In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957 (Nerode & Sauer 1957, p. ii). == Statement == Given a language L {\displaystyle L} , and a pair of strings x {\displaystyle x} and y {\displaystyle y} , define a distinguishing extension to be a string z {\displaystyle z} such that exactly one of the two strings x z {\displaystyle xz} and y z {\displaystyle yz} belongs to L {\displaystyle L} . Define a relation ∼ L {\displaystyle \sim _{L}} on strings as x ∼ L y {\displaystyle x\;\sim _{L}\ y} if there is no distinguishing extension for x {\displaystyle x} and y {\displaystyle y} . It is easy to show that ∼ L {\displaystyle \sim _{L}} is an equivalence relation on strings, and thus it divides the set of all strings into equivalence classes. The Myhill–Nerode theorem states that a language L {\displaystyle L} is regular if and only if ∼ L {\displaystyle \sim _{L}} has a finite number of equivalence classes, and moreover, that this number is equal to the number of states in the minimal deterministic finite automaton (DFA) accepting L {\displaystyle L} . Furthermore, every minimal DFA for the language is isomorphic to the canonical one (Hopcroft & Ullman 1979). Generally, for any language, the constructed automaton is a state automaton acceptor. However, it does not necessarily have finitely many states. The Myhill–Nerode theorem shows that finiteness is necessary and sufficient for language regularity. Some authors refer to the ∼ L {\displaystyle \sim _{L}} relation as Nerode congruence, in honor of Anil Nerode. == Use and consequences == The Myhill–Nerode theorem may be used to show that a language L {\displaystyle L} is regular by proving that the number of equivalence classes of ∼ L {\displaystyle \sim _{L}} is finite. This may be done by an exhaustive case analysis in which, beginning from the empty string, distinguishing extensions are used to find additional equivalence classes until no more can be found. For example, the language consisting of binary representations of numbers that can be divided by 3 is regular. Given two binary strings x , y {\displaystyle x,y} , extending them by one digit gives 2 x + b , 2 y + b {\displaystyle 2x+b,2y+b} , so 2 x + b ≡ 2 y + b mod 3 {\displaystyle 2x+b\equiv 2y+b\mod 3} iff x ≡ y mod 3 {\displaystyle x\equiv y\mod 3} . Thus, 00 {\displaystyle 00} (or 11 {\displaystyle 11} ), 01 {\displaystyle 01} , and 10 {\displaystyle 10} are the only distinguishing extensions, resulting in the 3 classes. The minimal automaton accepting our language would have three states corresponding to these three equivalence classes. Another immediate corollary of the theorem is that if for a language L {\displaystyle L} the relation ∼ L {\displaystyle \sim _{L}} has infinitely many equivalence classes, it is not regular. It is this corollary that is frequently used to prove that a language is not regular. == Generalizations == The Myhill–Nerode theorem can be generalized to tree automata.
Data-driven model
Data-driven models are a class of computational models that primarily rely on historical data collected throughout a system's or process' lifetime to establish relationships between input, internal, and output variables. Commonly found in numerous articles and publications, data-driven models have evolved from earlier statistical models, overcoming limitations posed by strict assumptions about probability distributions. These models have gained prominence across various fields, particularly in the era of big data, artificial intelligence, and machine learning, where they offer valuable insights and predictions based on the available data. == Background == These models have evolved from earlier statistical models, which were based on certain assumptions about probability distributions that often proved to be overly restrictive. The emergence of data-driven models in the 1950s and 1960s coincided with the development of digital computers, advancements in artificial intelligence research, and the introduction of new approaches in non-behavioural modelling, such as pattern recognition and automatic classification. == Key Concepts == Data-driven models encompass a wide range of techniques and methodologies that aim to intelligently process and analyse large datasets. Examples include fuzzy logic, fuzzy and rough sets for handling uncertainty, neural networks for approximating functions, global optimization and evolutionary computing, statistical learning theory, and Bayesian methods. These models have found applications in various fields, including economics, customer relations management, financial services, medicine, and the military, among others. Machine learning, a subfield of artificial intelligence, is closely related to data-driven modelling as it also focuses on using historical data to create models that can make predictions and identify patterns. In fact, many data-driven models incorporate machine learning techniques, such as regression, classification, and clustering algorithms, to process and analyse data. In recent years, the concept of data-driven models has gained considerable attention in the field of water resources, with numerous applications, academic courses, and scientific publications using the term as a generalization for models that rely on data rather than physics. This classification has been featured in various publications and has even spurred the development of hybrid models in the past decade. Hybrid models attempt to quantify the degree of physically based information used in hydrological models and determine whether the process of building the model is primarily driven by physics or purely data-based. As a result, data-driven models have become an essential topic of discussion and exploration within water resources management and research. The term "data-driven modelling" (DDM) refers to the overarching paradigm of using historical data in conjunction with advanced computational techniques, including machine learning and artificial intelligence, to create models that can reveal underlying trends, patterns, and, in some cases, make predictions Data-driven models can be built with or without detailed knowledge of the underlying processes governing the system behavior, which makes them particularly useful when such knowledge is missing or fragmented.
Digital Cinema Initiatives
Digital Cinema Initiatives, LLC (DCI) is a consortium of major motion picture studios, formed to establish specifications for a common systems architecture for digital cinema systems. The organization was formed in March 2002 by Metro-Goldwyn-Mayer, Paramount Pictures, Sony Pictures, 20th Century Studios, Universal Studios, Walt Disney Studios and Warner Bros. Entertainment The primary purpose of DCI is to establish and document specifications for an open architecture for digital cinema that ensures a uniform and high level of technical performance, reliability and quality. By establishing a common set of content requirements, distributors, studios, exhibitors, d-cinema manufacturers and vendors can be assured of interoperability and compatibility. Because of the relationship of DCI to many of Hollywood's key studios, conformance to DCI's specifications is considered a requirement by software developers or equipment manufacturers targeting the digital cinema market. == Specification == On July 20, 2005, DCI released Version 1.0 of its "Digital Cinema System Specification", commonly referred to as the "DCI Specification". The document describes overall system requirements and specifications for digital cinema. Between March 28, 2006, and March 21, 2007, DCI issued 148 errata to Version 1.0. DCI released Version 1.1 of the DCI Specification on April 12, 2007, incorporating the previous 148 errata into the DCI Specification. On April 15, 2007, at the annual NAB Digital Cinema Summit, DCI announced the new version, as well as some future plans. They released the "Stereoscopic Digital Cinema Addendum" to begin to establish 3-D technical specifications in response to the popularity of 3-D stereoscopic films. It was also announced "which studios would take over the leadership roles in DCI after the current leadership term expires at the end of September." Subsequently, between August 27, 2007, and February 1, 2008, DCI issued 100 errata to Version 1.1. So, DCI released Version 1.2 of the DCI Specification on March 7, 2008, again incorporating the previous 100 errata into the specification document. An additional 96 errata were issued by August 30, 2012, so a revised Version 1.2 incorporating those additional errata was approved on October 10, 2012. DCI approved DCI Specification Version 1.3 on June 27, 2018, integrating the 45 errata issued to the previous version into a new document. On July 20, 2020, fifteen years to the day after Version 1.0, DCI issued a new DCI Specification Version 1.4 that assimilated 29 errata issued since Version 1.3. On October 13, 2021, DCI approved a new DCI Specification Version 1.4.1 that integrated the 23 errata that had been issued to DCI Specification Version 1.4. For the convenience of users, DCI also created an online HTML version of DCI Specification, Version 1.4.1. Due to the HTML conversion process, the footnotes in the DCSS now appear as endnotes. The PDF version contains pagination and page numbers whereas the HTML version does not. DCI Specification Version 1.4.2, dated June 15, 2022, includes revisions and refinements respecting Object-Based Audio Essence (OBAE), also known as Immersive Audio Bitstream (IAB). Version 1.4.2 also implements post-show log record collection utilizing SMPTE 430-17 SMS-OMB Communications Protocol Specification. Additionally, Version 1.4.2 incorporated two prior addenda: the Digital Cinema Object-Based Audio Addendum, dated October 1, 2018 and the Stereoscopic Digital Cinema Addendum, Version 1.0, dated July 11, 2007. Users using Version 1.4.2 no longer need to refer to the separate addenda. Previous DCSS versions are archived on the DCI web site. Based on many SMPTE and ISO standards, such as JPEG 2000-compressed image and "broadcast wave" PCM/WAV sound, the DCI Specification explains the route to create an entire Digital Cinema Package (DCP) from a raw collection of files known as the Digital Cinema Distribution Master (DCDM), as well as the specifics of its content protection, encryption, and forensic marking. The DCI Specification also establishes standards for the decoder requirements and the presentation environment itself, such as ambient light levels, pixel aspect and shape, image luminance, white point chromaticity, and those tolerances to be kept. Even though it specifies what kind of information is required, the DCI Specification does not include specific information about how data within a distribution package is to be formatted. Formatting of this information is defined by the Society of Motion Picture and Television Engineers (SMPTE) digital cinema standards and related documents. == Image and audio capability overview == === 2D image === 2048×1080 (2K) at 24 frame/s or 48 frame/s, or 4096×2160 (4K) at 24 frame/s In 2K, for Scope (2.39:1) presentation 2048×858 pixels of the imager is used In 2K, for Flat (1.85:1) presentation 1998×1080 pixels of the imager is used In 4K, for Scope (2.39:1) presentation 4096×1716 pixels of the imager is used In 4K, for Flat (1.85:1) presentation 3996×2160 pixels of the imager is used 12 bits per color component (36 bits per pixel) via dual HD-SDI (encrypted) 10 bits only permitted for 2K at 48 frame/s CIE XYZ color space, gamma-corrected TIFF 6.0 container format (one file per frame) JPEG 2000 compression From 0 to 5 or from 1 to 6 wavelet decomposition levels for 2K or 4K resolutions, respectively Compression rate of 4.71 bits/pixel (2K @ 24 frame/s), 2.35 bits/pixel (2K @ 48 frame/s), 1.17 bits/pixel (4K @ 24 frame/s) 250 Mbit/s maximum image bit rate === Stereoscopic 3D image === 2048×1080 (2K) at 48 frame/s - 24 frame/s per eye (4096×2160 4K not supported) In 2K, for Scope (2.39:1) presentation 2048×858 pixels of the imager is used In 2K, for Flat (1.85:1) presentation 1998×1080 pixels of the imager is used Optionally, in the HD-SDI link only: 12 bit color, YCxCz 4:2:2 (i.e. chroma subsampling in XYZ space), each eye in separate stream === Audio === 24 bits per sample, 48 kHz or 96 kHz Up to 16 channels WAV container, uncompressed PCM DCI has additionally published a document outlining recommended practice for High Frame Rate digital cinema. This document discloses the following proposed frame rates: 60, 96, and 120 frames per second for 2D at 2K resolution; 48 and 60 for stereoscopic 3D at 2K resolution; 48 and 60 for 2D at 4K resolution. The maximum compressed bit rate for support of all proposed frame rates should be 500 Mbit/s. == Related information == The idea for DCI was originally mooted in late 1999 by Tom McGrath, then COO of Paramount Pictures, who applied to the U.S. Department of Justice for anti-trust waivers to allow the joint cooperation of all seven major motion picture studios. Universal Pictures made one of the first feature-length DCPs created to DCI specifications, using their film Serenity. Although it was not distributed theatrically, it had one public screening on November 7, 2005, at the USC Entertainment Technology Center's Digital Cinema Laboratory in the Pacific Theatre, Hollywood. Inside Man (2006) was Universal's first DCP commercial release, and, in addition to 35mm film distribution, was delivered via hard drive to 20 theatres in the United States along with two trailers. The Academy Film Archive houses the Digital Cinema Initiatives, LLC Collection, which includes film and digital elements from DCI's Standard Evaluation Material (StEM), a 12-minute production shot on 35mm and 65mm film, created for vendors and standards organizations to test and evaluate image compression and digital projection technologies.
X2 transceiver
The X2 transceiver format is a 10 gigabit per second modular fiber optic interface intended for use in routers, switches and optical transport platforms. It is an early generation 10 gigabit interface related to the similar XENPAK and XPAK formats. X2 may be used with 10 Gigabit Ethernet or OC-192/STM-64 speed SDH/SONET equipment. X2 modules are smaller and consume less power than first-generation XENPAK modules, but larger and consume more energy than the newer XFP transceiver standard and SFP+ standards. As of 2016 this format is relatively uncommon and has been replaced by 10 Gbit/s SFP+ in most new equipment.
Institute of Telecommunications Professionals
The Institute of Telecommunications Professionals (ITP) is a membership organisation for professionals in the telecommunications industry, based in the United Kingdom. The Institute was originally founded in 1906. It is now a registered company with Companies House in the United Kingdom, incorporated in 2002. Brendan O' Mahony has been the chief executive of the ITP. Lucy Woods presided over ITP for fifteen years, until 2018, when the organization named Kevin Paige chairman for five years. In 2022 the ITP appointed its new CEO, Charlotte Goodwill. In 2021, the ITP assisted a UK fibre network Vorboss in establishing its training academy. In 2023, the ITP appointed Tim Creswick, the CEO of Vorboss, as the new chair of its board of directors. The institute has an associated journal, the Journal of the Institute of Telecommunications Professionals, established in 2007 and published quarterly.
Artipic
Artipic is a graphics editor developed for Microsoft Windows. An older version for macOS is still available but unsupported. Artipic features drawing, editing, retouching, transforming and composing images including color corrections, effects and layer-based operations. It converts all common image formats and imports camera raw formats. In the global image editing ecosystem Artipic can be positioned somewhere in the middle. It differs from simple free photo editors by more advanced capabilities, however it does not cover the complete professional-level functionality pack provided by industry leaders like Adobe Photoshop. == History == Artipic developed by Swedish company Artipic AB. Artipic 1.0 was released in March 2014 as a free version. The first commercial version on Microsoft Windows was released in November 2014, on macOS – in October 2015. == Features == Supports Microsoft Windows and macOS Standard tools: select, crop, move, rotate, transform, stamp, color picking, text Advanced tools: custom brushes, gradients, shapes, paths, layers and masks Special tools: healing brush, red-eye effect reduction, dodge and burn brushes Adjustments: Brightness & Contrast, Hue & Saturation, Curves, Levels, Color Balance, Gamma Correction, Exposure, Color Temperature, Tint, Color Enhancer, Photo Filter Simulation, Posterization, Thresholding Filters: Smoothen, Sharpen, Vignetting, High-pass, Diffuse Glow, Shadow, Gaussian Blur Reversible (non-destructive) stylization presets Batch processing White balance RAW-converter including Gray Card Adobe Photoshop images supported == Version history ==
Fediverse
The Fediverse (commonly shortened to fedi) is a collection of social networking services that can communicate with each other (formally known as federation) using a common protocol. Users of different websites can send and receive status updates, multimedia files and other data across the network. The term Fediverse is a portmanteau of federation and universe. The majority of Fediverse platforms are based on free and open-source software, and create connections between servers using the ActivityPub protocol. Some software still supports older federation protocols as well, such as OStatus, the Diaspora protocol and Zot, while newer protocols such as AT Protocol connect via network bridges. Diaspora is the only actively developed software project classified under the original definition of Fediverse that does not support ActivityPub. == Design == While a traditional social networking service will host all its content on servers managed by the owner of the website, the decentralized structure of the Fediverse allows any individual or organization to host a social platform using their own servers (referred to as an "instance"). Every instance is independent, and can set its own rules and expectations. Even so, much like how users of one email service such as Gmail can still send emails to users of another service such as Outlook, users may still view content and interact with users on any other instance in the Fediverse. A user on one Mastodon instance, for example, may view and interact with posts made by a user on a different instance even if it is not running Mastodon. Instances hosted by different social networking services may also communicate with one another. A user on the microblogging platform Misskey, for example, may view and interact with posts made by users on Mastodon. Some Fediverse networks even allow users to interact with different social networking formats from the same platform. For example, a user on a social news instance running Lemmy can interact with another post from an mbin instance, a similar service, as well as microblog statuses from Mastodon. === Content moderation and user safety === Decentralized social networking platforms introduce new challenges and difficulties for user trust and safety. By nature of the Fediverse, operators of an instance are solely responsible for moderation of its content. As there is no form of centralized governance or moderation across the Fediverse, it is impossible for an instance to be "removed" from the Fediverse; it can only be defederated per an instance operator's choice, which makes that instance's content inaccessible from the operator's instance. Individual instances are responsible for defining their own content policies, which may then be enforced by its staff. Moderation of a Fediverse instance differs significantly from that of traditional social media platforms, as moderators are responsible not only for content posted by users of that instance ("local users"), but also for content posted by users of other instances ("remote users"). == History == === Historical protocols === The concept and the functionality of the Fediverse existed before the ActivityPub protocol and the term itself. One of the first projects that included support for a decentralized social networking service was Laconica, a microblogging platform which implemented the OpenMicroBlogging protocol for communicating between different installations of the software. The software was later renamed to StatusNet in 2009, before being merged into the GNU social project in 2013 along with Free Social, with the two latter servers being a fork of StatusNet. Over time, the limitations of the OpenMicroBlogging protocol became more apparent, being designed as a one-way text messaging system. To replace the ageing protocol, OStatus was devised as an open standard for microblogging, combining various other technologies like Salmon, Atom, WebSub and ActivityStreams into a single protocol used for communicating between instances. StatusNet first implemented the OStatus protocol on March 3, 2010, with version 0.9.0, and OStatus quickly became the most popular federated protocol in usage. Around the same time as OStatus was gaining popularity, the Diaspora social network was formed, using its own federated protocol. To illustrate the differences between the two protocols, the terms of the Fediverse and the federation began to enter common usage, mainly after 2017. The term "the Fediverse" was used to describe the network formed by software using the OStatus protocol, such as GNU Social, Mastodon, and Friendica, in contrast to the competing diaspora protocol under "the federation". === ActivityPub === In December 2012, the flagship StatusNet instance at the time, identi.ca, transitioned away to a new software named pump.io, with a new federation protocol to replace OStatus. The new protocol was designed to be useful for general activity streams and not just status updates, and replaced many of OStatus' external dependencies with JSON-LD and a REST API for its messaging and inbox systems, as well as making more use of ActivityStreams. While not as utilized as its OStatus predecessor, it would later become influential in the development of the ActivityPub standard. In January 2018, the W3C presented the ActivityPub protocol as a recommended standard. The standard aimed to improve the interoperability between different software packages running on a wide network of servers and to supersede both the OStatus protocol and Pump.io. By 2019, almost all software that was using OStatus had added support for ActivityPub. While Mastodon began to remove OStatus support, other projects maintained it in their code, such as Friendica (which also maintained diaspora support along with ActivityPub). === AT Protocol === A major protocol often contrasted with ActivityPub is the AT Protocol, which powers the Bluesky social network. While both protocols aim to create decentralized social networks, they employ different technical philosophies regarding user identity. Developers of the AT Protocol, including Bluesky CEO Jay Graber, have stated they chose not to use ActivityPub because it did not natively support easy "account portability", the ability for a user to move their account, data, and social graph to a new provider without relying on the original server to authorize the move. In the ActivityPub model (used by Mastodon), a user's identity is typically tied to a specific server, similar to an email address; if that server goes offline, the identity can be lost. The AT Protocol aims to solve this by separating identity from hosting, allowing users to switch providers without losing their identity. Although the two protocols are technically incompatible by default, third-party "bridges" such as Bridgy Fed have been developed to allow users on ActivityPub networks to follow and interact with users on the AT Protocol network, and vice versa. === Other Fediverse protocols === While the Fediverse has traditionally been the network most commonly referred to and used as an example regarding the subject of decentralized social networks, alternatives to it and the accompanying ActivityPub have been developed and deployed. Smaller competitors such as Nostr and Farcaster have become popular within the cryptocurrency community. These protocols have used ActivityPub as a frame of reference for which to design their own architecture, as these newer protocols use a different federation model based on publishing content to relays for distribution rather than ActivityPub's server-centric model. Despite their differences, software exists that permit the bridging of user content between these protocols, including "double-bridges" that span multiple protocols for the purpose of distributing the same content. == Adoption == Users have been slow to embrace the Fediverse due to poor user experience and excessive complexity. Following the acquisition of Twitter by Elon Musk in November 2022, certain major social networks, including Threads, Tumblr and Flipboard, expressed interest in supporting the ActivityPub protocol, as a large number of users began to migrate to Mastodon, a server that supports the Fediverse and was also the most popular alternative to Twitter at the time. Flickr also expressed support in supporting ActivityPub. As of November 2022, no information had been released by Flickr after the initial tweets by the CEO, with support for ActivityPub suspected to be on hold or cancelled. In 2024, the local government of the Stary Sącz municipality in Poland launched their own PeerTube instance in order to de facto abolish its presence on YouTube. According to the government, they stopped using YouTube for official communications "in order to adhere to the appropriate regulations". In the same year, VIVERSE, HTC Vive's metaverse platform, implemented support for ActivityPub in their chat feature, allowing users to send direct messages to other