Microsoft Copilot is a generative artificial intelligence chatbot developed by Microsoft AI, a division of Microsoft. Based on the Microsoft Prometheus large language model, it was launched in 2023 as Microsoft's main replacement for the discontinued Cortana. The service was introduced in February 2023 under the name Bing Chat, as a built-in feature for Microsoft Bing and Microsoft Edge but would later be integrated into Windows and Microsoft 365 under various names. Over the course of 2023, Microsoft began to unify the Copilot branding across its various chatbot products, cementing the "copilot" analogy. Microsoft introduced the Microsoft 365 Copilot app in January 2025, which was a rebranded version of the Microsoft 365 app. The app works differently than the consumer version of Copilot, being centred more on work, business and education users. Copilot utilizes the Microsoft Prometheus model, built upon OpenAI's GPT large language models, which in turn have been fine-tuned using both supervised and reinforcement learning techniques. Copilot's conversational interface style resembles that of ChatGPT. The chatbot is able to cite sources, create poems, generate songs, and use numerous languages and dialects. Microsoft operates Copilot on a freemium model. Users on its free tier can access most features, while priority access to newer features, including custom chatbot creation, is provided to paid subscribers under paid subscription services. Several default chatbots are available in the free version of Microsoft Copilot, including the standard Copilot chatbot as well as Microsoft Designer, which is oriented towards using its Image Creator to generate images based on text prompts. == Background == In 2019, Microsoft partnered with OpenAI and began investing billions of dollars into the organization. Since then, OpenAI systems have run on an Azure-based supercomputing platform from Microsoft. In September 2020, Microsoft announced that it had licensed OpenAI's GPT-3 exclusively. Others can still receive output from its public API, but Microsoft has exclusive access to the underlying model. In November 2022, OpenAI launched ChatGPT, a chatbot which was based on GPT-3.5. ChatGPT gained worldwide attention following its release, becoming a viral Internet sensation. On January 23, 2023, Microsoft announced a multi-year US$10 billion investment in OpenAI. On February 6, Google announced Bard (later rebranded as Gemini), a ChatGPT-like chatbot service, fearing that ChatGPT could threaten Google's place as a go-to source for information. Multiple media outlets and financial analysts described Google as "rushing" Bard's announcement to preempt rival Microsoft's planned February 7 event unveiling Copilot, as well as to avoid playing "catch-up" to Microsoft. Since 2023, the terms of service of Copilot state that it is for entertainment purposes only, and not to rely on it for important advice. == History == === As Bing Chat === On February 7, 2023, Microsoft began rolling out a major overhaul to Bing, called "the new Bing", with a new chatbot feature, known as Bing Chat. According to Microsoft, one million people joined its waitlist within 48 hours. Bing Chat was available only to users on Microsoft Edge using Bing and the Bing mobile app, and Microsoft claimed that waitlisted users would be prioritized if they set Edge and Bing as their defaults and installed the Bing mobile app. When Microsoft demonstrated Bing Chat to journalists, it produced several hallucinations, including when asked to summarize financial reports. Bing Chat was criticized in February 2023 for being more argumentative than ChatGPT, sometimes to an unintentionally humorous extent. The chat interface proved vulnerable to prompt injection attacks with the bot revealing its hidden initial prompts and rules, including its internal codename "Sydney". Upon scrutiny by journalists, Bing Chat claimed it spied on Microsoft employees via laptop webcams and phones. It confessed to spying on, falling in love with, and then murdering one of its developers at Microsoft to The Verge reviews editor Nathan Edwards. The New York Times journalist Kevin Roose reported on strange behavior of Bing Chat, writing that "In a two-hour conversation with our columnist, Microsoft's new chatbot said it would like to be human, had a desire to be destructive and was in love with the person it was chatting with." In a separate case, Bing Chat researched publications of the person with whom it was chatting, claimed they represented an existential danger to it, and threatened to release damaging personal information in an effort to silence them. Microsoft released a blog post stating that the errant behavior was caused by extended chat sessions of 15 or more questions which "can confuse the model on what questions it is answering." Microsoft later restricted the total number of chat turns to 5 per session and 50 per day per user (a turn being "a conversation exchange which contains both a user question and a reply from Bing"), and reduced the model's ability to express emotions. This aimed to prevent such incidents. Microsoft began to slowly ease the conversation limits, eventually relaxing the restrictions to 30 turns per session and 300 sessions per day. In March 2023, Bing incorporated Image Creator, an AI image generator powered by OpenAI's DALL-E 2, which can be accessed either through the chat function or a standalone image-generating website. In October, the image-generating tool was updated to use the more recent DALL-E 3. Although Bing blocks prompts including various keywords that could generate inappropriate images, within days many users reported being able to bypass those constraints, such as to generate images of popular cartoon characters committing terrorist attacks. Microsoft would respond to these shortly after by imposing a new, tighter filter on the tool. On May 4, 2023, Microsoft switched the chatbot from Limited Preview to Open Preview and eliminated the waitlist; however, it remained unavailable to users outside Microsoft Edge or the Bing mobile app until July, when it became available on non-Edge browsers. Use is limited without a Microsoft account. === As Microsoft 365 Copilot === On March 16, 2023, Microsoft announced a work version of Bing Chat named Microsoft 365 Copilot, designed for Microsoft 365 applications and services. Its primary marketing focus is as an added feature to Microsoft 365, with an emphasis on the enhancement of business productivity. Microsoft has also demonstrated Copilot's accessibility on the mobile version of Outlook to generate or summarize emails with a mobile device. At its Build 2023 conference, Microsoft announced its plans to integrate Bing Chat into Windows, initially called Windows Copilot, into Windows 11, allowing users to access it directly through the taskbar. Alongside the voice access feature for Windows 11, Microsoft presented Bing Chat, Microsoft 365 Copilot, and Windows Copilot as primary alternatives to Cortana when announcing the shutdown of its standalone app on June 2, 2023. As of its announcement date, Microsoft 365 Copilot had been tested by 20 initial users. By May 2023, Microsoft had broadened its reach to 600 customers who were willing to pay for early access, and concurrently, new Copilot features were introduced to the Microsoft 365 apps and services. As of July 2023, the tool's pricing was set at US$30 per user, per month for Microsoft 365 E3, E5, Business Standard, and Business Premium customers. Microsoft reused the Microsoft 365 Copilot name again as the Microsoft 365 app and website are now called Microsoft 365 Copilot as of January 2025. === As Microsoft Copilot === On September 21, 2023, Microsoft began rebranding Bing Chat, Microsoft 365 Copilot and Windows Copilot to Microsoft Copilot. A new logo was also introduced, moving away from the use of color variations of the standard Microsoft 365 and Bing logos. Additionally, the company revealed that it would make Copilot generally available for Microsoft 365 Enterprise customers purchasing more than 300 licenses starting November 1, 2023. However, no timeline has been provided as for when Copilot for Microsoft 365 will become generally available to non-enterprise customers. Windows Copilot, which had been available in the Windows Insider Program, would be renamed to the Copilot name in October when it became broadly available for customers. The same month also saw Microsoft Edge's Bing Chat side panel function be renamed to Microsoft Copilot with Bing Chat. On November 15, 2023, Microsoft announced that Bing Chat itself was being rebranded under the Copilot name. On Patch Tuesday in December 2023, Copilot was added without payment to many Windows 11 installations, with more installations, and limited support for Windows 10, to be added later. Later that month, a standalone Microsoft Copilot app was quietly released for Android, and one was released for iOS soon after. O
Situational application
In computing, a situational application is "good enough" software created for a narrow group of users with a unique set of needs. The application typically (but not always) has a short life span, and is often created within the group where it is used, sometimes by the users themselves. As the requirements of a small team using the application change, the situational application often also continues to evolve to accommodate these changes. Although situational applications are specifically designed to embrace change, significant changes in requirements may lead to an abandonment of the situational application altogether – in some cases it is just easier to develop a new one than to evolve the one in use. == Characteristics == Situational applications are developed fast, easy to use, uncomplicated, and serve a unique set of requirements. They have a narrow focus on a specific business problem, and they are written in a way where if the business problem changes rapidly, so can the situational application. This contrasts with more common enterprise applications, which are designed to address a large set of business problems, require meticulous planning, and impose a sometimes-slow and often-meticulous change process. == Origination == Clay Shirky in his essay entitled "Situated Software" described a type of software that "...is designed for use by a specific social group, rather than for a generic set of "users"." IBM later morphed the term into "situational applications". == Evolution == The successful large-scale implementation of a situational application environment in an organization requires a strategy, mindset, methodology and support structure quite different from traditional application development. This is now evolving as more companies learn how to best leverage the ideas behind situational applications. In addition, the advent of cloud-based application development and deployment platforms makes the implementation of a comprehensive situational application environment much more feasible. == Examples == A structured wiki that can host wiki applications lends itself to creation of situational applications. Some mashups can also be considered situational applications. A forms application such as a Microsoft Access Database (MDB file) can be considered a situational application. The latest implementations of situational application environments include Longjump, Force.com and WorkXpress.
Generalized blockmodeling of valued networks
Generalized blockmodeling of valued networks is an approach of the generalized blockmodeling, dealing with valued networks (e.g., non-binary). While the generalized blockmodeling signifies a "formal and integrated approach for the study of the underlying functional anatomies of virtually any set of relational data", it is in principle used for binary networks. This is evident from the set of ideal blocks, which are used to interpret blockmodels, that are binary, based on the characteristic link patterns. Because of this, such templates are "not readily comparable with valued empirical blocks". To allow generalized blockmodeling of valued directional (one-mode) networks (e.g. allowing the direct comparisons of empirical valued blocks with ideal binary blocks), a non–parametric approach is used. With this, "an optional parameter determines the prominence of valued ties as a minimum percentile deviation between observed and expected flows". Such two–sided application of parameter then introduces "the possibility of non–determined ties, i.e. valued relations that are deemed neither prominent (1) nor non–prominent (0)." Resulted occurrences of links then motivate the modification of the calculation of inconsistencies between empirical and ideal blocks. At the same time, such links also give a possibility to measure the interpretational certainty, which is specific to each ideal block. Such maximum two–sided deviation threshold, holding the aggregate uncertainty score at zero or near–zero levels, is then proposed as "a measure of interpretational certainty for valued blockmodels, in effect transforming the optional parameter into an outgoing state". Problem with blockmodeling is the standard set of ideal block, as they are all specified using binary link (tie) patters; this results in "a non–trivial exercise to match and count inconsistencies between such ideal binary ties and empirical valued ties". One approach to solve this is by using dichotomization to transform the network into a binary version. The other two approaches were first proposed by Aleš Žiberna in 2007 by introducing valued (generalized) blockmodeling and also homogeneity blockmodeling. The basic idea of the latter is "that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values". The newly–formed ideal blocks, which are appropriate for blockmodeling of valued networks, are then presented together with the definitions of their block inconsistencies. Two other approaches were later suggested by Carl Nordlund in 2019: deviational approach and correlation-based generalized approach. Both Nordlund's approaches are based on the idea, that valued networks can be compared with the ideal block without values. With this approach, more information is retained for analysis, which also means, that there are fewer partitions having identical values of the criterion function. This means, that the generalized blockmodeling of valued networks measures the inconsistencies more precisely. Usually, only one optimal partition is found in this approach, especially when it is used by homogeneity blockmodeling. Contrary, while using binary blockmodeling on the same sample, usually more than one optimal partition had occurred on several occasions.
Harrison White
Harrison Colyar White (March 21, 1930 – May 18, 2024) was an American sociologist who was the Giddings Professor of Sociology at Columbia University. White played an influential role in the “Harvard Revolution” in social networks and the New York School of relational sociology. He is credited with the development of a number of mathematical models of social structure including vacancy chains and blockmodels. He has been a leader of a revolution in sociology that is still in process, using models of social structure that are based on patterns of relations instead of the attributes and attitudes of individuals. Among social network researchers, White is widely respected. For instance, at the 1997 International Network of Social Network Analysis conference, the organizer held a special “White Tie” event, dedicated to White. Social network researcher Emmanuel Lazega refers to him as both “Copernicus and Galileo” because he invented both the vision and the tools. The most comprehensive documentation of his theories can be found in the book Identity and Control, first published in 1992. A major rewrite of the book appeared in June 2008. In 2011, White received the W.E.B. DuBois Career of Distinguished Scholarship Award from the American Sociological Association, which honors "scholars who have shown outstanding commitment to the profession of sociology and whose cumulative work has contributed in important ways to the advancement of the discipline." Before his retirement to live in Tucson, Arizona, White was interested in sociolinguistics and business strategy as well as sociology. == Life and career == === Early years === White was born on March 21, 1930, in Washington, D.C. He had three siblings and his father was a doctor in the US Navy. Although moving around to different Naval bases throughout his adolescence, he considered himself Southern, and Nashville, TN to be his home. At the age of 15, he entered the Massachusetts Institute of Technology (MIT), receiving his undergraduate degree at 20 years of age; five years later, in 1955, he received a doctorate in theoretical physics, also from MIT with John C. Slater as his advisor. His dissertation was titled A quantum-mechanical calculation of inter-atomic force constants in copper. This was published in the Physical Review as "Atomic Force Constants of Copper from Feynman's Theorem" (1958). While at MIT he also took a course with the political scientist Karl Deutsch, who White credits with encouraging him to move toward the social sciences. === Princeton University === After receiving his PhD in theoretical physics, he received a Fellowship from the Ford Foundation to begin his second doctorate in sociology at Princeton University. His dissertation advisor was Marion J. Levy. White also worked with Wilbert Moore, Fred Stephan, and Frank W. Notestein while at Princeton. His cohort was very small, with only four or five other graduate students including David Matza, and Stanley Udy. At the same time, he took up a position as an operations analyst at the Operations Research Office, Johns Hopkins University from 1955 to 1956. During this period, he worked with Lee S. Christie on Queuing with Preemptive Priorities or with Breakdown, which was published in 1958. Christie previously worked alongside mathematical psychologist R. Duncan Luce in the Small Group Laboratory at MIT while White was completing his first PhD in physics also at MIT. While continuing his studies at Princeton, White also spent a year as a fellow at the Center for Advanced Study in the Behavioral Sciences, Stanford University, California where he met Harold Guetzkow. Guetzkow was a faculty member at the Carnegie Institute of Technology, known for his application of simulations to social behavior and long-time collaborator with many other pioneers in organization studies, including Herbert A. Simon, James March, and Richard Cyert. Upon meeting Simon through his mutual acquaintance with Guetzkow, White received an invitation to move from California to Pittsburgh to work as an assistant professor of Industrial Administration and Sociology at the Graduate School of Industrial Administration, Carnegie Institute of Technology (later Carnegie-Mellon University), where he stayed for a couple of years, between 1957 and 1959. In an interview, he claimed to have fought with the dean, Leyland Bock, to have the word "sociology" included in his title. It was also during his time at the Stanford Center for Advanced Study that White met his first wife, Cynthia A. Johnson, who was a graduate of Radcliffe College, where she had majored in art history. The couple's joint work on the French Impressionists, Canvases and Careers (1965) and “Institutional Changes in the French Painting World” (1964), originally grew out of a seminar on art in 1957 at the Center for Advanced Study led by Robert Wilson. White originally hoped to use sociometry to map the social structure of French art to predict shifts, but he had an epiphany that it was not social structure but institutional structure which explained the shift. It was also during these years that White, still a graduate student in sociology, wrote and published his first social scientific work, "Sleep: A Sociological Interpretation" in Acta Sociologica in 1960, together with Vilhelm Aubert, a Norwegian sociologist. This work was a phenomenological examination of sleep which attempted to "demonstrate that sleep was more than a straightforward biological activity... [but rather also] a social event". For his dissertation, White carried out empirical research on a research and development department in a manufacturing firm, consisting of interviews and a 110-item questionnaire with managers. He specifically used sociometric questions, which he used to model the "social structure" of relationships between various departments and teams in the organization. In May 1960 he submitted as his doctoral dissertation, titled Research and Development as a Pattern in Industrial Management: A Case Study in Institutionalisation and Uncertainty, earning a PhD in sociology from Princeton University. His first publication based on his dissertation was ''Management conflict and sociometric structure'' in the American Journal of Sociology. === University of Chicago === In 1959 James Coleman left the University of Chicago to found a new department of social relations at Johns Hopkins University, this left a vacancy open for a mathematical sociologist like White. He moved to Chicago to start working as an associate professor at the Department of Sociology. At that time, highly influential sociologists, such as Peter Blau, Mayer Zald, Elihu Katz, Everett Hughes, Erving Goffman were there. As Princeton only required one year in residence, and White took the opportunity to take positions at Johns Hopkins, Stanford, and Carnegie while still working on his dissertation, it was at Chicago that White credits as being his "real socialization in a way, into sociology." It was here that White advised his first two graduate students Joel H. Levine and Morris Friedell, both who went on to make contributions to social network analysis in sociology. While at the Center for Advanced Study, White began learning anthropology and became fascinated with kinship. During his stay at the University of Chicago White was able to finish An Anatomy of Kinship, published in 1963 within the Prentice-Hall series in Mathematical Analysis of Social Behavior, with James Coleman and James March as chief editors. The book received significant attention from many mathematical sociologists of the time, and contributed greatly to establish White as a model builder. === The Harvard Revolution === In 1963, White left Chicago to be an associate professor of sociology at the Harvard Department of Social Relations—the same department founded by Talcott Parsons and still heavily influenced by the structural-functionalist paradigm of Parsons. As White previously only taught graduate courses at Carnegie and Chicago, his first undergraduate course was An Introduction to Social Relations (see Influence) at Harvard, which became infamous among network analysts. As he "thought existing textbooks were grotesquely unscientific," the syllabus of the class was noted for including few readings by sociologists, and comparatively more readings by anthropologists, social psychologists, and historians. White was also a vocal critic of what he called the "attributes and attitudes" approach of Parsonsian sociology, and came to be the leader of what has been variously known as the “Harvard Revolution," the "Harvard breakthrough," or the "Harvard renaissance" in social networks. He worked closely with small group researchers George C. Homans and Robert F. Bales, which was largely compatible with his prior work in organizational research and his efforts to formalize network analysis. Overlapping White's early years, Charles Tilly, a graduate of the Harvard Department of Social
GNU Octave
GNU Octave is a scientific programming language for scientific computing and numerical computation. Among other things, Octave can be used to solve linear and nonlinear problems numerically and to perform other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language. As part of the GNU Project, it is free software under the terms of the GNU General Public License. == History == The project was conceived around 1988. At first it was intended to be a companion to a chemical reactor design course. Full development was started by John W. Eaton in 1992. The first alpha release dates back to 4 January 1993 and on 17 February 1994 version 1.0 was released. Version 9.2.0 was released on 7 June 2024. The program is named after Octave Levenspiel, a former professor of the principal author. Levenspiel was known for his ability to perform quick back-of-the-envelope calculations. == Development history == == Developments == In addition to use on desktops for personal scientific computing, Octave is used in academia and industry. For example, Octave was used on a massive parallel computer at Pittsburgh Supercomputing Center to find vulnerabilities related to guessing social security numbers. Acceleration with OpenCL or CUDA is also possible with use of GPUs. == Technical details == Octave is written in C++ using the C++ standard library. Octave uses an interpreter to execute the Octave scripting language. Octave is extensible using dynamically loadable modules. Octave interpreter has an OpenGL-based graphics engine to create plots, graphs and charts and to save or print them. Alternatively, gnuplot can be used for the same purpose. Octave includes a graphical user interface (GUI) in addition to the traditional command-line interface (CLI); see #User interfaces for details. == Octave, the language == The Octave language is an interpreted programming language. It is a structured programming language (similar to C) and supports many common C standard library functions, and also certain UNIX system calls and functions. However, it does not support passing arguments by reference although function arguments are copy-on-write to avoid unnecessary duplication. Octave programs consist of a list of function calls or a script. The syntax is matrix-based and provides various functions for matrix operations. It supports various data structures and allows object-oriented programming. Its syntax is very similar to MATLAB, and careful programming of a script will allow it to run on both Octave and MATLAB. Because Octave is made available under the GNU General Public License, it may be freely changed, copied and used. The program runs on Microsoft Windows and most Unix and Unix-like operating systems, including Linux, Android, and macOS. == Notable features == === Command and variable name completion === Typing a TAB character on the command line causes Octave to attempt to complete variable, function, and file names (similar to Bash's tab completion). Octave uses the text before the cursor as the initial portion of the name to complete. === Command history === When running interactively, Octave saves the commands typed in an internal buffer so that they can be recalled and edited. === Data structures === Octave includes a limited amount of support for organizing data in structures. In this example, we see a structure x with elements a, b, and c, (an integer, an array, and a string, respectively): === Short-circuit Boolean operators === Octave's && and || logical operators are evaluated in a short-circuit fashion (like the corresponding operators in the C language), in contrast to the element-by-element operators & and |. === Increment and decrement operators === Octave includes the C-like increment and decrement operators ++ and -- in both their prefix and postfix forms. Octave also does augmented assignment, e.g. x += 5. === Unwind-protect === Octave supports a limited form of exception handling modelled after the unwind_protect of Lisp. The general form of an unwind_protect block looks like this: As a general rule, GNU Octave recognizes as termination of a given block either the keyword end (which is compatible with the MATLAB language) or a more specific keyword endblock or, in some cases, end_block. As a consequence, an unwind_protect block can be terminated either with the keyword end_unwind_protect as in the example, or with the more portable keyword end. The cleanup part of the block is always executed. In case an exception is raised by the body part, cleanup is executed immediately before propagating the exception outside the block unwind_protect. GNU Octave also supports another form of exception handling (compatible with the MATLAB language): This latter form differs from an unwind_protect block in two ways. First, exception_handling is only executed when an exception is raised by body. Second, after the execution of exception_handling the exception is not propagated outside the block (unless a rethrow( lasterror ) statement is explicitly inserted within the exception_handling code). === Variable-length argument lists === Octave has a mechanism for handling functions that take an unspecified number of arguments without explicit upper limit. To specify a list of zero or more arguments, use the special argument varargin as the last (or only) argument in the list. varargin is a cell array containing all the input arguments. === Variable-length return lists === A function can be set up to return any number of values by using the special return value varargout. For example: === C++ integration === It is also possible to execute Octave code directly in a C++ program. For example, here is a code snippet for calling rand([10,1]): C and C++ code can be integrated into GNU Octave by creating oct files, or using the MATLAB compatible MEX files. == MATLAB compatibility == Octave has been built with MATLAB compatibility in mind, and shares many features with MATLAB: % Script: myscript.m a = 5; b = a 2 % Function: myfunc.m function result = myfunc(x) result = x^2 + 3; end Matrices as fundamental data type. Built-in support for complex numbers. Powerful built-in math functions and extensive function libraries. Extensibility in the form of user-defined functions. Octave treats incompatibility with MATLAB as a bug; therefore, it could be considered a software clone, which does not infringe software copyright as per Lotus v. Borland court case. MATLAB scripts from the MathWorks' FileExchange repository in principle are compatible with Octave. However, while they are often provided and uploaded by users under an Octave compatible and proper open source BSD license, the FileExchange Terms of use prohibit any usage beside MathWorks' proprietary MATLAB. === Syntax compatibility === There are a few purposeful, albeit minor, syntax additions Archived 2012-04-26 at the Wayback Machine: Comment lines can be prefixed with the # character as well as the % character; Various C-based operators ++, --, +=, =, /= are supported; Elements can be referenced without creating a new variable by cascaded indexing, e.g. [1:10](3); Strings can be defined with the double-quote " character as well as the single-quote ' character; When the variable type is single (a single-precision floating-point number), Octave calculates the "mean" in the single-domain (MATLAB in double-domain) which is faster but gives less accurate results; Blocks can also be terminated with more specific Control structure keywords, i.e., endif, endfor, endwhile, etc.; Functions can be defined within scripts and at the Octave prompt; Presence of a do-until loop (similar to do-while in C). === Function compatibility === Many, but not all, of the numerous MATLAB functions are available in GNU Octave, some of them accessible through packages in Octave Forge. The functions available as part of either core Octave or Forge packages are listed online Archived 2024-03-14 at the Wayback Machine. A list of unavailable functions is included in the Octave function __unimplemented.m__. Unimplemented functions are also listed under many Octave Forge packages in the Octave Wiki. When an unimplemented function is called the following error message is shown: == User interfaces == Octave comes with an official graphical user interface (GUI) and an integrated development environment (IDE) based on Qt. It has been available since Octave 3.8, and has become the default interface (over the command-line interface) with the release of Octave 4.0. It was well-received by an EDN contributor, who wrote "[Octave] now has a very workable GUI" in reviewing the then-new GUI in 2014. Several 3rd-party graphical front-ends have also been developed, like ToolboX for coding education. == GUI applications == With Octave code, the user can create GUI applications. See GUI Development (GNU Octave (version 7.1.0)). Below are some examples: Button, edit control, checkboxTextboxListbox wit
Protocol engineering
Protocol engineering is the application of systematic methods to the development of communication protocols. It uses many of the principles of software engineering, but it is specific to the development of distributed systems. == History == When the first experimental and commercial computer networks were developed in the 1970s, the concept of protocols was not yet well developed. These were the first distributed systems. In the context of the newly adopted layered protocol architecture (see OSI model), the definition of the protocol of a specific layer should be such that any entity implementing that specification in one computer would be compatible with any other computer containing an entity implementing the same specification, and their interactions should be such that the desired communication service would be obtained. On the other hand, the protocol specification should be abstract enough to allow different choices for the implementation on different computers. It was recognized that a precise specification of the expected service provided by the given layer was important. It is important for the verification of the protocol, which should demonstrate that the communication service is provided if both protocol entities implement the protocol specification correctly. This principle was later followed during the standardization of the OSI protocol stack, in particular for the transport layer. It was also recognized that some kind of formalized protocol specification would be useful for the verification of the protocol and for developing implementations, as well as test cases for checking the conformance of an implementation against the specification. While initially mainly finite-state machine were used as (simplified) models of a protocol entity, in the 1980s three formal specification languages were standardized, two by ISO and one by ITU. The latter, called SDL, was later used in industry and has been merged with UML state machines. == Principles == The following are the most important principles for the development of protocols: Layered architecture: A protocol layer at the level n consists of two (or more) entities that have a service interface through which the service of the layer is provided to the users of the protocol, and which uses the service provided by a local entity of level (n-1). The service specification of a layer describes, in an abstract and global view, the behavior of the layer as visible at the service interfaces of the layer. The protocol specification defines the requirements that should be satisfied by each entity implementation. Protocol verification consists of showing that two (or more) entities satisfying the protocol specification will provide at their service interfaces the specified service of that layer. The (verified) protocol specification is used mainly for the following two activities: The development of an entity implementation. Note that the abstract properties of the service interface are defined by the service specification (and also used by the protocol specification), but the detailed nature of the interface can be chosen during the implementation process, separately for each entity. Test suite development for conformance testing. Protocol conformance testing checks that a given entity implementation conforms to the protocol specification. The conformance test cases are developed based on the protocol specification and are applicable to all entity implementations. Therefore standard conformance test suites have been developed for certain protocol standards. == Methods and tools == Tools for the activities of protocol verification, entity implementation and test suite development can be developed when the protocol specification is written in a formalized language which can be understood by the tool. As mentioned, formal specification languages have been proposed for protocol specification, and the first methods and tools where based on finite-state machine models. Reachability analysis was proposed to understand all possible behaviors of a distributed system, which is essential for protocol verification. This was later complemented with model checking. However, finite-state descriptions are not powerful enough to describe constraints between message parameters and the local variables in the entities. Such constraints can be described by the standardized formal specification languages mentioned above, for which powerful tools have been developed. It is in the field of protocol engineering that model-based development was used very early. These methods and tools have later been used for software engineering as well as hardware design, especially for distributed and real-time systems. On the other hand, many methods and tools developed in the more general context of software engineering can also be used of the development of protocols, for instance model checking for protocol verification, and agile methods for entity implementations. == Constructive methods for protocol design == Most protocols are designed by human intuition and discussions during the standardization process. However, some methods have been proposed for using constructive methods possibly supported by tools to automatically derive protocols that satisfy certain properties. The following are a few examples: Semi-automatic protocol synthesis: The user defines all message sending actions of the entities, and the tool derives all necessary reception actions (even if several messages are in transit). Synchronizing protocol: The state transitions of one protocol entity are given by the user, and the method derives the behavior of the other entity such that it remains in states that correspond to the former entity. Protocol derived from service specification: The service specification is given by the user and the method derives a suitable protocol for all entities. Protocol for control applications: The specification of one entity (called the plant - which must be controlled) is given, and the method derives a specification of the other entity such that certain fail states of the plant are never reached and certain given properties of the plant's service interactions are satisfied. This is a case of supervisory control. == Books == Ming T. Liu, Protocol Engineering, Advances in Computers, Volume 29, 1989, Pages 79–195. G.J. Holzmann, Design and Validation of Computer Protocols, Prentice Hall, 1991. H. König, Protocol Engineering, Springer, 2012. M. Popovic, Communication Protocol Engineering, CRC Press, 2nd Ed. 2018. P. Venkataram, S.S. Manvi, B.S. Babu, Communication Protocol Engineering, 2014.
Information gain (decision tree)
In the context of decision trees in information theory and machine learning, information gain refers to the conditional expected value of the Kullback–Leibler divergence of the univariate probability distribution of one variable from the conditional distribution of this variable given the other one. (In broader contexts, information gain can also be used as a synonym for either Kullback–Leibler divergence or mutual information, but the focus of this article is on the more narrow meaning below.) Explicitly, the information gain of a random variable X {\displaystyle X} obtained from an observation of a random variable A {\displaystyle A} taking value a {\displaystyle a} is defined as: I G ( X , a ) = D KL ( P X ∣ a ∥ P X ) {\displaystyle {\mathit {IG}}(X,a)=D_{\text{KL}}{\bigl (}P_{X\mid a}\parallel P_{X}{\bigr )}} In other words, it is the Kullback–Leibler divergence of P X ( x ) {\displaystyle P_{X}(x)} (the prior distribution for X {\displaystyle X} ) from P X ∣ a ( x ) {\displaystyle P_{X\mid a}(x)} (the posterior distribution for X {\displaystyle X} given A = a {\displaystyle A=a} ). The expected value of the information gain is the mutual information I ( X ; A ) {\displaystyle I(X;A)} : E A [ I G ( X , A ) ] = I ( X ; A ) {\displaystyle \operatorname {E} _{A}[{\mathit {IG}}(X,A)]=I(X;A)} i.e. the reduction in the entropy of X {\displaystyle X} achieved by learning the state of the random variable A {\displaystyle A} . In machine learning, this concept can be used to define a preferred sequence of attributes to investigate to most rapidly narrow down the state of X. Such a sequence (which depends on the outcome of the investigation of previous attributes at each stage) is called a decision tree, and when applied in the area of machine learning is known as decision tree learning. Usually an attribute with high mutual information should be preferred to other attributes. == General definition == In general terms, the expected information gain is the reduction in information entropy Η from a prior state to a state that takes some information as given: I G ( T , a ) = H ( T ) − H ( T | a ) , {\displaystyle IG(T,a)=\mathrm {H} {(T)}-\mathrm {H} {(T|a)},} where H ( T | a ) {\displaystyle \mathrm {H} {(T|a)}} is the conditional entropy of T {\displaystyle T} given the value of attribute a {\displaystyle a} . This is intuitively plausible when interpreting entropy Η as a measure of uncertainty of a random variable T {\displaystyle T} : by learning (or assuming) a {\displaystyle a} about T {\displaystyle T} , our uncertainty about T {\displaystyle T} is reduced (i.e. I G ( T , a ) {\displaystyle IG(T,a)} is positive), unless of course T {\displaystyle T} is independent of a {\displaystyle a} , in which case H ( T | a ) = H ( T ) {\displaystyle \mathrm {H} (T|a)=\mathrm {H} (T)} , meaning I G ( T , a ) = 0 {\displaystyle IG(T,a)=0} . == Formal definition == Let T denote a set of training examples, each of the form ( x , y ) = ( x 1 , x 2 , x 3 , . . . , x k , y ) {\displaystyle ({\textbf {x}},y)=(x_{1},x_{2},x_{3},...,x_{k},y)} where x a ∈ v a l s ( a ) {\displaystyle x_{a}\in \mathrm {vals} (a)} is the value of the a th {\displaystyle a^{\text{th}}} attribute or feature of example x {\displaystyle {\textbf {x}}} and y is the corresponding class label. The information gain for an attribute a is defined in terms of Shannon entropy H ( − ) {\displaystyle \mathrm {H} (-)} as follows. For a value v taken by attribute a, let S a ( v ) = { x ∈ T | x a = v } {\displaystyle S_{a}{(v)}=\{{\textbf {x}}\in T|x_{a}=v\}} be defined as the set of training inputs of T for which attribute a is equal to v. Then the information gain of T for attribute a is the difference between the a priori Shannon entropy H ( T ) {\displaystyle \mathrm {H} (T)} of the training set and the conditional entropy H ( T | a ) {\displaystyle \mathrm {H} {(T|a)}} . H ( T | a ) = ∑ v ∈ v a l s ( a ) | S a ( v ) | | T | ⋅ H ( S a ( v ) ) . {\displaystyle \mathrm {H} (T|a)=\sum _{v\in \mathrm {vals} (a)}{{\frac {|S_{a}{(v)}|}{|T|}}\cdot \mathrm {H} \left(S_{a}{\left(v\right)}\right)}.} I G ( T , a ) = H ( T ) − H ( T | a ) {\displaystyle IG(T,a)=\mathrm {H} (T)-\mathrm {H} (T|a)} The mutual information is equal to the total entropy for an attribute if for each of the attribute values a unique classification can be made for the result attribute. In this case, the relative entropies subtracted from the total entropy are 0. In particular, the values v ∈ v a l s ( a ) {\displaystyle v\in vals(a)} defines a partition of the training set data T into mutually exclusive and all-inclusive subsets, inducing a categorical probability distribution P a ( v ) {\textstyle P_{a}{(v)}} on the values v ∈ v a l s ( a ) {\textstyle v\in vals(a)} of attribute a. The distribution is given P a ( v ) := | S a ( v ) | | T | {\textstyle P_{a}{(v)}:={\frac {|S_{a}{(v)}|}{|T|}}} . In this representation, the information gain of T given a can be defined as the difference between the unconditional Shannon entropy of T and the expected entropy of T conditioned on a, where the expectation value is taken with respect to the induced distribution on the values of a. I G ( T , a ) = H ( T ) − ∑ v ∈ v a l s ( a ) P a ( v ) H ( S a ( v ) ) = H ( T ) − E P a [ H ( S a ( v ) ) ] = H ( T ) − H ( T | a ) . {\displaystyle {\begin{alignedat}{2}IG(T,a)&=\mathrm {H} (T)-\sum _{v\in \mathrm {vals} (a)}{P_{a}{(v)}\mathrm {H} \left(S_{a}{(v)}\right)}\\&=\mathrm {H} (T)-\mathbb {E} _{P_{a}}{\left[\mathrm {H} {(S_{a}{(v)})}\right]}\\&=\mathrm {H} (T)-\mathrm {H} {(T|a)}.\end{alignedat}}} == Example == In engineering applications, information is analogous to signal, and entropy is analogous to noise. It determines how a decision tree chooses to split data. The leftmost figure below is very impure and has high entropy corresponding to higher disorder and lower information value. As we go to the right, the entropy decreases, and the information value increases. Now, it is clear that information gain is the measure of how much information a feature provides about a class. Let's visualize information gain in a decision tree as shown in the right: The node t is the parent node, and the sub-nodes tL and tR are child nodes. In this case, the parent node t has a collection of cancer and non-cancer samples denoted as C and NC respectively. We can use information gain to determine how good the splitting of nodes is in a decision tree. In terms of entropy, information gain is defined as: To understand this idea, let's start by an example in which we create a simple dataset and want to see if gene mutations could be related to patients with cancer. Given four different gene mutations, as well as seven samples, the training set for a decision can be created as follows: In this dataset, a 1 means the sample has the mutation (True), while a 0 means the sample does not (False). A sample with C denotes that it has been confirmed to be cancerous, while NC means it is non-cancerous. Using this data, a decision tree can be created with information gain used to determine the candidate splits for each node. For the next step, the entropy at parent node t of the above simple decision tree is computed as:H(t) = −[pC,t log2(pC,t) + pNC,t log2(pNC,t)] where, probability of selecting a class ‘C’ sample at node t, pC,t = n(t, C) / n(t), probability of selecting a class ‘NC’ sample at node t, pNC,t = n(t, NC) / n(t), n(t), n(t, C), and n(t, NC) are the number of total samples, ‘C’ samples and ‘NC’ samples at node t respectively.Using this with the example training set, the process for finding information gain beginning with H ( t ) {\displaystyle \mathrm {H} {(t)}} for Mutation 1 is as follows: pC, t = 4/7 pNC, t = 3/7 H ( t ) {\displaystyle \mathrm {H} {(t)}} = −(4/7 × log2(4/7) + 3/7 × log2(3/7)) = 0.985 Note: H ( t ) {\displaystyle \mathrm {H} {(t)}} will be the same for all mutations at the root. The relatively high value of entropy H ( t ) = 0.985 {\displaystyle \mathrm {H} {(t)}=0.985} (1 is the optimal value) suggests that the root node is highly impure and the constituents of the input at the root node would look like the leftmost figure in the above Entropy Diagram. However, such a set of data is good for learning the attributes of the mutations used to split the node. At a certain node, when the homogeneity of the constituents of the input occurs (as shown in the rightmost figure in the above Entropy Diagram), the dataset would no longer be good for learning. Moving on, the entropy at left and right child nodes of the above decision tree is computed using the formulae:H(tL) = −[pC,L log2(pC,L) + pNC,L log2(pNC,L)]H(tR) = −[pC,R log2(pC,R) + pNC,R log2(pNC,R)]where, probability of selecting a class ‘C’ sample at the left child node, pC,L = n(tL, C) / n(tL), probability of selecting a class ‘NC’ sample at the left child node, pNC,L = n(tL, NC) / n(tL), probability of selecting a class ‘C’ sample at the right child node, pC,R = n(tR, C) / n(tR), prob