. The focus for project management is the analysis of project performance to determine whether a change is needed in the plan for the remaining project activities to achieve the project goals. == Other management aspects of project management == === Project risk management === Risk identification consists of determining which risks are likely to affect the project and documenting the characteristics of each. === Project communication management === Project communication management is about how communication is carried out during the course of the project === Project quality management === It is of no use completing a project within the set time and budget if the final product is of poor quality. The project manager has to ensure that the final product meets the quality expectations of the stakeholders. This is done by good: Quality planning: Identifying what quality standards are relevant to the project and determining how to meet them. Quality assurance: Evaluating overall project performance on a regular basis to provide confidence that the project will satisfy the relevant quality standards. Quality control: Monitoring specific project results to determine if they comply with relevant quality standards and identifying ways to remove causes of poor performance. == Project workforce management vs. traditional management == There are three main differences between Project Workforce Management and traditional project management and workforce management disciplines and solutions: === Workflow-driven === All project and workforce processes are designed, controlled and audited using a built-in graphical workflow engine. Users can design, control and audit the different processes involved in the project. The graphical workflow is quite attractive for the users of the system and allows the users to have a clear idea of the workflow engine. === Organisation and work breakdown structures === Project Workforce Management provides organization and work breakdown structures to create, manage and report on functional and approval hierarchies, and to track information at any level of detail. Users can create, manage, edit and report work breakdown structures. Work breakdown structures have different abstraction

    Read more →
  • Mistral Vibe

    Mistral Vibe

    Mistral Vibe or Vibe (Le Chat until May 2026), is a chatbot that uses generative artificial intelligence developed in France by Mistral AI. Mistral Vibe is available in iOS and Android. Its services are operated on a freemium model. == History == In February 2024, Mistral AI released Le Chat. In January 2025, Mistral AI made a content deal with Agence France-Presse (AFP) that lets Le Chat query AFP's entire archive dating back to 1983. On 6 February 2025, a mobile app for Le Chat was released for iOS and Android, and a subscription tier, Pro, was introduced at a cost of $14.99 per month. In July 2025, Mistral AI released Voxtral, an open-source language model that understands and generates audio. Mistral introduced a voice mode for chatting that uses Voxtral, and projects, which allows grouping chats and files. In September 2025, Le Chat introduced the capability to remember previous conversations. In May 2026, Mistral AI announced the rebrand from Le Chat to Mistral Vibe and new features were introduced at the same time.

    Read more →
  • Artificial intelligence in architecture

    Artificial intelligence in architecture

    Artificial intelligence in architecture is the use of artificial intelligence in automation, design, and planning in the architectural process or in assisting human skills in the field of architecture. AI has been used by some architects for design, and has been proposed as a way to automate planning and routine tasks in the field. == Implications == === Benefits === Artificial intelligence, according to ArchDaily, is said to potentially significantly augment the architectural profession through its ability to improve the design and planning process as well as increasing productivity. Through its ability to handle a large amount of data, AI is said to potentially allow architects a range of design choices with criteria considerations such as budget, requirements adjusted to space, and sustainability goals calculated as part of the design process. ArchDaily said this may allow the design of optimized alternatives that can then undergo human review. AI tools are also said to potentially allow architects to assimilate urban and environmental data to inform their designs, streamlining initial stages of project planning and increasing efficiency and productivity. The advances in generative design through the input of specific prompts allow architects to produce visual designs, including photorealistic images, and thus render and explore various material choices and spatial configurations. ArchDaily noted this could speed the creative process as well as allow for experimentation and sophistication in the design. Additionally, AI's capacity for pattern recognition and coding could aid architects in organizing design resources and developing custom applications, thus enhancing the efficiency and collaboration between both architects and AI. AI is thought to also be able to contribute to the sustainability of buildings by analyzing various factors and following recommended energy-efficient modifications, thus pushing the industry towards greener practices. The use of AI in building maintenance, project management, and the creation of immersive virtual reality experiences are also thought of as potentially augmenting the architectural design process and workflow. Examples include the use of text-to-image systems such as Midjourney to create detailed architectural images, and the use of AI optimization systems from companies such as Finch3D and Autodesk to automatically generate floor plans from simple programmatic inputs. In contrast to digital-only creative practices, the high materiality of architectural outputs requires transitions from ephemeral digital files to permanent physical structures that are subject to strict safety regulations, material constraints, sensory intuition, and site-specific cultural contexts, making full automation difficult. Early adopters such as architect Stephen Coorlas have actively challenged the boundaries of architectural practice through AI. His early experimental initiative, Speculations on AI and Architecture, confronts the discipline's traditional workflows by training text-to-image AI tools such as Midjourney, Luma AI, and PromeAI to generate more nuanced architectural illustrations including construction documents, architectural details, and assembly sequences for various structures. Coorlas inputs precise terminology and architectural language to provoke the AI into producing axonometric drawings that resemble conventional documentation, then experiments with animating the outputs using AI generated depth maps and other AI image-to-3D wireframe tools. Stephen's inventive process invites architects and designers to reconsider authorship, automation, and the future of visual communication in the built environment. Rather than treating AI as a peripheral tool, Stephen has advocated for AI to be a speculative collaborator capable of engaging with discipline-specific challenges. His work contributes to the growing discourse on generative design, parametric optimization, and the philosophical implications of machine-assisted creativity raising urgent questions about how such technologies will reshape architectural agency, precision, and pedagogy. Another prominent advocate is Architect Andrew Kudless, who in an interview to Dezeen recounted that he uses AI to innovate in architectural design by incorporating materials and scenes not usually present in initial plans, which he believes can significantly alter client presentations. He told Dezeen he believes one should show clients renderings from the onset, with AI assisting in this work, arguing that changes in design should be a positive aspect of the client-designer relationship by actively involving clients in the process. Additionally, Kudless highlighted the AI's potential to facilitate labor in architectural firms, particularly in automating rendering tasks, thus reducing the workload on junior staff while maintaining control over the creative output. === Emergent aesthetics === In an interview for the AItopia series to Dezeen, designer Tim Fu discussed the transformative potential of AI in architecture, and proposed a future where AI could herald a "neoclassical futurist" style, blending the grandeur of classical aesthetics with futuristic design. Through his collaborative project, The AI Stone Carver, Fu showcased how AI can innovate traditional practices by generating design concepts that are then realized through human craftsmanship, such as stone carving by mason Till Apfel. This approach, he believed, celebrated the fusion of diverse architectural styles and also emphasized the unique capabilities of AI in enhancing creative design processes. Fu told Dezeen he envisions the integration of AI in design as a means to revive the ornamentation and detailed aesthetics characteristic of classical architecture, moving away from minimalism, which he said dominates contemporary architecture. He argued that AI's involvement in the ideation phase of design allows for a reversal in the roles of machine and human, enabling architects and designers to focus on creating more intricate and ornamental structures. Fu's optimistic outlook extended to the broader impact of AI on the architectural field, seeing it as an indispensable tool that will shift rather than replace human roles, enriching the field with innovative designs that pay homage to the beauty and qualities of classical architecture not present in contemporary architecture while embracing new technologies. This perspective resonates with designers like Manas Bhatia, whose explorations similarly embrace generative AI as a co-creator and a medium to express ideas, blend architectural traditions, and speculate spatial futures. === Concerns === As AI continues to expand its presence across various industries, its impact on the architectural profession has become a topic of growing discussion. These discussions focus on how AI processes may influence traditional architectural practices, potentially altering job roles, and shaping the nature of creativity. While AI-driven processes may increase efficiency in some aspects of the profession, they also raise questions about the potential loss of unique design perspectives. These thoughts have been countered by many prominent creative figures in the realm of AI architecture, such as Stephen Coorlas, Tim Fu, Hassan Ragab, and Manas Bhatia who have showcased the amplification of creativity in design and potential benefits in terms of restoring creative power to the designer. A key concern is that AI-powered tools could diminish the need for human involvement in specific tasks traditionally performed by architects. This has led to speculation that the profession may increasingly shift toward roles focused on oversight, coordination, and strategic decision-making rather than hands-on design work. In some design scenarios, algorithmically generated solutions can be adjusted to prioritize efficiency and cost-effectiveness, which some argue may overshadow the creative and contextual nuances that define individual architectural styles. As with any discipline though, it has been determined that AI can be configured to provide beneficial results based on inputs and end goals the architect or designer assigns it. There are also concerns about the potential for AI to exacerbate inequalities within the architectural profession. For instance, larger firms with greater resources to invest in advanced AI technologies may gain a competitive edge over smaller firms and independent architects. This dynamic could contribute to industry consolidation, potentially limiting the diversity of architectural practice and stifling innovation. Ethical considerations in regard to cultural sensitivity have also been raised due to the datasets used to train AI. Without proper vetting of data or implementing failsafe overrides, AI generated outcomes can trend toward overly documented and prioritized content.

    Read more →
  • Knowledge spillover

    Knowledge spillover

    Knowledge spillover is an exchange of ideas among individuals. Knowledge spillover is usually replaced by terminations of technology spillover, R&D spillover and/or spillover (economics) when the concept is specific to technology management and innovation economics. In knowledge management economics, knowledge spillovers are non-rival knowledge market costs incurred by a party not agreeing to assume the costs that has a spillover effect of stimulating technological improvements in a neighbor through one's own innovation. Such innovations often come from specialization within an industry. There are two kinds of knowledge spillovers: internal and external. Internal knowledge spillover occurs if there is a positive impact of knowledge between individuals within an organization that produces goods and/or services. An external knowledge spillover occurs when the positive impact of knowledge is between individuals outside of a production organization. Marshall–Arrow–Romer (MAR) spillovers, Porter spillovers and Jacobs spillovers are three types of spillovers. == Conceptualizations == === Marshall–Arrow–Romer === Marshall–Arrow–Romer (MAR) spillover has its origins in 1890, where the English economist Alfred Marshall developed a theory of knowledge spillovers. Knowledge spillovers later were extended by economists Kenneth Arrow (1962) and Paul Romer (1986). In 1992, Edward Glaeser, Hedi Kallal, José Scheinkman, and Andrei Shleifer pulled together the Marshall–Arrow–Romer views on knowledge spillovers and accordingly named the view MAR spillover in 1992. Under the Marshall–Arrow–Romer (MAR) spillover view, the proximity of firms within a common industry often affects how well knowledge travels among firms to facilitate innovation and growth. The closer the firms are to one another, the greater the MAR spillover. The exchange of ideas is largely from employee to employee, in that employees from different firms in an industry exchange ideas about new products and new ways to produce goods. The opportunity to exchange ideas that lead to innovations key to new products and improved production methods. Research on the Cambridge IT Cluster (UK) suggests that technological knowledge spillovers might only happen rarely and are less important than other cluster benefits such as labour market pooling. === Porter === Porter (1990), like MAR, argues that knowledge spillovers in specialized, geographically concentrated industries stimulate growth. He insists, however, that local competition, as opposed to local monopoly, fosters the pursuit and rapid adoption of innovation. He gives examples of Italian ceramics and gold jewellery industries, in which hundreds of firms are located together and fiercely compete to innovate since the alternative to innovation is demise. Porter's externalities are maximized in cities with geographically specialized, competitive industries. === Jacobs === Under the Jacobs spillover view, the proximity of firms from different industries affect how well knowledge travels among firms to facilitate innovation and growth. This is in contrast to MAR spillovers, which focus on firms in a common industry. The diverse proximity of a Jacobs spillover brings together ideas among individuals with different perspectives to encourage an exchange of ideas and foster innovation in an industrially diverse environment. Developed in 1969 by urbanist Jane Jacobs and John Jackson the concept that Detroit’s shipbuilding industry from the 1830s was the critical antecedent leading to the 1890s development of the auto industry in Detroit since the gasoline engine firms easily transitioned from building gasoline engines for ships to building them for automobiles. == Incoming and outgoing spillovers == Knowledge spillover has asymmetric directions. The focal entity and receives or outflows know-how to others, creating incoming and outgoing spillovers. Cassiman and Veugelers (2002) use survey data and estimate incoming and outgoing spillover and study the economic impacts. Incoming spillover increases growth opportunity and productivity improvements of receivers, while outgoing spillover leads to free rider problem in the technology competition. Chen et al. (2013) use econometric method to gauge incoming spillover, a way that applies for all companies without survey. They find that incoming spillover explains R&D profits of industrial firms. == Policy implications == As information is largely non-rival in nature, certain measures must be taken to ensure that, for the originator, the information remains a private asset. As the market cannot do this efficiently, public regulations have been implemented to facilitate a more appropriate equilibrium. As a result, the concept of intellectual property rights have developed and ensure the ability of entrepreneurs to temporarily hold on to the profitability of their ideas through patents, copyrights, trade secrets, and other governmental safeguards. Conversely, such barriers to entry prevent the exploitation of informational developments by rival firms within an industry. For example, Wang (2023) indicates that technology spillovers are reduced by 27% to 51% when trade secrets laws are implemented by the Uniform Trade Secrets Act in the US. On the other hand, when the research and development of a private firm results in a social benefit, unaccounted for within the market price, often greater than the private return of the firm's research, then a subsidy to offset the underproduction of that benefit might be offered to the firm in return for its continued output of that benefit. Government subsidies are often controversial, and while they might often result in a more appropriate social equilibrium, they could also lead to undesirable political repercussions as such a subsidy must come from taxpayers, some of whom may not directly benefit from the researching firm's subsidized knowledge spillover. The concept of knowledge spillover is also used to justify subsidies to foreign direct investment, as foreign investors help diffuse technology among local firms. == Examples == Business parks are a good specific example of concentrated businesses that may benefit from MAR spillover. Many semiconductor firms intentionally located their research and development facilities in Silicon Valley to take advantage of MAR spillover. In addition, the film industry in Los Angeles, California, and elsewhere relies on a geographic concentration of specialists (directors, producers, scriptwriters, and set designers) to bring together narrow aspects of movie-making into a final product. A general example of a knowledge spillover could be the collective growth associated with the research and development of online social networking tools like Facebook, YouTube, and Twitter. Such tools have not only created a positive feedback loop, and a host of originally unintended benefits for their users, but have also created an explosion of new software, programming platforms, and conceptual breakthroughs that have perpetuated the development of the industry as a whole. The advent of online marketplaces, the utilization of user profiles, the widespread democratization of information, and the interconnectivity between tools within the industry have all been products of each tool's individual developments. These developments have since spread outside the industry into the mainstream media as news and entertainment firms have developed their own market feedback applications within the tools themselves, and their own versions of online networking tools (e.g. CNN’s iReport).

    Read more →
  • Synthetic data

    Synthetic data

    Synthetic data are artificially generated data not produced by real-world events. Typically created using algorithms, synthetic data can be deployed to validate mathematical models and to train machine learning models. Data generated by a computer simulation can be seen as synthetic data. This encompasses most applications of physical modeling, such as music synthesizers or flight simulators. The output of such systems approximates the real thing, but is fully algorithmically generated. Synthetic data is used in a variety of fields as a filter for information that would otherwise compromise the confidentiality of particular aspects of the data. In many sensitive applications, datasets theoretically exist but cannot be released to the general public; synthetic data sidesteps the privacy issues that arise from using real consumer information without permission or compensation. == Usefulness == Synthetic data is generated to meet specific needs or certain conditions that may not be found in the original, real data. One of the hurdles in applying up-to-date machine learning approaches for complex scientific tasks is the scarcity of labeled data, a gap effectively bridged by the use of synthetic data, which closely replicates real experimental data. This can be useful when designing many systems, from simulations based on theoretical value, to database processors, etc. This helps detect and solve unexpected issues such as information processing limitations. Synthetic data are often generated to represent the authentic data and allows a baseline to be set. Another benefit of synthetic data is to protect the privacy and confidentiality of authentic data, while still allowing for use in testing systems. Computer security experts claim generated synthetic data "... enables us to create realistic behavior profiles for users and attackers. The data is used to train the fraud detection system itself, thus creating the necessary adaptation of the system to a specific environment." In defense and military contexts, synthetic data is seen as a potentially valuable tool to develop and improve complex AI systems, particularly in contexts where high-quality real-world data is scarce. At the same time, synthetic data together with the testing approach can give the ability to model real-world scenarios. == History == Scientific modelling of physical systems has a long history that runs concurrent with the history of physics. For example, research into synthesis of audio and voice can be traced back to the 1930s and before, driven forward by the developments of the telephone and audio recording technologies. Digitization gave rise to software synthesizers from the 1970s onwards. In the context of privacy-preserving statistical analysis, in 1993, the idea of original fully synthetic data was created by Donald Rubin. Rubin originally designed this to synthesize the Decennial Census long form responses for the short form households. He then released samples that did not include any actual long form records - in this he preserved anonymity of the household. Later that year, the idea of original partially synthetic data was created by Little. Little used this idea to synthesize the sensitive values on the public use file. A 1993 work fitted a statistical model to 60,000 MNIST digits, then it was used to generate over 1 million examples. Those were used to train a LeNet-4 to reach state of the art performance. In 1994, Stephen Fienberg introduced 'critical refinement', in which a parametric posterior predictive distribution (instead of a Bayes bootstrap) is used to do the sampling. Later, other important contributors to the development of synthetic data generation were Trivellore Raghunathan, Jerry Reiter, Donald Rubin, John M. Abowd, and Jim Woodcock. Collectively they came up with a solution for how to treat partially synthetic data with missing data. Similarly, they developed the technique of Sequential Regression Multivariate Imputation. == Calculations == Researchers test the framework on synthetic data, which is "the only source of ground truth on which they can objectively assess the performance of their algorithms". Synthetic data can be generated through the use of random lines, having different orientations and starting positions. Datasets can get fairly complicated. A more complicated dataset can be generated by using a synthesizer build. To create a synthesizer build, first use the original data to create a model or equation that fits the data the best. This model or equation will be called a synthesizer build. This build can be used to generate more data. Constructing a synthesizer build involves constructing a statistical model. In a linear regression line example, the original data can be plotted, and a best fit linear line can be created from the data. This line is a synthesizer created from the original data. The next step will be generating more synthetic data from the synthesizer build or from this linear line equation. In this way, the new data can be used for studies and research, and it protects the confidentiality of the original data. David Jensen from the Knowledge Discovery Laboratory explains how to generate synthetic data: "Researchers frequently need to explore the effects of certain data characteristics on their data model." To help construct datasets exhibiting specific properties, such as auto-correlation or degree disparity, proximity can generate synthetic data having one of several types of graph structure: random graphs that are generated by some random process; lattice graphs having a ring structure; lattice graphs having a grid structure, etc. In all cases, the data generation process follows the same process: Generate the empty graph structure. Generate attribute values based on user-supplied prior probabilities. Since the attribute values of one object may depend on the attribute values of related objects, the attribute generation process assigns values collectively. == Applications == === Fraud detection and confidentiality systems === Testing and training fraud detection and confidentiality systems are devised using synthetic data. Specific algorithms and generators are designed to create realistic data, which then assists in teaching a system how to react to certain situations or criteria. For example, intrusion detection software is tested using synthetic data. This data is a representation of the authentic data and may include intrusion instances that are not found in the authentic data. The synthetic data allows the software to recognize these situations and react accordingly. If synthetic data was not used, the software would only be trained to react to the situations provided by the authentic data and it may not recognize another type of intrusion. === Scientific research === Researchers doing clinical trials or any other research may generate synthetic data to aid in creating a baseline for future studies and testing. Real data can contain information that researchers may not want released, so synthetic data is sometimes used to protect the privacy and confidentiality of a dataset. Using synthetic data reduces confidentiality and privacy issues since it holds no personal information and cannot be traced back to any individual. Beyond privacy protection, synthetic data is also being explored for methodological innovation in drug development. For instance, synthetic data may be used to construct synthetic control arms as an alternative to conventional external control arms based on real-world data (RWD) or randomized controlled trials (RCTs). Collectively, regulatory agencies such as the FDA and EMA appear to be at various stages of recognizing and integrating AI-generated synthetic data into their methodologies. While there is growing consensus on the potential of such data to support model development and the broader lifecycle of medicinal products, to date no drug or medical device has been approved using solely or predominantly synthetic data—particularly not as a comparator arm generated entirely via data-driven algorithms. The quality and statistical handling of synthetic data are expected to become more prominent in future regulatory discussions, particularly in contexts such as predictive modeling (e.g., digital twins), where innovative approaches have already been referenced. === Machine learning === Synthetic data is increasingly being used for machine learning applications: a model is trained on a synthetically generated dataset with the intention of transfer learning to real data. Efforts have been made to enable more data science experiments via the construction of general-purpose synthetic data generators, such as the Synthetic Data Vault. In general, synthetic data has several natural advantages: once the synthetic environment is ready, it is fast and cheap to produce as much data as needed; synthetic data can have perfectly accurate labels, including labeling that may be very expensive or impo

    Read more →
  • Exploration–exploitation dilemma

    Exploration–exploitation dilemma

    The exploration–exploitation dilemma, also known as the explore–exploit tradeoff, is a fundamental concept in decision-making that arises in many domains. It is depicted as the balancing act between two opposing strategies. Exploitation involves choosing the best option based on current knowledge of the system (which may be incomplete or misleading), while exploration involves trying out new options that may lead to better outcomes in the future at the expense of an exploitation opportunity. Finding the optimal balance between these two strategies is a crucial challenge in many decision-making problems whose goal is to maximize long-term benefits. == Application in machine learning == In the context of machine learning, the exploration–exploitation tradeoff is fundamental in reinforcement learning (RL), a type of machine learning that involves training agents to make decisions based on feedback from the environment. Crucially, this feedback may be incomplete or delayed. The agent must decide whether to exploit the current best-known policy or explore new policies to improve its performance. === Multi-armed bandit methods === The multi-armed bandit (MAB) problem was a classic example of the tradeoff, and many methods were developed for it, such as epsilon-greedy, Thompson sampling, and the upper confidence bound (UCB). See the page on MAB for details. In more complex RL situations than the MAB problem, the agent can treat each choice as a MAB, where the payoff is the expected future reward. For example, if the agent performs an epsilon-greedy method, then the agent will often "pull the best lever" by picking the action that had the best predicted expected reward (exploit). However, it would pick a random action with probability epsilon (explore). Monte Carlo tree search, for example, uses a variant of the UCB method. === Exploration problems === There are some problems that make exploration difficult. Sparse reward. If rewards occur only once a long while, then the agent might not persist in exploring. Furthermore, if the space of actions is large, then the sparse reward would mean the agent would not be guided by the reward to find a good direction for deeper exploration. A standard example is Montezuma's Revenge. Deceptive reward. If some early actions give immediate small reward, but other actions give later large reward, then the agent might be lured away from exploring the other actions. Noisy TV problem. If certain observations are irreducibly noisy (such as a television showing random images), then the agent might be trapped exploring those observations (watching the television). === Exploration reward === This section based on. The exploration reward (also called exploration bonus) methods convert the exploration-exploitation dilemma into a balance of exploitations. That is, instead of trying to get the agent to balance exploration and exploitation, exploration is simply treated as another form of exploitation, and the agent simply attempts to maximize the sum of rewards from exploration and exploitation. The exploration reward can be treated as a form of intrinsic reward. We write these as r t i , r t e {\displaystyle r_{t}^{i},r_{t}^{e}} , meaning the intrinsic and extrinsic rewards at time step t {\displaystyle t} . However, exploration reward is different from exploitation in two regards: The reward of exploitation is not freely chosen, but given by the environment, but the reward of exploration may be picked freely. Indeed, there are many different ways to design r t i {\displaystyle r_{t}^{i}} described below. The reward of exploitation is usually stationary (i.e. the same action in the same state gives the same reward), but the reward of exploration is non-stationary (i.e. the same action in the same state should give less and less reward). Count-based exploration uses N n ( s ) {\displaystyle N_{n}(s)} , the number of visits to a state s {\displaystyle s} during the time-steps 1 : n {\displaystyle 1:n} , to calculate the exploration reward. This is only possible in small and discrete state space. Density-based exploration extends count-based exploration by using a density model ρ n ( s ) {\displaystyle \rho _{n}(s)} . The idea is that, if a state has been visited, then nearby states are also partly-visited. In maximum entropy exploration, the entropy of the agent's policy π {\displaystyle \pi } is included as a term in the intrinsic reward. That is, r t i = − ∑ a π ( a | s t ) ln ⁡ π ( a | s t ) + ⋯ {\displaystyle r_{t}^{i}=-\sum _{a}\pi (a|s_{t})\ln \pi (a|s_{t})+\cdots } . === Prediction-based === This section based on. The forward dynamics model is a function for predicting the next state based on the current state and the current action: f : ( s t , a t ) ↦ s t + 1 {\displaystyle f:(s_{t},a_{t})\mapsto s_{t+1}} . The forward dynamics model is trained as the agent plays. The model becomes better at predicting state transition for state-action pairs that had been done many times. A forward dynamics model can define an exploration reward by r t i = ‖ f ( s t , a t ) − s t + 1 ‖ 2 2 {\displaystyle r_{t}^{i}=\|f(s_{t},a_{t})-s_{t+1}\|_{2}^{2}} . That is, the reward is the squared-error of the prediction compared to reality. This rewards the agent to perform state-action pairs that had not been done many times. This is however susceptible to the noisy TV problem. Dynamics model can be run in latent space. That is, r t i = ‖ f ( s t , a t ) − ϕ ( s t + 1 ) ‖ 2 2 {\displaystyle r_{t}^{i}=\|f(s_{t},a_{t})-\phi (s_{t+1})\|_{2}^{2}} for some featurizer ϕ {\displaystyle \phi } . The featurizer can be the identity function (i.e. ϕ ( x ) = x {\displaystyle \phi (x)=x} ), randomly generated, the encoder-half of a variational autoencoder, etc. A good featurizer improves forward dynamics exploration. The Intrinsic Curiosity Module (ICM) method trains simultaneously a forward dynamics model and a featurizer. The featurizer is trained by an inverse dynamics model, which is a function for predicting the current action based on the features of the current and the next state: g : ( ϕ ( s t ) , ϕ ( s t + 1 ) ) ↦ a t {\displaystyle g:(\phi (s_{t}),\phi (s_{t+1}))\mapsto a_{t}} . By optimizing the inverse dynamics, both the inverse dynamics model and the featurizer are improved. Then, the improved featurizer improves the forward dynamics model, which improves the exploration of the agent. Random Network Distillation (RND) method attempts to solve this problem by teacher–student distillation. Instead of a forward dynamics model, it has two models f , f ′ {\displaystyle f,f'} . The f ′ {\displaystyle f'} teacher model is fixed, and the f {\displaystyle f} student model is trained to minimize ‖ f ( s ) − f ′ ( s ) ‖ 2 2 {\displaystyle \|f(s)-f'(s)\|_{2}^{2}} on states s {\displaystyle s} . As a state is visited more and more, the student network becomes better at predicting the teacher. Meanwhile, the prediction error is also an exploration reward for the agent, and so the agent learns to perform actions that result in higher prediction error. Thus, we have a student network attempting to minimize the prediction error, while the agent attempting to maximize it, resulting in exploration. The states are normalized by subtracting a running average and dividing a running variance, which is necessary since the teacher model is frozen. The rewards are normalized by dividing with a running variance. Exploration by disagreement trains an ensemble of forward dynamics models, each on a random subset of all ( s t , a t , s t + 1 ) {\displaystyle (s_{t},a_{t},s_{t+1})} tuples. The exploration reward is the variance of the models' predictions. === Noise === For neural network–based agents, the NoisyNet method changes some of its neural network modules by noisy versions. That is, some network parameters are random variables from a probability distribution. The parameters of the distribution are themselves learnable. For example, in a linear layer y = W x + b {\displaystyle y=Wx+b} , both W , b {\displaystyle W,b} are sampled from Gaussian distributions N ( μ W , Σ W ) , N ( μ b , Σ b ) {\displaystyle {\mathcal {N}}(\mu _{W},\Sigma _{W}),{\mathcal {N}}(\mu _{b},\Sigma _{b})} at every step, and the parameters μ W , Σ W , μ b , Σ b {\displaystyle \mu _{W},\Sigma _{W},\mu _{b},\Sigma _{b}} are learned via the reparameterization trick.

    Read more →
  • Information professional

    Information professional

    The term information professional or information specialist refers to professionals responsible for the collection, documentation, organization, storage, preservation, retrieval, and dissemination of printed and digital information. The service delivered to the client is known as an information service. The term "information professional" is a versatile one, used to describe similar and sometimes overlapping professions, such as librarians, archivists, information managers, information systems specialists, information scientists, records managers, and information consultants. However, terminology differs among sources and organisations. Information professionals are employed in a variety of private, public, and academic institutions, as well as independently. == Skills == Since the term information professional is broad, the skills required for this profession are also varied. A Gartner report in 2011 pointed out that "Professional roles focused on information management will be different to that of established IT roles. An 'information professional' will not be one type of role or skill set, but will in fact have a number of specializations". Thus, an information professional can possess a variety of different skills, depending on the sector in which the person is employed. Some essential cross-sector skills are: IT skills, such as word-processing and spreadsheets, digitisation skills, and conducting Internet searches, together with skills loan systems, databases, content management systems, and specially designed programmes and packages. Customer service. An information professional should have the ability to address the information needs of customers. Language proficiency. This is essential in order to manage the information at hand and deal with customer needs. Soft skills. These include skills such as negotiating, conflict resolution, and time management. Management training. An information professional should be familiar with notions such as strategic planning and project management. Moreover, an information professional should be skilled in planning and using relevant systems, in capturing and securing information, and in accessing it to deliver service whenever the information is required. == Associations == Most countries have a professional association who oversee the professional and academic standards of librarians and other information professionals. There are also international associations related to LIS (library and information science), the most prominent of which is the International Federation of Library Associations and Institutions (IFLA). In many countries, LIS courses are accredited by the relevant professional association, as the American Library Association (ALA) in the USA, the Chartered Institute of Library and Information Professionals (CILIP) in the UK, and the Australian Library and Information Association (ALIA) in Australia. == Qualifications == Educational institutions around the world offer academic degrees, or degrees on related subjects such as Archival Studies, Information Systems, Information Management, and Records Management. Some of the institutions offering information science education refer to themselves as an iSchool, such as the CiSAP (Consortium of iSchools Asia Pacific, founded 2006) in Asia and the iSchool Caucus in the USA. There are also online e-learning resources, some of which offer certification for information professionals. === Africa === Information development in Africa started later than in other continents, mainly due to a lack of internet access, expertise and resources to manage digital infrastructure, and "opportunities for capacity development and knowledge-sharing". Nowadays, academic degrees in information studies are available at many universities of African countries, such as the University of Pretoria (South Africa), University of Nairobi (Kenya), Makerere University (Uganda), University of Botswana (Botswana), and University of Nigeria (Nigeria). === Asia === LIS-related studies are available in more than 30 Asian countries. Some examples listed by iSchools Inc. are the University of Hong Kong, University of Tsukuba, Japan, Yonsei University, South Korea, National Taiwan University and Wuhan University, China. Centre of Library and Information Management Science (CLIMS) at Tata Institute of Social Science in Mumbai, India. In Southeast Asia, the Congress of Southeast Asian Librarians (CONSAL) connects librarians and libraries in more than 10 countries with resources, networking opportunities, and support for growing library systems. === Australasia === The Australian Library and Information Association (ALIA) as of 2021 lists six schools offering undergraduate and postgraduate accredited university courses for "Librarian and Information Specialists" on their website. In New Zealand, the Open Polytechnic of New Zealand and the Victoria University of Wellington offer undergraduate and postgraduate degree courses for information professionals. === Europe === The majority of European countries have universities, colleges, or schools which offer bachelor's degrees in LIS studies. Over 40 universities offer master's degrees in LIS-related fields, and many institutions, such as the Swedish School of Library and Information Science at the University of Borås (Sweden), the University of Barcelona (Spain), Loughborough University (UK), and Aberystwyth University (Wales, UK) also offer PhD degrees. === North America === Information studies and degrees are available at numerous academic institutions throughout the U.S. and Canada. U.S. professional associations, together with their European counterparts, have undertaken many educational initiatives and pioneered many advances in the field of Information studies, such as increased interdisciplinarity and more effective delivery of distance learning. The Association for Intelligent Information Management, based in Silver Spring, Maryland, offers a qualification called Certified Information Professional (CIP), earned upon passing an examination, with certification remaining valid for three years. === South America === There are many schools and colleges in Latin America, which offer courses in Library Science, Archival Studies, and Information Studies, however these subjects are taught completely separately.

    Read more →
  • Predictor–corrector method

    Predictor–corrector method

    In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps: The initial, "prediction" step, starts from a function fitted to the function-values and derivative-values at a preceding set of points to extrapolate ("anticipate") this function's value at a subsequent, new point. The next, "corrector" step refines the initial approximation by using the predicted value of the function and another method to interpolate that unknown function's value at the same subsequent point. == Predictor–corrector methods for solving ODEs == When considering the numerical solution of ordinary differential equations (ODEs), a predictor–corrector method typically uses an explicit method for the predictor step and an implicit method for the corrector step. === Example: Euler method with the trapezoidal rule === A simple predictor–corrector method (known as Heun's method) can be constructed from the Euler method (an explicit method) and the trapezoidal rule (an implicit method). Consider the differential equation y ′ = f ( t , y ) , y ( t 0 ) = y 0 , {\displaystyle y'=f(t,y),\quad y(t_{0})=y_{0},} and denote the step size by h {\displaystyle h} . First, the predictor step: starting from the current value y i {\displaystyle y_{i}} , calculate an initial guess value y ~ i + 1 {\displaystyle {\tilde {y}}_{i+1}} via the Euler method, y ~ i + 1 = y i + h f ( t i , y i ) . {\displaystyle {\tilde {y}}_{i+1}=y_{i}+hf(t_{i},y_{i}).} Next, the corrector step: improve the initial guess using trapezoidal rule, y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle y_{i+1}=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.} That value is used as the next step. === PEC mode and PECE mode === There are different variants of a predictor–corrector method, depending on how often the corrector method is applied. The Predict–Evaluate–Correct–Evaluate (PECE) mode refers to the variant in the above example: y ~ i + 1 = y i + h f ( t i , y i ) , y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},y_{i}),\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.\end{aligned}}} It is also possible to evaluate the function f only once per step by using the method in Predict–Evaluate–Correct (PEC) mode: y ~ i + 1 = y i + h f ( t i , y ~ i ) , y i + 1 = y i + 1 2 h ( f ( t i , y ~ i ) + f ( t i + 1 , y ~ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},{\tilde {y}}_{i}),\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},{\tilde {y}}_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )}.\end{aligned}}} Additionally, the corrector step can be repeated in the hope that this achieves an even better approximation to the true solution. If the corrector method is run twice, this yields the PECECE mode: y ~ i + 1 = y i + h f ( t i , y i ) , y ^ i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ~ i + 1 ) ) , y i + 1 = y i + 1 2 h ( f ( t i , y i ) + f ( t i + 1 , y ^ i + 1 ) ) . {\displaystyle {\begin{aligned}{\tilde {y}}_{i+1}&=y_{i}+hf(t_{i},y_{i}),\\{\hat {y}}_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\tilde {y}}_{i+1}){\bigr )},\\y_{i+1}&=y_{i}+{\tfrac {1}{2}}h{\bigl (}f(t_{i},y_{i})+f(t_{i+1},{\hat {y}}_{i+1}){\bigr )}.\end{aligned}}} The PECEC mode has one fewer function evaluation than PECECE mode. More generally, if the corrector is run k times, the method is in P(EC)k or P(EC)kE mode. If the corrector method is iterated until it converges, this could be called PE(CE)∞.

    Read more →