In automata theory, a Muller automaton is a type of an ω-automaton. The acceptance condition separates a Muller automaton from other ω-automata. The Muller automaton is defined using a Muller acceptance condition, i.e. the set of all states visited infinitely often must be an element of the acceptance set. Both deterministic and non-deterministic Muller automata recognize the ω-regular languages. They are named after David E. Muller, an American mathematician and computer scientist, who invented them in 1963. == Formal definition == Formally, a deterministic Muller-automaton is a tuple A = (Q,Σ,δ,q0,F) that consists of the following information: Q is a finite set. The elements of Q are called the states of A. Σ is a finite set called the alphabet of A. δ: Q × Σ → Q is a function, called the transition function of A. q0 is an element of Q, called the initial state. F is a set of sets of states. Formally, F ⊆ P(Q) where P(Q) is powerset of Q. F defines the acceptance condition. A accepts exactly those runs in which the set of infinitely often occurring states is an element of F In a non-deterministic Muller automaton, the transition function δ is replaced with a transition relation Δ that returns a set of states and the initial state q0 is replaced by a set of initial states Q0. Generally, 'Muller automaton' refers to a non-deterministic Muller automaton. For more comprehensive formalisation look at ω-automaton. == Equivalence with other ω-automata == The Muller automata are equally expressive as parity automata, Rabin automata, Streett automata, and non-deterministic Büchi automata, to mention some, and strictly more expressive than the deterministic Büchi automata. The equivalence of the above automata and non-deterministic Muller automata can be shown very easily as the accepting conditions of these automata can be emulated using the acceptance condition of Muller automata and vice versa. McNaughton's theorem demonstrates the equivalence of non-deterministic Büchi automaton and deterministic Muller automaton. Thus, deterministic and non-deterministic Muller automata are equivalent in terms of the languages they can accept. == Transformation to non-deterministic Muller automata == Following is a list of automata constructions that each transforms a type of ω-automata to a non-deterministic Muller automaton. From Büchi automata If B is the set of final states in a Büchi automaton with the set of states Q, we can construct a Muller automaton with same set of states, transition function and initial state with the Muller accepting condition as F = { X | X ∈ P(Q) ∧ X ∩ B ≠ ∅}. From Rabin automata/parity automata Similarly, the Rabin conditions ( E j , F j ) {\displaystyle (E_{j},F_{j})} can be emulated by constructing the acceptance set in the Muller automaton as all sets F ⊆ Q {\displaystyle F\subseteq Q} that satisfy F ∩ E j = ∅ {\displaystyle F\cap E_{j}=\emptyset } and F ∩ F j ≠ ∅ {\displaystyle F\cap F_{j}\neq \emptyset } , for some j. Note that this covers the case of parity automata too, as the parity acceptance condition can be expressed as a Rabin acceptance condition easily. From Streett automata The Streett conditions ( E j , F j ) {\displaystyle (E_{j},F_{j})} can be emulated by constructing the acceptance set in the Muller automaton as all sets F ⊆ Q {\displaystyle F\subseteq Q} that satisfy F ∩ F j = ∅ ⟹ F ∩ E j = ∅ {\displaystyle F\cap F_{j}=\emptyset \implies F\cap E_{j}=\emptyset } , for all j. == Transformation to deterministic Muller automata == From Büchi automaton McNaughton's theorem provides a procedure to transform any non-deterministic Büchi automaton into a deterministic Muller automaton.
StatMuse
StatMuse Inc. is an American artificial intelligence company founded in 2014. It operates an eponymous website that hosts a database of sports statistics covering the four major North American sports leagues, the Women's National Basketball Association (WNBA), NCAA Division I men's basketball, NCAA Division I Football Bowl Subdivision, the Big Five association football leagues in Europe, and various professional golf tours. == History == The company was founded by friends Adam Elmore and Eli Dawson in 2014. In email correspondence to the Springfield News-Leader, Elmore detailed that he and Dawson, fans of the National Basketball Association (NBA), were compelled to create StatMuse after they realized there was no online platform where they could search "Lebron James most points" [sic] and quickly get a result "showing his highest scoring games." As a startup, the company's goal was to utilize a type of artificial intelligence called natural language processing (NLP) for sports. In 2015, the company was part of the second group of startups accepted into the Disney Accelerator program. The company secured support from several investors, including The Walt Disney Company, Techstars, Allen & Company, the NFL Players Association, Greycroft and NBA Commissioner David Stern. As part of their partnership with Disney, StatMuse signed a content deal with ESPN (owned by Disney) to provide stats content on social media and television during the 2015–16 NBA season. Initially, the company only had stats available for the NBA, but eventually expanded to provide stats for the other major North American sports leagues. The company's initial demographic was players of fantasy sports, but it eventually expanded to target general sports fans as well. StatMuse offers responses to user queries in the voices of sports-related public figures. Dawson shared with VentureBeat that StatMuse brings people in and records them saying different words and phrases. These celebrity voices were made accessible through Google's Google Assistant service, Microsoft's Cortana virtual assistant, and Amazon's Echo devices. The company launched its phone app in September 2017. The app allows users to access StatMuse's sports statistics database by submitting queries in their natural language. Upon the launch of the phone app, Fitz Tepper of TechCrunch wrote that: "The technology isn't perfect – some of the pauses between words are a bit awkward, making it clear that some phrases are being stitched together on the fly. But this is the exception, and on the whole, most responses sound pretty good." StatMuse plug-ins for Slack and Facebook Messenger were also made, providing text-based sports stats. In 2019, StatMuse received investment from the Google Assistant Investment program. The service launched a premium option dubbed StatMuse+ in May 2023, offering options that had previously been included for free, such as unlimited searches and full results in data tables. The premium version also included early access to new features and a personalized search history, as well as not having ads. The app received a variety of feedback. In January 2024, the service launched a Premier League version of the website dubbed StatMuse FC. It is planned to introduce more leagues on the website.
MyPoolin
Mypoolin is a mobile peer-to-peer and group payment application. Their software allows the settling of debts and group-expenditure for events and activities. The software utilizes Unified Payment Interface of India to collect and settle daily expenses with friends. Users can also plan and pay together for group-gifting, movies, vacations, concerts, events, and parties. == Service == Mypoolin is a mobile payment provider that lets its users transfer money to other users via their mobile number. A user can create an account by verifying an OTP code which is sent to his mobile phone. It also allows the users to track their friends’ activities on the app. == History == Mypoolin was founded by Rohit Taneja (IIT Delhi) and Ankit Singh (FMS Delhi) in 2014 as a medium to aggregate money for various purposes in a hassle free and quick manner. Prior to the mobile app launch, Mypoolin was initially launched as a web application. == Funding == Mypoolin has been seed funded by angel investors. As winners of the QPrize 2015, Mypoolin jointly received an additional funding of $250,000 from Qualcomm Ventures. == Growth == Mypoolin reached INR 10 lakhs in revenue during its first four months of the web application launch, and was listed in the "Top ten free apps" in its category within the first 5 days of the Android app launch. It was one of the Top 50 start-ups in Asia at the Echelon Asia Summit held in Singapore. And among the top 3 start-ups in 1776 Cup Challenge 2016. Apple Inc also featured the app on their app store in India. == Features == Users are able to collect and share money on the app for daily uses like movies, events and trips. The money collected can then be redeemed in the form of an online voucher redeemable across several e-commerce sites. The amount can be redeemed also in the form of an offline debit card delivered to the address or in the form of a wire transfer. == Media coverage == Mypoolin was featured in The Economic Times and The Hindu Business Line after winning the Qualcomm Ventures' QPrize 2015. Digit magazine featured them recently as the app of the week. The app has mostly grown organically so far in the Indian urban millennial space.
IOS SDK
The iOS SDK (iOS Software Development Kit), formerly the iPhone SDK, is a software development kit (SDK) developed by Apple Inc. The kit allows for the development of mobile apps on Apple's iOS 17 and iPadOS operating systems. The iOS SDK is a free download for users of Macintosh (or Mac) personal computers. It is not available for Microsoft Windows PCs. The SDK contains sets giving developers access to various functions and services of iOS devices, such as hardware and software attributes. It also contains an iPhone simulator to mimic the look and feel of the device on the computer while developing. New versions of the SDK accompany new versions of iOS. In order to test applications, get technical support, and distribute apps through App Store, developers are required to subscribe to the Apple Developer Program. Combined with Xcode, the iOS SDK helps developers write iOS apps using officially supported programming languages, including Swift and Objective-C. Other companies have also created tools that allow for the development of native iOS apps using their respective programming languages. == History == While originally developing iPhone prior to its unveiling in 2007, Apple's then-CEO Steve Jobs did not intend to let third-party developers build native apps for the iOS operating system, instead directing them to make web applications for the Safari web browser. However, backlash from developers prompted the company to reconsider, with Jobs announcing on October 17, 2007, that Apple would have a software development kit (SDK) available for developers by February 2008. The SDK was released on March 6, 2008. == Features == The iOS SDK is a free download for Mac users. It is not available for Microsoft Windows. To test the application, get technical support, and distribute applications through App Store, developers are required to subscribe to the Apple Developer Program. The SDK contents are separated into the following sets: UIKit Multi-touch events and controls Accelerometer support View hierarchy Localization (i18n) Camera support Media OpenAL audio mixing and recording Video playback Image file formats Quartz Core Animation OpenGL ES Core Services Networking Embedded SQLite database Core Location Threads CoreMotion Mac OS X Kernel TCP/IP Sockets Power management File system Security The SDK also contains an iPhone simulator, a program used to simulate the look and feel of iPhone on the developer's computer. New SDK versions accompany new iOS versions. == Programming languages == The iOS SDK, combined with Xcode, helps developers write iOS applications using officially supported programming languages, including Swift and Objective-C. An .ipa (iOS App Store Package) file is an iOS application archive file which stores an iOS app. === Java === In 2008, Sun Microsystems announced plans to release a Java Virtual Machine (JVM) for iOS, based on the Java Platform, Micro Edition version of Java. This would enable Java applications to run on iPhone and iPod Touch. Soon after the announcement, developers familiar with the SDK's terms of agreement believed that by not allowing third-party applications to run in the background (answer a phone call and still run the application, for example), and not allowing an application to download code from another source, nor allowing an application to interact with a third-party application, Sun's development efforts could be hindered without Apple's cooperation. Sun also worked with a third-party company called Innaworks in attempts to get Java on iPhone. Despite the apparent lack of interest from Apple, a firmware leak of the 2007 iPhone release revealed an ARM chip with a processor with Jazelle support for embedded Java execution. === .NET === Novell announced in September 2009 that they had successfully developed MonoTouch, a software framework that let developers write native iPhone applications in the C# and .NET programming languages, while still maintaining compatibility with Apple's requirements. === Flash === iOS does not support Adobe Flash, and although Adobe has two versions of its software: Flash and Flash Lite, Apple views neither as suitable for the iPhone, claiming that full Flash is "too slow to be useful", and Flash Lite to be "not capable of being used with the Web". In October 2009, Adobe announced that an upcoming update to its Creative Suite would feature a component to let developers build native iPhone apps using the company's Flash development tools. The software was officially released as part of the company's Creative Suite 5 collection of professional applications. === 2010 policy on development tools === In April 2010, Apple made controversial changes to its iPhone Developer Agreement, requiring developers to use only "approved" programming languages in order to publish apps on App Store, and banning applications that used third-party development tools; the ban affected Adobe's Packager tool, which converted Flash apps into iOS apps. After developer backlash and news of a potential anti-trust investigation, Apple again revised its agreement in September, allowing the use of third-party development tools. === Mac Catalyst === Originally called "Project Marzipan", Mac Catalyst helps developers bring iPadOS app experiences to macOS, and make it easier to take apps developed for iPadOS devices to Macs by avoiding the need to write the underlying software code twice.
Microsoft Forms
Microsoft Forms (formerly Office 365 Forms) is an online survey creator, part of Microsoft 365. == Usage == Forms allows users to create surveys and quizzes with automatic marking. The data can be exported to Microsoft Excel, Power BI dashboards and viewed live using the Present feature. == Phishing and fraud == Due to a wave of phishing attacks utilizing Microsoft 365 in early 2021, Microsoft uses algorithms to automatically detect and block phishing attempts with Microsoft Forms. Also, Microsoft advises Forms users not to submit personal information, such as passwords, in a form or survey. It also place a similar advisory underneath the “Submit” button in every form created with Forms, warning users not to give out their password.
Augmented Analytics
Augmented Analytics is an approach of data analytics that employs the use of machine learning and natural language processing to automate analysis processes normally done by a specialist or data scientist. The term was introduced in 2017 by Rita Sallam, Cindi Howson, and Carlie Idoine in a Gartner research paper. Augmented analytics is based on business intelligence and analytics. In the graph extraction step, data from different sources are investigated. == Defining Augmented Analytics == Machine Learning – a systematic computing method that uses algorithms to sift through data to identify relationships, trends, and patterns. It is a process that allows algorithms to dynamically learn from data instead of having a set base of programmed rules. Natural language generation (NLG) – a software capability that takes unstructured data and translates it into plain-English, readable, language. Automating Insights – using machine learning algorithms to automate data analysis processes. Natural Language Query – enabling users to query data using business terms that are either typed onto a search box or spoken. == Data Democratization == Data Democratization is the democratizing data access in order to relieve data congestion and get rid of any sense of data "gatekeepers". This process must be implemented alongside a method for users to make sense of the data. This process is used in hopes of speeding up company decision making and uncovering opportunities hidden in data. There are three aspects to democratising data: Data Parameterisation and Characterisation. Data Decentralisation using an OS of blockchain and DLT technologies, as well as an independently governed secure data exchange to enable trust. Consent Market-driven Data Monetisation. When it comes to connecting assets, there are two features that will accelerate the adoption and usage of data democratisation: decentralized identity management and business data object monetization of data ownership. It enables multiple individuals and organizations to identify, authenticate, and authorize participants and organizations, enabling them to access services, data or systems across multiple networks, organizations, environments, and use cases. It empowers users and enables a personalized, self-service digital onboarding system so that users can self-authenticate without relying on a central administration function to process their information. Simultaneously, decentralized identity management ensures the user is authorized to perform actions subject to the system’s policies based on their attributes (role, department, organization, etc.) and/ or physical location. == Use cases == Agriculture – Farmers collect data on water use, soil temperature, moisture content and crop growth, augmented analytics can be used to make sense of this data and possibly identify insights that the user can then use to make business decisions. Smart Cities – Many cities across the United States, known as Smart Cities collect large amounts of data on a daily basis. Augmented analytics can be used to simplify this data in order to increase effectiveness in city management (transportation, natural disasters, etc.). Analytic Dashboards – Augmented analytics has the ability to take large data sets and create highly interactive and informative analytical dashboards that assist in many organizational decisions. Augmented Data Discovery – Using an augmented analytics process can assist organizations in automatically finding, visualizing and narrating potentially important data correlations and trends. Data Preparation – Augmented analytics platforms have the ability to take large amounts of data and organize and "clean" the data in order for it to be usable for future analyses. Business – Businesses collect large amounts of data, daily. Some examples of types of data collected in business operations include; sales data, consumer behavior data, distribution data. An augmented analytics platform provides access to analysis of this data, which could be used in making business decisions.
Art Recognition
Art Recognition is a Swiss technology company headquartered in Adliswil, within the Zurich metropolitan area, Switzerland. Art Recognition specializes in the application of artificial intelligence (AI) for art authentication and the detection of art forgeries. == Overview == Art Recognition was established in 2019 by Dr. Carina Popovici and Christiane Hoppe-Oehl. Art Recognition employs a combination of machine learning techniques, computer vision algorithms, and deep neural networks to assess the authenticity of artworks. The company's technology undergoes a process of data collection, dataset preparation, and training. === Academic partnerships and grants === Art Recognition has established a relationship with Innosuisse, a Swiss innovation agency, to expand its research and development initiatives. It has also formed a strategic collaboration with Nils Büttner, an art historian and professor at the State Academy of Fine Arts Stuttgart (ABK Stuttgart). === Notable developments === In May 2024, Art Recognition played a key role in identifying counterfeit artworks, including alleged Monets and Renoirs, being sold on eBay. Germann Auction in November 2024 became the first auction house to successfully conduct a sale of artwork authenticated entirely by artificial intelligence. As of January 2025, Art Recognition has appointed art crime expert and Pulitzer Prize finalist Noah Charney as an advisor. === Recognition and debates === The company was featured on the front page of The Wall Street Journal for its involvement in the authentication case of the Flaget Madonna, believed to have been partly painted by Raphael. A broadcast by the Swiss public television SRF covered how the algorithm can be used to detect art forgeries with high accuracy. The technology developed by Art Recognition has been recognized for its role in providing a technology-based art authentication solution, compared to traditional methods. == Controversial cases == Art Recognition's AI algorithm has been applied to several high-profile and controversial artworks, sparking significant interest and debate in the art world. Samson and Delilah at the National Gallery in London: The National Gallery's "Samson and Delilah", traditionally attributed to the artist Rubens, has also been examined using Art Recognition's AI, which has assessed the painting as non-authentic. De Brecy Tondo Madonna. A research team from Bradford University and the University of Nottingham initially attributed the painting to Raphael, employing an AI face recognition software, while the AI developed at Art Recognition returned a negative result. The Bradford group's AI was trained on 49 images, whereas Art Recognition employed a larger dataset of over 100 images. Lucian Freud Painting Controversy: Featured in The New Yorker, a painting attributed to Lucian Freud became a subject of dispute. Art Recognition's AI analysis played a big role in examining the painting's authenticity. Titian at Kunsthaus Zürich: A painting attributed to Titian, housed at Kunsthaus Zürich, has been a topic of debate among art experts. The application of Art Recognition's technology offered a new perspective. Following this debate, Kunsthaus Zürich has announced plans to initiate a comprehensive project aimed at resolving the authenticity questions surrounding the painting. Art Recognition has contributed to the authentication debate surrounding The Polish Rider, a painting traditionally attributed to Rembrandt but subject to scholarly debate.