In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant. In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a certain class of possible functions. The goal is that, with high probability (the "probably" part), the selected function will have low generalization error (the "approximately correct" part). The learner must be able to learn the concept given any arbitrary approximation ratio, probability of success, or distribution of the samples. The model was later extended to treat noise (misclassified samples). An important innovation of the PAC framework is the introduction of computational complexity theory concepts to machine learning. In particular, the learner is expected to find efficient functions (time and space requirements bounded to a polynomial of the example size), and the learner itself must implement an efficient procedure (requiring an example count bounded to a polynomial of the concept size, modified by the approximation and likelihood bounds). == Definitions and terminology == In order to give the definition for something that is PAC-learnable, we first have to introduce some terminology. For the following definitions, two examples will be used. The first is the problem of character recognition given an array of n {\displaystyle n} bits encoding a binary-valued image. The other example is the problem of finding an interval that will correctly classify points within the interval as positive and the points outside of the range as negative. Let X {\displaystyle X} be a set called the instance space or the encoding of all the samples. In the character recognition problem, the instance space is X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} . In the interval problem the instance space, X {\displaystyle X} , is the set of all bounded intervals in R {\displaystyle \mathbb {R} } , where R {\displaystyle \mathbb {R} } denotes the set of all real numbers. A concept is a subset c ⊂ X {\displaystyle c\subset X} . One concept is the set of all patterns of bits in X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} that encode a picture of the letter "P". An example concept from the second example is the set of open intervals, { ( a , b ) ∣ 0 ≤ a ≤ π / 2 , π ≤ b ≤ 13 } {\displaystyle \{(a,b)\mid 0\leq a\leq \pi /2,\pi \leq b\leq {\sqrt {13}}\}} , each of which contains only the positive points. A concept class C {\displaystyle C} is a collection of concepts over X {\displaystyle X} . This could be the set of all subsets of the array of bits that are skeletonized 4-connected (width of the font is 1). Let EX ( c , D ) {\displaystyle \operatorname {EX} (c,D)} be a procedure that draws an example, x {\displaystyle x} , using a probability distribution D {\displaystyle D} and gives the correct label c ( x ) {\displaystyle c(x)} , that is 1 if x ∈ c {\displaystyle x\in c} and 0 otherwise. Now, given 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} , assume there is an algorithm A {\displaystyle A} and a polynomial p {\displaystyle p} in 1 / ϵ , 1 / δ {\displaystyle 1/\epsilon ,1/\delta } (and other relevant parameters of the class C {\displaystyle C} ) such that, given a sample of size p {\displaystyle p} drawn according to EX ( c , D ) {\displaystyle \operatorname {EX} (c,D)} , then, with probability of at least 1 − δ {\displaystyle 1-\delta } , A {\displaystyle A} outputs a hypothesis h ∈ C {\displaystyle h\in C} that has an average error less than or equal to ϵ {\displaystyle \epsilon } on X {\displaystyle X} with the same distribution D {\displaystyle D} . Further if the above statement for algorithm A {\displaystyle A} is true for every concept c ∈ C {\displaystyle c\in C} and for every distribution D {\displaystyle D} over X {\displaystyle X} , and for all 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} then C {\displaystyle C} is (efficiently) PAC learnable (or distribution-free PAC learnable). We can also say that A {\displaystyle A} is a PAC learning algorithm for C {\displaystyle C} . == Equivalence == Under some regularity conditions these conditions are equivalent: The concept class C is PAC learnable. The VC dimension of C is finite. C is a uniformly Glivenko-Cantelli class. C is compressible in the sense of Littlestone and Warmuth
Concept mining
Concept mining is an activity that results in the extraction of concepts from artifacts. Solutions to the task typically involve aspects of artificial intelligence and statistics, such as data mining and text mining. Because artifacts are typically a loosely structured sequence of words and other symbols (rather than concepts), the problem is nontrivial, but it can provide powerful insights into the meaning, provenance and similarity of documents. == Methods == Traditionally, the conversion of words to concepts has been performed using a thesaurus, and for computational techniques the tendency is to do the same. The thesauri used are either specially created for the task, or a pre-existing language model, usually related to Princeton's WordNet. The mappings of words to concepts are often ambiguous. Typically each word in a given language will relate to several possible concepts. Humans use context to disambiguate the various meanings of a given piece of text, where available machine translation systems cannot easily infer context. For the purposes of concept mining, however, these ambiguities tend to be less important than they are with machine translation, for in large documents the ambiguities tend to even out, much as is the case with text mining. There are many techniques for disambiguation that may be used. Examples are linguistic analysis of the text and the use of word and concept association frequency information that may be inferred from large text corpora. Recently, techniques that base on semantic similarity between the possible concepts and the context have appeared and gained interest in the scientific community. == Applications == === Detecting and indexing similar documents in large corpora === One of the spin-offs of calculating document statistics in the concept domain, rather than the word domain, is that concepts form natural tree structures based on hypernymy and meronymy. These structures can be used to generate simple tree membership statistics, that can be used to locate any document in a Euclidean concept space. If the size of a document is also considered as another dimension of this space then an extremely efficient indexing system can be created. This technique is currently in commercial use locating similar legal documents in a 2.5 million document corpus. === Clustering documents by topic === Standard numeric clustering techniques may be used in "concept space" as described above to locate and index documents by the inferred topic. These are numerically far more efficient than their text mining cousins, and tend to behave more intuitively, in that they map better to the similarity measures a human would generate.
Digital edition
A digital edition is an online magazine or online newspaper delivered in electronic form which is formatted identically to the print version. Digital editions are often called digital facsimiles to underline the likeness to the print version. Digital editions have the benefit of reduced cost to the publisher and reader by avoiding the time and the expense to print and deliver paper edition. This format is considered more environmentally friendly due to the reduction of paper and energy use. These editions also often feature interactive elements such as hyperlinks both within the publication itself and to other internet resources, search option and bookmarking, and can also incorporate multimedia such as video or animation to enhance articles themselves or for advertisement purposes. Some delivery methods also include animation and sound effects that replicate turning of the page to further enhance the experience of their print counterparts. Magazine publishers have traditionally relied on two revenue sources: selling ads and selling magazines. Additionally some publishers are using other electronic publication methods such as RSS to reach out to readers and inform them when new digital editions are available. Current technologies are generally either reader-based, requiring a download of an application and subsequent download of each edition, or browser-based, often using Macromedia Flash, requiring no application download (such as Adobe Acrobat). Some application-based readers allow users to access editions while not connected to internet. Dedicated hardware such as the Amazon Kindle and the iPad is also available for reading digital editions of select books, popular national magazines such as Time, The Atlantic, and Forbes and popular national newspapers such as the New York Times, Wall Street Journal, and Washington Post. Archives of print newspapers, in some cases dating hundreds of years back, are being digitized and made available online. Google is indexing existing digital archives produced by the newspapers themselves or by third parties. Newspaper and magazine archival began with microform film formats solving the problem of efficiently storing and preserving. This format, however, lacked accessibility. Many libraries, especially state libraries in the United States are archiving their collections digitally and converting existing microfilm to digital format. The Library of Congress provides project planning assistance and the National Endowment for the Humanities procures funding through grants from its National Digital Newspaper Program. Digital magazines, ezines, e-editions and emags are sometimes referred to as digital editions, however some of these formats are published only in digital format unlike digital editions which replicate a printed edition as well. == Digital magazines == Digital-replica magazines number in thousands—consumer and business publications, house magazines for associations, institutions and corporations – and conversion from print to digital was still increasing as of 2009. A 2008 report funded by digital-replica technology providers and auditing agencies counted 1,786 digital-replica editions having more than 7 million circulation among business-to-business publications, of which 230 editions were audited The same report counted 1,470 digital-replica editions of consumer magazines having 5.5 million digital circulation, of which 240 editions were audited. These authors estimated that by year end of 2009 there would be 8,000 digital magazines, having a combined distribution of more than 30 million people. Surveys have shown that, while not all subscribers prefer a digital edition, some do because of the environmental benefit and also because digital magazines are searchable and may easily be passed along or linked to. One such survey funded by a digital publisher reported on inputs from more than 30,000 subscribers to business, consumer and other digital magazines. == Digital magazine business models == === Reduced printing and distribution costs === The publishers' choice to save by moving some or all subscribers from print to digital is widely accepted. Oracle magazine, which has 176,000 of its 516,000 subscribers receiving digital according to its June 2009 BPA circulation statement, is said to be the most widely circulated digital edition of a business-to-business publication. Publishers who do this need to choose whether to make some issues all-digital, move some subscribers to digital edition, add some digital-only subscribers, or send all subscribers the digital edition. === Paid subscription revenue === In 2009, a major consumer magazine, PC Magazine, went all-digital, charging an annual subscription fee for its digital-replica edition. Many consumer magazines and newspapers are already available in eReader formats that are sold through booksellers. === Sponsorship and advertising revenue === Digital editions often carry special "front cover" advertising, or advertising on the email message alerting the subscriber of the digital edition. Publishers also produce special digital-only inserts and rich-media ads or advertorials. === Designed-for-digital issues === Another approach is to fully replace printed issues with digital ones, or to use digital editions for extra issues that would otherwise have to be printed.
Digital zombie
A digital zombie is a person so engaged with digital technology or social media they are unable to separate themselves from a persistent online presence. Writing in 2017, University of Sydney researcher Andrew Campbell expressed concerns over whether or not the individual can truly live a full and healthy life while they are preoccupied with the digital world. Other individuals have also begun referencing certain types of behaviour with being a digital zombie. Stefanie Valentic, managing editor of EHS Today, refers to it as people hunting digital creatures through their smartphones in public spaces, always fixed on their phones. The University of Warwick has used the term to argue that further research needs to be done with people who exist in digital form after death to help people grieve their loss. == Modern applications == === Distracted walking === The term digital zombie can refer to a person performing distracted walking, which has been labelled dangerous by the American Academy of Orthopaedic Surgeons. They created the "Digital Deadwalkers" campaign after physicians became aware of the risks associated with walking across intersections and sidewalks while paying attention only to smartphones and not one's surroundings. Also stating that the name is derived from the fact that "they're oblivious to everyone else, so it's like they're dead-walking, sleepwalking." === Living through media === The Department of Sociology, University of Warwick has also identified the term, digital zombie, to refer to an individual who has died but is digitally resurrected, reanimated and socially active. These digital zombies do things in death they did not do when they were alive as they "live" again through a digital self on a digital medium. Dead celebrities sometimes become digital zombies when they are reanimated to appear in commercial advertisements (such as Audrey Hepburn and Bob Monkhouse). Other accidental digital zombies include Tupac Shakur and Michael Jackson who were both digitally resurrected and recreated to perform "live" on stage years after their death. Researchers at the University of Warwick have carried out research into the area of human-computer interaction. in an effort to understand the affect these digital zombies have on grief and bereavement. === Mobile gaming === Writer for EHS Today, Stefanie Valentic, has made observations with the mobile phone video game Pokémon Go, which offers players the experience to hunt and collect digital creatures called Pokémon through their smartphone in real world. Players can be observed simultaneously gazing at their phone while also obliviously walking around their environments looking for Pokémon. Stefanie references these individuals as "digital zombies" since they walk around with no cognition of their surroundings while engaged with their phone. == Health risks == === Heavy use of technology === Research by the University of Sydney has begun looking at how new technology such as digital media and smartphones impact our lives and questioning whether they can create new compulsions and obsessions. The research demonstrates that increased heavy technological use can have negative health consequences similar to drugs, smoking, and alcohol. Marcel O'Gorman, an associate professor of English at the University of Waterloo, has commented on the body of research examining how technology impacts cognition, stating currently that there is no empirical evidence to support any theories that suggest that technology can damage memory and attention span. === Heightened risk to children === Manfred Spitzer, a German psychiatrist, has raised concerns with providing digital devices to children. During the early childhood stage while their brains are rapidly growing, increased exposure to digital devices may deprive them of necessary development required to facilitate brain growth. These concerns are also shared by Korean doctors who believe giving digital devices, like smartphones to children, limits their cognitive development.
Digital Cinema Package
A Digital Cinema Package (DCP) is a collection of digital files used to store and convey digital cinema (DC) audio, image, and data streams. The term was popularized by Digital Cinema Initiatives, LLC in its original recommendation for packaging DC contents. However, the industry tends to apply the term to the structure more formally known as the composition. A DCP is a container format for compositions, a hierarchical file structure that represents a title version. The DCP may carry a partial composition (e.g. not a complete set of files), a single complete composition, or multiple and complete compositions. The composition consists of a Composition Playlist (in XML format) that defines the playback sequence of a set of Track Files. Track Files carry the essence (audio, image, subtitles), which is wrapped using Material eXchange Format (MXF). Track Files must contain only one essence type. Two track files at a minimum must be present in every composition (see SMPTE ST429-2 D-Cinema Packaging – DCP Constraints, or Cinepedia): a track file carrying picture essence, and a track file carrying audio essence. The composition, consisting of a Composition Playlist (CPL) and associated track files, are distributed as a Digital Cinema Package (DCP). A composition is a complete representation of a title version, while the DCP need not carry a full composition. However, as already noted, it is commonplace in the industry to discuss the title in terms of a DCP, as that is the deliverable to the cinema. The Picture Track File essence is compressed using JPEG 2000 and the Audio Track File carries a 24-bit linear PCM uncompressed multichannel WAV file. Encryption may optionally be applied to the essence of a track file to protect it from unauthorized use. The encryption used is AES 128-bit in CBC mode. In practice, there are two versions of composition in use. The original version is called Interop DCP. In 2009, a specification was published by SMPTE (SMPTE ST 429-2 Digital Cinema Packaging – DCP Constraints) for what is commonly referred to as SMPTE DCP. SMPTE DCP is similar but not backwards compatible with Interop DCP, resulting in an uphill effort to transition the industry from Interop DCP to SMPTE DCP. SMPTE DCP requires significant constraints to ensure success in the field, as shown by ISDCF. While legacy support for Interop DCP is necessary for commercial products, new productions are encouraged to be distributed in SMPTE DCP. == Technical specifications == The DCP root folder (in the storage medium) contains a number of files, some used to store the image and audio contents, and some other used to organize and manage the whole playlist. === Picture MXF files === Picture contents may be stored in one or more reels corresponding to one or more MXF files. Each reel contains pictures as MPEG-2 or JPEG 2000 essence, depending on the adopted codec. MPEG-2 is no longer compliant with the DCI specification. JPEG 2000 is the only accepted compression format. Supported frame rates are: SMPTE (JPEG 2000) 24, 25, 30, 48, 50, and 60 fps @ 2K 24, 25, and 30 fps @ 4K 24 and 48 fps @ 2K stereoscopic MXF Interop (JPEG 2000) – Deprecated 24 and 48 fps @ 2K (MXF Interop can be encoded at 25 frame/s but support is not guaranteed) 24 fps @ 4K 24 fps @ 2K stereoscopic MXF Interop (MPEG-2) – Deprecated 23.976 and 24 fps @ 1920 × 1080 Maximum frame sizes are 2048 × 1080 for 2K DC, and 4096 × 2160 for 4K DC. Common formats are: SMPTE (JPEG 2000) Flat (1998 × 1080 or 3996 × 2160), = 1.85:1 aspect ratio Scope (2048 × 858 or 4096 × 1716), ~2.39:1 aspect ratio HDTV (1920 × 1080 or 3840 × 2160), 16:9 aspect ratio (~1.78:1) (although not specifically defined in the DCI specification, this resolution is DCI compliant per section 8.4.3.2). Full (2048 × 1080 or 4096 × 2160) (~1.9:1 aspect ratio, official name by DCI is Full Container. Not widely accepted in cinemas.) MXF Interop (MPEG-2) – Deprecated Full Frame (1920 × 1080) 12 bits per component precision (36 bits total per pixel) XYZ' colorspace; the prime mark indicates gamma encoding (gamma=2.6) Maximum bit rate is 250 Mbit/s (1.3 MBytes per frame at 24 frame per second) === Sound MXF files === Sound contents are also stored in reels corresponding to picture reels in number and duration. In case of multilingual features, separate reels are required to convey different languages. Each file contains linear PCM essence. Sampling rate is 48,000 or 96,000 samples per second Sample precision of 24 bits Linear mapping (no companding) Up to 16 independent channels === Asset map file === List of all files included in the DCP, in XML format. === Composition playlist file === Defines the playback order during presentation. The order is saved in XML format in this file; each picture and sound reel is identified by its UUID. In the following example, a reel is composed by picture and sound: === Packing list file or package key list (PKL) === All files in the composition are hashed and their hash is stored here, in XML format. This file is generally used during ingestion in a digital cinema server to verify if data have been corrupted or tampered with in some way. For example, an MXF picture reel is identified by the following
Image analysis
Image analysis or imagery analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Image analysis tasks can be as simple as reading bar coded tags or as sophisticated as identifying a person from their face. Computers are indispensable for the analysis of large amounts of data, for tasks that require complex computation, or for the extraction of quantitative information. On the other hand, the human visual cortex is an excellent image analysis apparatus, especially for extracting higher-level information, and for many applications — including medicine, security, and remote sensing — human analysts still cannot be replaced by computers. For this reason, many important image analysis tools such as edge detectors and neural networks are inspired by human visual perception models. == Digital == Digital Image Analysis or Computer Image Analysis is when a computer or electrical device automatically studies an image to obtain useful information from it. Note that the device is often a computer but may also be an electrical circuit, a digital camera or a mobile phone. It involves the fields of computer or machine vision, and medical imaging, and makes heavy use of pattern recognition, digital geometry, and signal processing. This field of computer science developed in the 1950s at academic institutions such as the MIT A.I. Lab, originally as a branch of artificial intelligence and robotics. It is the quantitative or qualitative characterization of two-dimensional (2D) or three-dimensional (3D) digital images. 2D images are, for example, to be analyzed in computer vision, and 3D images in medical imaging. The field was established in the 1950s—1970s, for example with pioneering contributions by Azriel Rosenfeld, Herbert Freeman, Jack E. Bresenham, or King-Sun Fu. == Techniques == There are many different techniques used in automatically analysing images. Each technique may be useful for a small range of tasks, however there still aren't any known methods of image analysis that are generic enough for wide ranges of tasks, compared to the abilities of a human's image analysing capabilities. Examples of image analysis techniques in different fields include: 2D and 3D object recognition, image segmentation, motion detection e.g. Single particle tracking, video tracking, optical flow, medical scan analysis, 3D Pose Estimation. == Deep learning == Since the early 2010s, deep learning methods have substantially advanced the field of image analysis. In 2012, a deep convolutional neural network (CNN) known as AlexNet achieved a significant reduction in error rates on the ImageNet large-scale image classification benchmark, demonstrating the effectiveness of deep learning for visual recognition tasks. Subsequent architectures such as ResNet introduced residual connections that enabled training of much deeper networks, further improving accuracy across image analysis tasks. Real-time object detection became practical with frameworks such as YOLO (You Only Look Once), which unified detection and classification into a single network pass. In 2020, the Vision Transformer (ViT) demonstrated that transformer architectures, originally developed for natural language processing, could achieve competitive results on image classification when applied directly to sequences of image patches. More recently, foundation models trained on large-scale datasets have enabled zero-shot generalisation across image analysis tasks. The Segment Anything Model (SAM), trained on over one billion masks, can segment arbitrary objects in images without task-specific fine-tuning. These advances have made image analysis techniques increasingly accessible through browser-based tools and open-source implementations. == Applications == The applications of digital image analysis are continuously expanding through all areas of science and industry, including: anatomy, allows for precise measurements, visualization, and statistical analysis of anatomical structures. assay micro plate reading, such as detecting where a chemical was manufactured. astronomy, such as calculating the size of a planet. automated species identification (e.g. plant and animal species) defense error level analysis filtering machine vision, such as to automatically count items in a factory conveyor belt. materials science, such as determining if a metal weld has cracks. medicine, such as detecting cancer in a mammography scan. metallography, such as determining the mineral content of a rock sample. microscopy, such as counting the germs in a swab. automatic number plate recognition; optical character recognition, such as automatic license plate detection. remote sensing, such as detecting intruders in a house, and producing land cover/land use maps. robotics, such as to avoid steering into an obstacle. security, such as detecting a person's eye color or hair color. == Object-based == Object-based image analysis (OBIA) involves two typical processes, segmentation and classification. Segmentation helps to group pixels into homogeneous objects. The objects typically correspond to individual features of interest, although over-segmentation or under-segmentation is very likely. Classification then can be performed at object levels, using various statistics of the objects as features in the classifier. Statistics can include geometry, context and texture of image objects. Over-segmentation is often preferred over under-segmentation when classifying high-resolution images. Object-based image analysis has been applied in many fields, such as cell biology, medicine, earth sciences, and remote sensing. For example, it can detect changes of cellular shapes in the process of cell differentiation.; it has also been widely used in the mapping community to generate land cover. When applied to earth images, OBIA is known as geographic object-based image analysis (GEOBIA), defined as "a sub-discipline of geoinformation science devoted to (...) partitioning remote sensing (RS) imagery into meaningful image-objects, and assessing their characteristics through spatial, spectral and temporal scale". The international GEOBIA conference has been held biannually since 2006. OBIA techniques are implemented in software such as eCognition or the Orfeo toolbox.
Bootstrap (front-end framework)
Bootstrap (formerly Twitter Bootstrap) is a free and open-source CSS framework directed at responsive, mobile-first front-end web development. It contains HTML, CSS and (optionally) JavaScript-based design templates for typography, forms, buttons, navigation, and other interface components. As of May 2023, Bootstrap is the 17th most starred project (4th most starred library) on GitHub, with over 164,000 stars. According to W3Techs, Bootstrap is used by 19.2% of all websites. == Features == Bootstrap is an HTML, CSS and JS library that focuses on simplifying the development of informative web pages (as opposed to web applications). The primary purpose of adding it to a web project is to apply Bootstrap's choices of color, size, font and layout to that project. As such, the primary factor is whether the developers in charge find those choices to their liking. Once added to a project, Bootstrap provides basic style definitions for all HTML elements. The result is a uniform appearance for prose, tables and form elements across web browsers. In addition, developers can take advantage of CSS classes defined in Bootstrap to further customize the appearance of their contents. For example, Bootstrap has provisioned for light- and dark-colored tables, page headings, more prominent pull quotes, and text with a highlight. Bootstrap also comes with several JavaScript components which do not require other libraries like jQuery. They provide additional user interface elements such as dialog boxes, tooltips, progress bars, navigation drop-downs, and carousels. Each Bootstrap component consists of an HTML structure, CSS declarations, and in some cases accompanying JavaScript code. They also extend the functionality of some existing interface elements, including for example an auto-complete function for input fields. The most prominent components of Bootstrap are its layout components, as they affect an entire web page. The basic layout component is called "Container", as every other element in the page is placed in it. Developers can choose between a fixed-width container and a fluid-width container. While the latter always fills the width with the web page, the former uses one of the five predefined fixed widths, depending on the size of the screen showing the page: Smaller than 576 pixels 576–768 pixels 768–992 pixels 992–1200 pixels 1200–1400 pixels Larger than 1400 pixels Once a container is in place, other Bootstrap layout components implement a CSS Flexbox layout through defining rows and columns. A precompiled version of Bootstrap is available in the form of one CSS file and three JavaScript files that can be readily added to any project. The raw form of Bootstrap, however, enables developers to implement further customization and size optimizations. This raw form is modular, meaning that the developer can remove unneeded components, apply a theme and modify the uncompiled Sass files. == History == === Early beginnings === Bootstrap, originally named Twitter Blueprint, was developed by Mark Otto and Jacob Thornton at Twitter in 2010 as a framework to encourage consistency across internal tools. Before Bootstrap, various libraries were used for interface development, which led to inconsistencies and a high maintenance burden. According to Otto: A super small group of developers and I got together to design and build a new internal tool and saw an opportunity to do something more. Through that process, we saw ourselves build something much more substantial than another internal tool. Months later, we ended up with an early version of Bootstrap as a way to document and share common design patterns and assets within the company. After a few months of development by a small group, many developers at Twitter began to contribute to the project as a part of Hack Week, a hackathon-style week for the Twitter development team. It was renamed from Twitter Blueprint to Twitter Bootstrap and released as an open-source project on August 19, 2011. It has continued to be maintained by Otto, Thornton, a small group of core developers, and a large community of contributors. === Bootstrap 2 === On January 31, 2012, Bootstrap 2 was released, which added built-in support for Glyphicons, several new components, as well as changes to many of the existing components. This version supports responsive web design, meaning the layout of web pages adjusts dynamically, taking into account the characteristics of the device used (whether desktop, tablet, mobile phone). Shortly before the release of Bootstrap 2.1.2, Otto and Thornton left Twitter, but committed to continue to work on Bootstrap as an independent project. === Bootstrap 3 === On August 19, 2013, Bootstrap 3 was released. It redesigned components to use flat design and a mobile first approach. Bootstrap 3 features new plugin system with namespaced events. Bootstrap 3 dropped Internet Explorer 7 and Firefox 3.6 support, but there is an optional polyfill for these browsers. Bootstrap 3 was also the first version released under the twbs organization on GitHub instead of the Twitter one. === Bootstrap 4 === Otto announced Bootstrap 4 on October 29, 2014. The first alpha version of Bootstrap 4 was released on August 19, 2015. The first beta version was released on August 10, 2017. Otto suspended work on Bootstrap 3 on September 6, 2016, to free up time to work on Bootstrap 4. Bootstrap 4 was finalized on January 18, 2018. Significant changes include: Major rewrite of the code Replacing Less with Sass Addition of Reboot, a collection of element-specific CSS changes in a single file, based on Normalize Dropping support for IE8, IE9, and iOS 6 CSS Flexible Box support Adding navigation customization options Adding responsive spacing and sizing utilities Switching from the pixels unit in CSS to root ems Increasing global font size from 14px to 16px for enhanced readability Dropping the panel, thumbnail, pager, and well components Dropping the Glyphicons icon font Huge number of utility classes Improved form styling, buttons, drop-down menus, media objects and image classes Bootstrap 4 supports the latest versions of Google Chrome, Firefox, Internet Explorer, Opera, and Safari (except on Windows). It additionally supports back to IE10 and the latest Firefox Extended Support Release (ESR). === Bootstrap 5 === Bootstrap 5 was officially released on May 5, 2021. Major changes include: New offcanvas menu component Removing dependence on jQuery in favor of vanilla JavaScript Rewriting the grid to support responsive gutters and columns placed outside of rows Migrating the documentation from Jekyll to Hugo Dropping support for Internet Explorer Moving testing infrastructure from QUnit to Jasmine Adding custom set of SVG icons Adding CSS custom properties Improved API Enhanced grid system Improved customizing docs Updated forms RTL support Built in darkmode support