AI Coding Kiro

AI Coding Kiro — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Research software engineering

  Research software engineering is the application of software engineering practices, methods and techniques for research software, i.e. software that was made for and is mainly used within research projects. As usual for software engineering, this also includes knowledge of other (and in this case varying) research fields as well as open science that need to be incorporated into a software development process. The term was proposed in a research paper in 2010 in response to an empirical survey on tools used for software development in research projects. It started to be used in United Kingdom in 2012, when it was needed to define the type of software development needed in research. This focuses on reproducibility, reusability, and accuracy of data analysis and applications created for research. == Support == Various type of associations and organisations have been created around this role to support the creation of posts in universities and research institutes. In 2014 a Research Software Engineer Association was created in UK, which attracted 160 members in the first three months and which lead to the creation of the Society of Research Software Engineering in 2019. Other countries like the Netherlands, Germany, and the USA followed creating similar communities and there are similar efforts being pursued in Asia, Australia, Canada, New Zealand, the Nordic countries, and Belgium. In January 2021 the International Council of RSE Associations was introduced. UK counts over 40 universities and institutes with groups that provide access to software expertise to different areas of research. Additionally, the Engineering and Physical Sciences Research Council created a Research Software Engineer fellowship to promote this role and help the creation of RSE groups across UK, with calls in 2015, 2017, and 2020. The world first RSE conference took place in UK in September 2016 and it has been repeated annually (except for a gap in 2020) since. In 2019 the first national RSE conferences in Germany and the Netherlands were held, next editions were planned for 2020 and then cancelled. US-RSE held its first national conference in 2023. The Research Software Alliance was formed in 2019 to advance the global research software ecosystem by collaborating with decision makers and key influencers. The SORSE (A Series of Online Research Software Events) community was established in late‑2020 in response to the COVID-19 pandemic and ran its first online event in September 2020.

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  Data independence

  Data independence is the type of data transparency that matters for a centralized DBMS. It refers to the immunity of user applications to changes made in the definition and organization of data. Application programs should not, ideally, be exposed to details of data representation and storage. The DBMS provides an abstract view of the data that hides such details. There are two types of data independence: physical and logical data independence. The data independence and operation independence together gives the feature of data abstraction. There are two levels of data independence. == Logical data independence == The logical structure of the data is known as the 'schema definition'. In general, if a user application operates on a subset of the attributes of a relation, it should not be affected later when new attributes are added to the same relation. Logical data independence indicates that the conceptual schema can be changed without affecting the existing schemas. == Physical data independence == The physical structure of the data is referred to as "physical data description". Physical data independence deals with hiding the details of the storage structure from user applications. The application should not be involved with these issues since, conceptually, there is no difference in the operations carried out against the data. There are three types of data independence: Logical data independence: The ability to change the logical (conceptual) schema without changing the External schema (User View) is called logical data independence. For example, the addition or removal of new entities, attributes, or relationships to the conceptual schema or having to rewrite existing application programs. Physical data independence: The ability to change the physical schema without changing the logical schema is called physical data independence. For example, a change to the internal schema, such as using different file organization or storage structures, storage devices, or indexing strategy, should be possible without having to change the conceptual or external schemas. View level data independence: always independent no effect, because there doesn't exist any other level above view level. == Data independence == Data independence can be explained as follows: Each higher level of the data architecture is immune to changes of the next lower level of the architecture. The logical scheme stays unchanged even though the storage space or type of some data is changed for reasons of optimization or reorganization. In this, external schema does not change. In this, internal schema changes may be required due to some physical schema were reorganized here. Physical data independence is present in most databases and file environment in which hardware storage of encoding, exact location of data on disk, merging of records, so on this are hidden from user. == Data independence types == The ability to modify schema definition in one level without affecting schema of that definition in the next higher level is called data independence. There are two levels of data independence, they are Physical data independence and Logical data independence. Physical data independence is the ability to modify the physical schema without causing application programs to be rewritten. Modifications at the physical level are occasionally necessary to improve performance. It means we change the physical storage/level without affecting the conceptual or external view of the data. The new changes are absorbed by mapping techniques. Logical data independence is the ability to modify the logical schema without causing application programs to be rewritten. Modifications at the logical level are necessary whenever the logical structure of the database is altered (for example, when money-market accounts are added to banking system). Logical Data independence means if we add some new columns or remove some columns from table then the user view and programs should not change. For example: consider two users A & B. Both are selecting the fields "EmployeeNumber" and "EmployeeName". If user B adds a new column (e.g. salary) to his table, it will not affect the external view for user A, though the internal schema of the database has been changed for both users A & B. Logical data independence is more difficult to achieve than physical data independence, since application programs are heavily dependent on the logical structure of the data that they access.

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  Batch cryptography

  Batch cryptography is a field of cryptology focused on the design of cryptographic protocols that perform operations—such as encryption, decryption, key exchange, and authentication—on multiple inputs simultaneously, rather than processing each input individually. Batching cryptographic operations can significantly reduce the marginal cost of handling individual inputs—a principle that was first introduced by Amos Fiat in 1989.

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  Semi-Automatic Ground Environment

  The Semi-Automated Ground Environment (SAGE) was a system of large computers and associated networking equipment that coordinated data from many radar sites and processed it to produce a single unified image of the airspace over a wide area. SAGE directed and controlled the NORAD response to a possible Soviet air attack, operating in this role from the late 1950s into the 1980s. The processing power behind SAGE was supplied by the largest discrete component-based computer ever built, the AN/FSQ-7, manufactured by IBM. Each SAGE Direction Center (DC) housed an FSQ-7 which occupied an entire floor, approximately 22,000 square feet (2,000 m2) not including supporting equipment. The FSQ-7 was actually two computers, "A" side and "B" side. Computer processing was switched from "A" side to "B" side on a regular basis, allowing maintenance on the unused side. Information was fed to the DCs from a network of radar stations as well as readiness information from various defense sites. The computers, based on the raw radar data, developed "tracks" for the reported targets, and automatically calculated which defenses were within range. Operators used light guns to select targets on-screen for further information, select one of the available defenses, and issue commands to attack. These commands would then be automatically sent to the defense site via teleprinter. Connecting the various sites was an enormous network of telephones, modems and teleprinters. Later additions to the system allowed SAGE's tracking data to be sent directly to CIM-10 Bomarc missiles and some of the US Air Force's interceptor aircraft in-flight, directly updating their autopilots to maintain an intercept course without operator intervention. Each DC also forwarded data to a Combat Center (CC) for "supervision of the several sectors within the division" ("each combat center [had] the capability to coordinate defense for the whole nation"). SAGE became operational in the late 1950s and early 1960s at an estimated total cost between 8 and 12 billion dollars, four times the cost of the Manhattan Project. Throughout its development, there were continual concerns about its real ability to deal with large attacks, and the Operation Sky Shield tests showed that only about one-fourth of enemy bombers would have been intercepted. Nevertheless, SAGE was the backbone of NORAD's air defense system into the 1980s, by which time the tube-based FSQ-7s were increasingly costly to maintain and completely outdated. Today the same command and control task is carried out by microcomputers, based on the same basic underlying data. == Background == === Earlier systems === Just prior to World War II, Royal Air Force (RAF) tests with the new Chain Home (CH) radars had demonstrated that relaying information to the fighter aircraft directly from the radar sites was not feasible. The radars determined the map coordinates of the enemy, but could generally not see the fighters at the same time. This meant the fighters had to be able to determine where to fly to perform an interception but were often unaware of their own exact location and unable to calculate an interception while also flying their aircraft. The solution was to send all of the radar information to a central control station where operators collated the reports into single tracks, and then reported these tracks to the airbases, or sectors. The sectors used additional systems to track their own aircraft, plotting both on a single large map. Operators viewing the map could then see what direction their fighters would have to fly to approach their targets and relay that simply by telling them to fly along a certain heading or vector. This Dowding system was the first ground-controlled interception (GCI) system of large scale, covering the entirety of the UK. It proved enormously successful during the Battle of Britain, and is credited as being a key part of the RAF's success. The system was slow, often providing information that was up to five minutes out of date. Against propeller driven bombers flying at perhaps 225 miles per hour (362 km/h) this was not a serious concern, but it was clear the system would be of little use against jet-powered bombers flying at perhaps 600 miles per hour (970 km/h). The system was extremely expensive in manpower terms, requiring hundreds of telephone operators, plotters and trackers in addition to the radar operators. This was a serious drain on manpower, making it difficult to expand the network. The idea of using a computer to handle the task of taking reports and developing tracks had been explored beginning late in the war. By 1944, analog computers had been installed at the CH stations to automatically convert radar readings into map locations, eliminating two people. Meanwhile, the Royal Navy began experimenting with the Comprehensive Display System (CDS), another analog computer that took X and Y locations from a map and automatically generated tracks from repeated inputs. Similar systems began development with the Royal Canadian Navy, DATAR, and the US Navy, the Naval Tactical Data System (NTDS). A similar system was also specified for the Nike SAM project, specifically referring to a US version of CDS, coordinating the defense over a battle area so that multiple batteries did not fire on a single target. All of these systems were relatively small in geographic scale, generally tracking within a city-sized area. === Valley Committee === When the Soviet Union tested its first atomic bomb in August 1949, the topic of air defense of the US became important for the first time. A study group, the "Air Defense Systems Engineering Committee", was set up under the direction of Dr. George Valley to consider the problem and is known to history as the "Valley Committee". Their December report noted a key problem in air defense using ground-based radars. A bomber approaching a radar station would detect the signals from the radar long before the reflection off the bomber was strong enough to be detected by the station. The committee suggested that when this occurred, the bomber would descend to low altitude, thereby greatly limiting the radar horizon, allowing the bomber to fly past the station undetected. Although flying at low altitude greatly increased fuel consumption, the team calculated that the bomber would only need to do this for about 10% of its flight, making the fuel penalty acceptable. The only solution to this problem was to build a huge number of stations with overlapping coverage. At that point the problem became one of managing the information. Manual plotting was ruled out as too slow, and a computerized solution was the only possibility. To handle this task, the computer would need to be fed information directly, eliminating any manual translation by phone operators, and it would have to be able to analyze that information and automatically develop tracks. A system tasked with defending cities against the predicted future Soviet bomber fleet would have to be dramatically more powerful than the models used in the NTDS or DATAR. The Committee then had to consider whether or not such a computer was possible. The Valley Committee was introduced to Jerome Wiesner, associate director of the Research Laboratory of Electronics at MIT. Wiesner noted that the Servomechanisms Laboratory had already begun development of a machine that might be fast enough. This was the Whirlwind I, originally developed for the Office of Naval Research as a general purpose flight simulator that could simulate any current or future aircraft by changing its software. Wiesner introduced the Valley Committee to Whirlwind's project lead, Jay Forrester, who convinced him that Whirlwind was sufficiently capable. In September 1950, an early microwave early-warning radar system at Hanscom Field was connected to Whirlwind using a custom interface developed by Forrester's team. An aircraft was flown past the site, and the system digitized the radar information and successfully sent it to Whirlwind. With this demonstration, the technical concept was proven. Forrester was invited to join the committee. === Project Charles === With this successful demonstration, Louis Ridenour, chief scientist of the Air Force, wrote a memo stating "It is now apparent that the experimental work necessary to develop, test, and evaluate the systems proposals made by ADSEC will require a substantial amount of laboratory and field effort." Ridenour approached MIT President James Killian with the aim of beginning a development lab similar to the war-era Radiation Laboratory that made enormous progress in radar technology. Killian was initially uninterested, desiring to return the school to its peacetime civilian charter. Ridenour eventually convinced Killian the idea was sound by describing the way the lab would lead to the development of a local electronics industry based on the needs of the lab and the students who would leave the lab to start their

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  Edits (app)

  Edits is an American photo and short form video editing software service owned by Meta Platforms. It allows users to create videos and edit them by using features like green screens, and AI animation, and also provides real-time statistics to Instagram creators to track their accounts. Accounts directly from Instagram can be imported, and videos can be exported vice-versa. It is available solely on iOS and Android. On Apple, it supports over 32 different languages, including French, Spanish, and Chinese. It has been noted by critics as a direct competitor for apps like CapCut, owned by Chinese brand ByteDance. The Instagram head, Adam Mosseri, also acknowledged these similarities. Launched on April 22 for both iOS and Android. It received over 5M+ users on Apple and Android combined in its first 4 days since its launch. == History == On January 19, 2025, following the ban of all ByteDance Apps from the Google Play Store, and App Store, Instagram head Adam Mosseri announced on Threads that they would be launching the app in February for iOS, followed by an Android counterpart. He said the app is working with select people to test its features. In a separate post, he emphasized that the app is "more for creators than casual video makers". == Features == Edits contains many similar features to other competition of video editors like KineMaster, Inshot, and CapCut. When creating a video, users have the option to export in resolution of HD, 4K, and 2K, along with having HDR and SDR support. Like many traditional video editing software, it includes a timeline, and basic undo-redo buttons. On the bottom bar, 7 tabs for editing exist, namely the Split, Volume, Adjust, Speed, Delete, Filters, Green Screen, Voice FX, Extract Audio, Mirror, Slip, Replace and Duplicate bars. Basic features, like splitting, and adjusting speed and volume of clips are present, along with more advanced Green Screens, and AI features. Being a mobile video editor app, Edits also has drag-and-drop features to ease customer usage. Users have the ability to record videos directly within the app. This feature allows users to create content without needing extra software or devices. They can choose from several focal lengths, which affect how close or wide the shot appears. The app also supports different frame rates. Users have the ability to record videos directly within the app. This feature allows users to create content without needing extra software or devices. Once users are done filming your clips, they can simply transfer them into a project to start editing immediately. Upcoming features for the app include Keyframes, AI-powered modification, Collaboration, and Enhanced creativity. == Reception == Since its release, it received over 5 million downloads in 4 days. Critically, the app received great rankings from many. From users, the app received an average of 4.45 stars over Google Play Store and App Store in the first few days, with Google Play Store receiving the least stars. As in reviews, it was received mixed by the public. Many people praised the smoothness and intuivity of the app. "The app is more than just a basic editor, offering a full suite of creative tools, including a dedicated tab for inspiration and trending audio, as well as a tab for managing drafts," said a blogger. Some users were disappointed with the range of editing tools, some users have noted that it could benefit from more transition options between clips. Some even reported crashing between clips.

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  Data steward

  A data steward is an oversight or data governance role within an organization, and is responsible for ensuring the quality and fitness for purpose of the organization's data assets, including the metadata for those data assets. A data steward may share some responsibilities with a data custodian, such as the awareness, accessibility, release, appropriate use, security and management of data. A data steward would also participate in the development and implementation of data assets. A data steward may seek to improve the quality and fitness for purpose of other data assets their organization depends upon but is not responsible for. Data stewards have a specialist role that utilizes an organization's data governance processes, policies, guidelines and responsibilities for administering an organizations' entire data in compliance with policy and/or regulatory obligations (e.g., GDPR, HIPAA). The overall objective of a data steward is the data quality of the data assets, datasets, data records and data elements. This includes documenting metainformation for the data, such as definitions, related rules/governance, physical manifestation, and related data models (most of these properties being specific to an attribute/concept relationship), identifying owners/custodian's various responsibilities, relations insight pertaining to attribute quality, aiding with project requirement data facilitation and documentation of capture rules. Data stewards begin the stewarding process with the identification of the data assets and elements which they will steward, with the ultimate result being standards, controls and data entry. The steward works closely with business glossary standards analysts (for standards), with data architect/modelers (for standards), with DQ analysts (for controls) and with operations team members (good-quality data going in per business rules) while entering data. Data stewardship roles are common when organizations attempt to exchange data precisely and consistently between computer systems and to reuse data-related resources. Master data management often makes references to the need for data stewardship for its implementation to succeed. Data stewardship must have precise purpose, fit for purpose or fitness. == Data steward responsibilities == A data steward ensures that each assigned data element: Has clear and unambiguous data element definition Does not conflict with other data elements in the metadata registry (removes duplicates, overlap etc.) Has clear enumerated value definitions if it is of type Code Is still being used (remove unused data elements) Is being used consistently in various computer systems Is being used, fit for purpose = Data Fitness Has adequate documentation on appropriate usage and notes Documents the origin and sources of authority on each metadata element Is protected against unauthorised access or change Responsibilities of data stewards vary between different organisations and institutions. For example, at Delft University of Technology, data stewards are perceived as the first contact point for any questions related to research data. They also have subject-specific background allowing them to easily connect with researchers and to contextualise data management problems to take into account disciplinary practices. == Types of data stewards == Depending on the set of data stewardship responsibilities assigned to an individual, there are 4 types (or dimensions of responsibility) of data stewards typically found within an organization: Data object data steward - responsible for managing reference data and attributes of one business data entity Business data steward - responsible for managing critical data, both reference and transactional, created or used by one business function. The data steward may also serve as a liaison between the organization's data users and technical teams, helping to bridge the gap between business needs and technical requirements. They may also play a role in educating others within the organization about best practices for data management, and advocating for data-driven decision-making. Process data steward - responsible for managing data across one business process System data steward - responsible for managing data for at least one IT system == Benefits of data stewardship == Systematic data stewardship can foster: Faster analysis Consistent use of data management resources Easy mapping of data between computer systems and exchange documents Lower costs associated with migration to (for example) service-oriented architecture (SOA) Mitigation of data risk Better control of dangers associated with privacy, legal, errors, etc. Assignment of each data element to a person sometimes seems like an unimportant process. But multiple groups have found that users have greater trust and usage rates in systems where they can contact a person with questions on each data element. == Examples == Delft University of Technology (TU Delft) offers an example of data stewardship implementation at a research institution. In 2017 the Data Stewardship Project was initiated at TU Delft to address research data management needs in a disciplinary manner across the whole campus. Dedicated data stewards with subject-specific background were appointed at every TU Delft faculty to support researchers with data management questions and to act as a linking point with the other institutional support services. The project is coordinated centrally by TU Delft Library, and it has its own website, blog and a YouTube channel. The [1]EPA metadata registry furnishes an example of data stewardship. Note that each data element therein has a "POC" (point of contact). In 2023, ETH Zurich launched the Data Stewardship Network (DSN) to facilitate collaboration among employees engaged in data management, analysis, and code development across research groups. The DSN serves as a platform for networking and knowledge exchange, aiming to professionalize the role of data stewards who support research data management and reproducible workflows. Established by the team for Research Data Management and Digital Curation at the ETH Library, the DSN collaborates with Scientific IT Services to provide expertise in areas such as storage infrastructure and reproducible workflows. == Data stewardship applications == Information stewardship applications are business solutions used by business users acting in the role of information steward (interpreting and enforcing information governance policy, for example). These developing solutions represent, for the most part, an amalgam of a number of disparate, previously IT-centric tools already on the market, but are organized and presented in such a way that information stewards (a business role) can support the work of information policy enforcement as part of their normal, business-centric, day-to-day work in a range of use cases. The initial push for the formation of this new category of packaged software came from operational use cases — that is, use of business data in and between transactional and operational business applications. This is where most of the master data management efforts are undertaken in organizations. However, there is also now a faster-growing interest in the new data lake arena for more analytical use cases.

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  Master/Session

  In cryptography, Master/Session is a key management scheme in which a pre-shared Key Encrypting Key (called the "Master" key) is used to encrypt a randomly generated and insecurely communicated Working Key (called the "Session" key). The Working Key is then used for encrypting the data to be exchanged. Its advantage is simplicity, but it suffers the disadvantage of having to communicate the pre-shared Key Exchange Key, which can be difficult to update in the event of compromise. The Master/Session technique was created in the days before asymmetric techniques, such as Diffie-Hellman, were invented. This technique still finds widespread use in the financial industry, and is routinely used between corporate parties such as issuers, acquirers, switches. Its use in device communications (such as PIN pads), however, is in decline given the advantages of techniques such as DUKPT.

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  Control break

  In computer programming, a control break is a change in the value of one of the keys on which a file is sorted, which requires some extra processing. For example, with an input file sorted by post code, the number of items found in each postal district might need to be printed on a report, and a heading shown for the next district. Quite often there is a hierarchy of nested control breaks in a program, such as streets within districts within areas, with the need for a grand total at the end. Structured programming techniques have been developed to ensure correct processing of control breaks in languages such as COBOL and to ensure that conditions such as empty input files and sequence errors are handled properly. With fourth-generation languages such as SQL, the programming language should handle most of the details of control breaks automatically.

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  Pandemonium architecture

  Pandemonium architecture is a theory in cognitive science that describes how visual images are processed by the brain. It has applications in artificial intelligence and pattern recognition. The theory was introduced by the artificial intelligence pioneer Oliver Selfridge in his 1959 paper "Pandemonium - A Paradigm for Learning". It describes the process of object recognition as the exchange of signals within a hierarchical system of detection and association, the elements of which Selfridge metaphorically termed "demons". This model is now recognized as the basis of visual perception in cognitive science. Pandemonium architecture arose in response to the inability of template matching theories to offer a biologically plausible explanation of the image constancy phenomenon. Contemporary researchers praise this architecture for its elegancy and creativity; that the idea of having multiple independent systems (e.g., feature detectors) working in parallel to address the image constancy phenomena of pattern recognition is powerful yet simple. The basic idea of the pandemonium architecture is that a pattern is first perceived in its parts before the "whole". Pandemonium architecture was one of the first computational models in pattern recognition. Although not perfect, the pandemonium architecture influenced the development of modern connectionist, artificial intelligence, and word recognition models. == History == Most research in perception has been focused on the visual system, investigating the mechanisms of how we see and understand objects. A critical function of our visual system is its ability to recognize patterns, but the mechanism by which this is achieved is unclear. The earliest theory that attempted to explain how we recognize patterns is the template matching model. According to this model, we compare all external stimuli against an internal mental representation. If there is "sufficient" overlap between the perceived stimulus and the internal representation, we will "recognize" the stimulus. Although some machines follow a template matching model (e.g., bank machines verifying signatures and accounting numbers), the theory is critically flawed in explaining the phenomena of image constancy: we can easily recognize a stimulus regardless of the changes in its form of presentation (e.g., T and T are both easily recognized as the letter T). It is highly unlikely that we have a stored template for all of the variations of every single pattern. As a result of the biological plausibility criticism of the template matching model, feature detection models began to rise. In a feature detection model, the image is first perceived in its basic individual elements before it is recognized as a whole object. For example, when we are presented with the letter A, we would first see a short horizontal line and two slanted long diagonal lines. Then we would combine the features to complete the perception of A. Each unique pattern consists of different combination of features, which means those that are formed with the same features will generate the same recognition. That is, regardless of how we rotate the letter A, is still perceived as the letter A. It is easy for this sort of architecture to account for the image constancy phenomena because you only need to "match" at the basic featural level, which is presumed to be limited and finite, thus biologically plausible. The best known feature detection model is called the pandemonium architecture. == Pandemonium architecture == The pandemonium architecture was originally developed by Oliver Selfridge in the late 1950s. The architecture is composed of different groups of "demons" working independently to process the visual stimulus. Each group of demons is assigned to a specific stage in recognition, and within each group, the demons work in parallel. There are four major groups of demons in the original architecture. The concept of feature demons, that there are specific neurons dedicated to perform specialized processing is supported by research in neuroscience. Hubel and Wiesel found there were specific cells in a cat's brain that responded to specific lengths and orientations of a line. Similar findings were discovered in frogs, octopuses and a variety of other animals. Octopuses were discovered to be only sensitive to verticality of lines, whereas frogs demonstrated a wider range of sensitivity. These animal experiments demonstrate that feature detectors seem to be a very primitive development. That is, it did not result from the higher cognitive development of humans. Not surprisingly, there is also evidence that the human brain possesses these elementary feature detectors as well. Moreover, this architecture is capable of learning, similar to a back-propagation styled neural network. The weight between the cognitive and feature demons can be adjusted in proportion to the difference between the correct pattern and the activation from the cognitive demons. To continue with our previous example, when we first learned the letter R, we know is composed of a curved, long straight, and a short angled line. Thus when we perceive those features, we perceive R. However, the letter P consists of very similar features, so during the beginning stages of learning, it is likely for this architecture to mistakenly identify R as P. But through constant exposure of confirming R's features to be identified as R, the weights of R's features to P are adjusted so the P response becomes inhibited (e.g., learning to inhibit the P response when a short angled line is detected). In principle, a pandemonium architecture can recognize any pattern. As mentioned earlier, this architecture makes error predictions based on the amount of overlapping features. Such as, the most likely error for R should be P. Thus, in order to show this architecture represents the human pattern recognition system we must put these predictions into test. Researchers have constructed scenarios where various letters are presented in situations that make them difficult to identify; then types of errors were observed, which was used to generate confusion matrices: where all of the errors for each letter are recorded. Generally, the results from these experiments matched the error predictions from the pandemonium architecture. Also as a result of these experiments, some researchers have proposed models that attempted to list all of the basic features in the Roman alphabet. == Criticism == A major criticism of the pandemonium architecture is that it adopts a completely bottom-up processing: recognition is entirely driven by the physical characteristics of the targeted stimulus. This means that it is unable to account for any top-down processing effects, such as context effects (e.g., pareidolia), where contextual cues can facilitate (e.g., word superiority effect: it is relatively easier to identify a letter when it is part of a word than in isolation) processing. However, this is not a fatal criticism to the overall architecture, because is relatively easy to add a group of contextual demons to work along with the cognitive demons to account for these context effects. Although the pandemonium architecture is built on the fact that it can account for the image constancy phenomena, some researchers have argued otherwise; and pointed out that the pandemonium architecture might share the same flaws from the template matching models. For example, the letter H is composed of 2 long vertical lines and a short horizontal line; but if we rotate the H 90 degrees in either direction, it is now composed of 2 long horizontal lines and a short vertical line. In order to recognize the rotated H as H, we would need a rotated H cognitive demon. Thus we might end up with a system that requires a large number of cognitive demons in order to produce accurate recognition, which would lead to the same biological plausibility criticism of the template matching models. However, it is rather difficult to judge the validity of this criticism because the pandemonium architecture does not specify how and what features are extracted from incoming sensory information, it simply outlines the possible stages of pattern recognition. But of course that raises its own questions, to which it is almost impossible to criticize such a model if it does not include specific parameters. Also, the theory appears to be rather incomplete without defining how and what features are extracted, which proves to be especially problematic with complex patterns (e.g., extracting the weight and features of a dog). Some researchers have also pointed out that the evidence supporting the pandemonium architecture has been very narrow in its methodology. Majority of the research that supports this architecture has often referred to its ability to recognize simple schematic drawings that are selected from a small finite set (e.g., letters in the Roman alphabet). Evidence from these types of exper

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  Data Transformation Services

  Data Transformation Services (DTS) is a Microsoft database tool with a set of objects and utilities to allow the automation of extract, transform and load operations to or from a database. The objects are DTS packages and their components, and the utilities are called DTS tools. DTS was included with earlier versions of Microsoft SQL Server, and was almost always used with SQL Server databases, although it could be used independently with other databases. DTS allows data to be transformed and loaded from heterogeneous sources using OLE DB, ODBC, or text-only files, into any supported database. DTS can also allow automation of data import or transformation on a scheduled basis, and can perform additional functions such as FTPing files and executing external programs. In addition, DTS provides an alternative method of version control and backup for packages when used in conjunction with a version control system, such as Microsoft Visual SourceSafe. DTS has been superseded by SQL Server Integration Services in later releases of Microsoft SQL Server though there was some backwards compatibility and ability to run DTS packages in the new SSIS for a time. == History == In SQL Server versions 6.5 and earlier, database administrators (DBAs) used SQL Server Transfer Manager and Bulk Copy Program, included with SQL Server, to transfer data. These tools had significant shortcomings, and many DBAs used third-party tools such as Pervasive Data Integrator to transfer data more flexibly and easily. With the release of SQL Server 7 in 1998, "Data Transformation Services" was packaged with it to replace all these tools. The concept, design, and implementation of the Data Transformation Services was led by Stewart P. MacLeod (SQL Server Development Group Program Manager), Vij Rajarajan (SQL Server Lead Developer), and Ted Hart (SQL Server Lead Developer). The goal was to make it easier to import, export, and transform heterogeneous data and simplify the creation of data warehouses from operational data sources. SQL Server 2000 expanded DTS functionality in several ways. It introduced new types of tasks, including the ability to FTP files, move databases or database components, and add messages into Microsoft Message Queue. DTS packages can be saved as a Visual Basic file in SQL Server 2000, and this can be expanded to save into any COM-compliant language. Microsoft also integrated packages into Windows 2000 security and made DTS tools more user-friendly; tasks can accept input and output parameters. DTS comes with all editions of SQL Server 7 and 2000, but was superseded by SQL Server Integration Services in the Microsoft SQL Server 2005 release in 2005. == DTS packages == The DTS package is the fundamental logical component of DTS; every DTS object is a child component of the package. Packages are used whenever one modifies data using DTS. All the metadata about the data transformation is contained within the package. Packages can be saved directly in a SQL Server, or can be saved in the Microsoft Repository or in COM files. SQL Server 2000 also allows a programmer to save packages in a Visual Basic or other language file (when stored to a VB file, the package is actually scripted—that is, a VB script is executed to dynamically create the package objects and its component objects). A package can contain any number of connection objects, but does not have to contain any. These allow the package to read data from any OLE DB-compliant data source, and can be expanded to handle other sorts of data. The functionality of a package is organized into tasks and steps. A DTS Task is a discrete set of functionalities executed as a single step in a DTS package. Each task defines a work item to be performed as part of the data movement and data transformation process or as a job to be executed. Data Transformation Services supplies a number of tasks that are part of the DTS object model and that can be accessed graphically through the DTS Designer or accessed programmatically. These tasks, which can be configured individually, cover a wide variety of data copying, data transformation and notification situations. For example, the following types of tasks represent some actions that you can perform by using DTS: executing a single SQL statement, sending an email, and transferring a file with FTP. A step within a DTS package describes the order in which tasks are run and the precedence constraints that describe what to do in the case damage or of failure. These steps can be executed sequentially or in parallel. Packages can also contain global variables which can be used throughout the package. SQL Server 2000 allows input and output parameters for tasks, greatly expanding the usefulness of global variables. DTS packages can be edited, password protected, scheduled for execution, and retrieved by version. == DTS tools == DTS tools packaged with SQL Server include the DTS wizards, DTS Designer, and DTS Programming Interfaces. === DTS wizards === The DTS wizards can be used to perform simple or common DTS tasks. These include the Import/Export Wizard and the Copy of Database Wizard. They provide the simplest method of copying data between OLE DB data sources. There is a great deal of functionality that is not available by merely using a wizard. However, a package created with a wizard can be saved and later altered with one of the other DTS tools. A Create Publishing Wizard is also available to schedule packages to run at certain times. This only works if SQL Server Agent is running; otherwise the package will be scheduled, but will not be executed. === DTS Designer === The DTS Designer is a graphical tool used to build complex DTS Packages with workflows and event-driven logic. DTS Designer can also be used to edit and customize DTS Packages created with the DTS wizard. Each connection and task in DTS Designer is shown with a specific icon. These icons are joined with precedence constraints, which specify the order and requirements for tasks to be run. One task may run, for instance, only if another task succeeds (or fails). Other tasks may run concurrently. The DTS Designer has been criticized for having unusual quirks and limitations, such as the inability to visually copy and paste multiple tasks at one time. Many of these shortcomings have been overcome in SQL Server Integration Services, DTS's successor. === DTS Query Designer === A graphical tool used to build queries in DTS. === DTS Run Utility === DTS Packages can be run from the command line using the DTSRUN Utility. The utility is invoked using the following syntax: dtsrun /S server_name[\instance_name] { {/[~]U user_name [/[~]P password]} | /E } ] { {/[~]N package_name } | {/[~]G package_guid_string} | {/[~]V package_version_guid_string} } [/[~]M package_password] [/[~]F filename] [/[~]R repository_database_name] [/A global_variable_name:typeid=value] [/L log_file_name] [/W NT_event_log_completion_status] [/Z] [/!X] [/!D] [/!Y] [/!C] ] When passing in parameters which are mapped to Global Variables, you are required to include the typeid. This is rather difficult to find on the Microsoft site. Below are the TypeIds used in passing in these values.

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  Data integration

  Data integration is the process of combining, sharing, or synchronizing data from multiple sources to provide users with a unified view. There are a wide range of possible applications for data integration, from commercial (such as when a business merges multiple databases) to scientific (combining research data from different bioinformatics repositories). The decision to integrate data tends to arise when the volume, complexity (that is, big data) and need to share existing data explodes. It has become the focus of extensive theoretical work, and numerous open problems remain unsolved. Data integration encourages collaboration between internal as well as external users. The data being integrated must be received from a heterogeneous database system and transformed to a single coherent data store that provides synchronous data across a network of files for clients. A common use of data integration is in data mining when analyzing and extracting information from existing databases that can be useful for Business information. == History == Issues with combining heterogeneous data sources, often referred to as information silos, under a single query interface have existed for some time. In the early 1980s, computer scientists began designing systems for interoperability of heterogeneous databases. The first data integration system driven by structured metadata was designed in 1991 at the University of Minnesota for the Integrated Public Use Microdata Series (IPUMS). IPUMS used a data warehousing approach, which extracts, transforms, and loads data from heterogeneous sources into a unique view schema so data from different sources become compatible. By making thousands of population databases interoperable, IPUMS demonstrated the feasibility of large-scale data integration. The data warehouse approach offers a tightly coupled architecture because the data are already physically reconciled in a single queryable repository, so it usually takes little time to resolve queries. The data warehouse approach is less feasible for data sets that are frequently updated, requiring the extract, transform, load (ETL) process to be continuously re-executed for synchronization. Difficulties also arise in constructing data warehouses when one has only a query interface to summary data sources and no access to the full data. This problem frequently emerges when integrating several commercial query services like travel or classified advertisement web applications. A trend began in 2009 favoring the loose coupling of data and providing a unified query-interface to access real time data over a mediated schema (see Figure 2), which allows information to be retrieved directly from original databases. This is consistent with the SOA approach popular in that era. This approach relies on mappings between the mediated schema and the schema of original sources, and translating a query into decomposed queries to match the schema of the original databases. Such mappings can be specified in two ways: as a mapping from entities in the mediated schema to entities in the original sources (the "Global-as-View" (GAV) approach), or as a mapping from entities in the original sources to the mediated schema (the "Local-as-View" (LAV) approach). The latter approach requires more sophisticated inferences to resolve a query on the mediated schema, but makes it easier to add new data sources to a (stable) mediated schema. As of 2010, some of the work in data integration research concerns the semantic integration problem. This problem addresses not the structuring of the architecture of the integration, but how to resolve semantic conflicts between heterogeneous data sources. For example, if two companies merge their databases, certain concepts and definitions in their respective schemas like "earnings" inevitably have different meanings. In one database it may mean profits in dollars (a floating-point number), while in the other it might represent the number of sales (an integer). A common strategy for the resolution of such problems involves the use of ontologies which explicitly define schema terms and thus help to resolve semantic conflicts. This approach represents ontology-based data integration. On the other hand, the problem of combining research results from different bioinformatics repositories requires bench-marking of the similarities, computed from different data sources, on a single criterion such as positive predictive value. This enables the data sources to be directly comparable and can be integrated even when the natures of experiments are distinct. As of 2011, it was determined that current data modeling methods were imparting data isolation into every data architecture in the form of islands of disparate data and information silos. This data isolation is an unintended artifact of the data modeling methodology that results in the development of disparate data models. Disparate data models, when instantiated as databases, form disparate databases. Enhanced data model methodologies have been developed to eliminate the data isolation artifact and to promote the development of integrated data models. One enhanced data modeling method recasts data models by augmenting them with structural metadata in the form of standardized data entities. As a result of recasting multiple data models, the set of recast data models will now share one or more commonality relationships that relate the structural metadata now common to these data models. Commonality relationships are a peer-to-peer type of entity relationships that relate the standardized data entities of multiple data models. Multiple data models that contain the same standard data entity may participate in the same commonality relationship. When integrated data models are instantiated as databases and are properly populated from a common set of master data, then these databases are integrated. Since 2011, data hub approaches have been of greater interest than fully structured (typically relational) Enterprise Data Warehouses. Since 2013, data lake approaches have risen to the level of Data Hubs. (See all three search terms popularity on Google Trends.) These approaches combine unstructured or varied data into one location, but do not necessarily require an (often complex) master relational schema to structure and define all data in the Hub. In recent times, as the number of applications being used have increased many fold and application to application integration have become critical and this has given rise to [Unified APIs] that help application developers integrate their apps with other apps and more recently with [MCP - Model Context Protocol] taking it a step further for AI Agents. Data integration plays a big role in business regarding data collection used for studying the market. Converting the raw data retrieved from consumers into coherent data is something businesses try to do when considering what steps they should take next. Organizations are more frequently using data mining for collecting information and patterns from their databases, and this process helps them develop new business strategies to increase business performance and perform economic analyses more efficiently. Compiling the large amount of data they collect to be stored in their system is a form of data integration adapted for Business intelligence to improve their chances of success. == Example == Consider a web application where a user can query a variety of information about cities (such as crime statistics, weather, hotels, demographics, etc.). Traditionally, the information must be stored in a single database with a single schema. But any single enterprise would find information of this breadth somewhat difficult and expensive to collect. Even if the resources exist to gather the data, it would likely duplicate data in existing crime databases, weather websites, and census data. A data-integration solution may address this problem by considering these external resources as materialized views over a virtual mediated schema, resulting in "virtual data integration". This means application-developers construct a virtual schema—the mediated schema—to best model the kinds of answers their users want. Next, they design "wrappers" or adapters for each data source, such as the crime database and weather website. These adapters simply transform the local query results (those returned by the respective websites or databases) into an easily processed form for the data integration solution (see figure 2). When an application-user queries the mediated schema, the data-integration solution transforms this query into appropriate queries over the respective data sources. Finally, the virtual database combines the results of these queries into the answer to the user's query. This solution offers the convenience of adding new sources by simply constructing an adapter or an application software blade for them. It contrasts with ETL systems or with a si

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  Cognos ReportNet

  Cognos ReportNet (CRN) was a web-based software product for creating and managing ad hoc and custom-made reports. ReportNet was developed by the Ottawa-based company Cognos (formerly Cognos Incorporated), an IBM company. The web-based reporting tool was launched in September 2003. Since IBM's acquisition of Cognos, ReportNet has been renamed IBM Cognos ReportNet like all other Cognos products. ReportNet uses web services standards such as XML and Simple Object Access Protocol and also supports dynamic HTML and Java. ReportNet is compatible with multiple databases including Oracle, SAP, Teradata, Microsoft SQL server, DB2 and Sybase. The product provides interface in over 10 languages, has Web Services architecture to meet the needs of multi-national, diversified enterprises and helps reduce total cost of ownership. Multiple versions of Cognos ReportNet have since been released by the company. Cognos ReportNet was awarded the Software and Information Industry Association (SIIA) 2005 Codie awards for the "Best Business Intelligence or Knowledge Management Solution" category. CRN's capabilities have been further used in IBM Cognos 8 BI (2005), the latest reporting tool. CRN comes with its own software development kit (SDK). == Launch == Early adopters of Cognos ReportNet for their corporate reporting needs included Bear Stearns, BMW and Alfred Publishing. Around this same time of launch, Cognos competitor Business Objects released version 6.1 of its enterprise reporting tool. Cognos ReportNet has been successful since its launch, raising revenues in 2004 from licensing fees. == Controversy == Cognos rival Business Objects announced in 2005 that BusinessObjects XI significantly outperformed Cognos ReportNet in benchmark tests conducted by VeriTest, an independent software testing firm. The tests performed showed Cognos ReportNet performed poorly when processing styled reports, complex business reports and combination of both. The tests reported a massive 21 times higher report throughput for BusinessObjects XI than Cognos ReportNet at capacity loads. Cognos soon dismissed the claims by stating Business Objects dictated the environment and testing criteria and Cognos did not provide the software to participate in benchmark test. Cognos later performed their own test to demonstrate Cognos ReportNet capabilities. == Components == Cognos Report Studio – A Web-based product for creating complex professional looking reports. Cognos Query Studio - A Web-based product for creating ad-hoc reports. Cognos Framework Manager – A metadata modeling tool to create BI metadata for reporting and dashboard applications. Cognos Connection – Main portal used to access reports, schedule reports and perform administrator activities. == Versions == Cognos ReportNet 1.1 – Java EE-style professional web-based authoring tool. (base version) Cognos ReportNet IBM Special Edition – comes with an embedded version of IBM WebSphere as its application server and IBM DB2 as its data store. Cognos Linux – for Intel-based Linux platforms.

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  Bandhan Tod

  Bandhan Tod is a mobile app to stop child marriage in India's Bihar state through SOS button in the app. When the SOS on Bandhan Tod is activated, the nearest small NGO will attempt to resolve the issue. If the family resists, then the police gets notified. Till now so many child marriages has been cancelled through Bandhan Tod interventions. Bandhan Tod is an initiative of Gender Alliance managed by Prashanti Tiwari to support the state government's efforts to end child marriage and dowry.

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  TikTokification

  TikTokification (also written TikTok-ification) is a term used to describe the widespread adoption of TikTok's short-form, vertical video format and its algorithmic content-delivery model across the broader social media landscape. The phenomenon encompasses the strategic and cultural changes made by competing platforms such as Instagram, YouTube, Facebook, Snapchat, and LinkedIn in response to TikTok's global dominance. Beyond platform design, the term is also used more broadly to describe shifts in media consumption habits, advertising strategies, and, more critically, the potential cognitive and psychological effects associated with constant short-form video consumption. == Background == === Origins of short-form video === The short-form video format predates TikTok. Vine, launched in 2013, popularised six-second looping videos before shutting down in 2017. TikTok itself, known as Douyin in the Chinese market, was created by the Chinese technology company ByteDance in September 2016. Following its international expansion and its 2018 merger with Musical.ly, TikTok grew rapidly. By 2020, the application had surpassed two billion total downloads worldwide, with over 800 million monthly active users. A key driver of TikTok's success was its recommendation algorithm. The platform's "For You Page" (FYP) serves content to users based on behaviour rather than follower count, making it possible for unknown creators to achieve widespread reach organically. Analysts noted that TikTok serves "fast, visually engaging, and authentic videos that feel more like entertainment than advertising," fundamentally reshaping consumer expectations of digital content. TikTok has been described as "the center of the internet for young people," where users go for entertainment, news, trends, and shopping. As of the mid-2020s, TikTok had approximately 1.12 billion monthly active users. == Platform responses == TikTok's success compelled nearly every major social media platform to restructure its product around short-form video. In 2020, Instagram launched Reels and YouTube launched Shorts, both directly in response to TikTok's growth. Platforms like Meta's Instagram Reels and Google's YouTube Shorts subsequently expanded aggressively, launching new features, creator tools, and even considering separate standalone applications to compete. LinkedIn, traditionally a professional networking site, began experimenting with TikTok-style short-form vertical video feeds. Facebook launched a singular unified video feed combining Reels, long videos, and live videos, similar in structure to TikTok's feed. Snapchat redesigned its application to combine Stories and Spotlight into a unified entertainment feed. YouTube extended its Shorts format to allow videos up to three minutes in length, up from the previous limit of sixty seconds, as of October 2024. Despite these adaptations, experts noted that none of TikTok's rivals had matched its algorithmic precision as of mid-2025. == Societal and cultural impact == === Media and journalism === News organisations have also been affected by TikTokification. Short-form video grew rapidly as a format for news content, driven in large part by TikTok's popularity. According to Pew Research Center, 17% of adults in the United States reported regularly getting news from TikTok in 2024, with 63% of teenagers saying they used the platform as a news source. In response, major publishers began creating bespoke short-form content for TikTok's audience, with organisations such as the BBC building dedicated internal TikTok teams. === Advertising and commerce === TikTokification has had significant effects on the advertising industry. US social video advertising spending was projected to surpass linear television advertising spending for the first time in 2025. Global social commerce sales were projected to reach approximately $900 billion in 2025, with platforms like Douyin and TikTok driving a large share of that growth. TikTok itself generated an estimated $23.6 billion in advertising revenue in 2024. Short-form video has been described as bridging the gap between brand awareness and direct conversion. Surveys have found that consumers trust user-generated content 8.7 times more than influencer content and 6.6 times more than branded content, prompting brands to favour creator-led video formats. === Attention spans and cognitive effects === A growing body of research has examined the cognitive consequences of heavy short-form video consumption, a set of effects sometimes referred to as "TikTok Brain." A large systematic review and meta-analysis published in Psychological Bulletin, analysing data from 98,299 participants across 71 studies, found that the more short-form video content a person watches, the poorer their cognitive performance in attention and inhibitory control. The review also found that greater engagement with short-form video was associated with higher levels of anxiety, depression, and stress, as well as sleep disturbances. The platform's inherent demand for engaging content has resulted in the proliferation of sludge content, a genre of split screen video with the main video on the top and an unrelated attention-grabbing video on the bottom, typically repetitive gameplay (notably of the endless runner mobile game Subway Surfers) or oddly satisfying videos, designed to maximize viewer retention in cases where the main video may appear uninteresting and would normally cause the viewer to skip it. Sludge content is often described as overstimulating, reflecting and contributing to declining attention spans, though the scholarly evidence supporting such claims is not conclusive. Dr. Yann Poncin, associate professor at the Child Study Center at Yale University, noted that "infinite scrolling and short-form video are designed to capture your attention in short bursts," contrasting this with earlier entertainment formats that guided audiences through longer narratives. Research suggests that children and teenagers may be particularly vulnerable, with early exposure to rapid frame changes potentially conditioning the brain's neural pathways to require constant stimulation, making it more challenging to engage with slower-paced activities. A separate study published in Nature Communications by researchers at the Technical University of Denmark documented a notable decrease in collective attention span over time, attributing it in part to the increasing volume and pace of content production and consumption online. Researchers caution, however, that the majority of relevant studies are cross-sectional, meaning they capture data at a single point in time and cannot establish causality. It remains possible that individuals with pre-existing conditions such as anxiety or attention deficits may be more likely to engage heavily with these platforms as a coping mechanism. === Academic and sociological analysis === Scholars have framed TikTokification within the context of the attention economy. A 2024 academic analysis described TikTok as representing "a new paradigm of social media communication" shaped by youth culture, mobile technology, and the economics of attention, in which spectators become active contributors to a shared content pipeline. The same analysis noted that TikTok "reflects a new mode of communication influenced by avant-garde cinema, the use of mobile technology, and the social habits of particular social groups." US social media users were projected to spend 61.1% of their time on social networks watching videos in 2025, up from 33.3% in 2019, before TikTok became widely popular, underscoring the scale of the behavioural shift. == Monetisation challenges == Despite high engagement levels, monetising short-form video has remained difficult for platforms and creators alike. Unlike long-form YouTube content, short clips offer limited space for advertisers to insert advertisements. YouTube Shorts pays approximately four cents per 1,000 views, considerably less than its long-form counterpart. From 2025 onward, platforms began introducing creator funds, advertisements, and AI-driven content recommendations as part of broader efforts to make short-form video economically sustainable for creators.

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  Symmetric Boolean function

  In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on the number of ones (or zeros) in the input. For this reason they are also known as Boolean counting functions. There are 2n+1 symmetric n-ary Boolean functions. Instead of the truth table, traditionally used to represent Boolean functions, one may use a more compact representation for an n-variable symmetric Boolean function: the (n + 1)-vector, whose i-th entry (i = 0, ..., n) is the value of the function on an input vector with i ones. Mathematically, the symmetric Boolean functions correspond one-to-one with the functions that map n+1 elements to two elements, f : { 0 , 1 , . . . , n } → { 0 , 1 } {\displaystyle f:\{0,1,...,n\}\rightarrow \{0,1\}} . Symmetric Boolean functions are used to classify Boolean satisfiability problems. == Special cases == A number of special cases are recognized: Majority function: their value is 1 on input vectors with more than n/2 ones Threshold functions: their value is 1 on input vectors with k or more ones for a fixed k All-equal and not-all-equal function: their values is 1 when the inputs do (not) all have the same value Exact-count functions: their value is 1 on input vectors with k ones for a fixed k One-hot or 1-in-n function: their value is 1 on input vectors with exactly one one One-cold function: their value is 1 on input vectors with exactly one zero Congruence functions: their value is 1 on input vectors with the number of ones congruent to k mod m for fixed k, m Parity function: their value is 1 if the input vector has odd number of ones The n-ary versions of AND, OR, XOR, NAND, NOR and XNOR are also symmetric Boolean functions. == Properties == In the following, f k {\displaystyle f_{k}} denotes the value of the function f : { 0 , 1 } n → { 0 , 1 } {\displaystyle f:\{0,1\}^{n}\rightarrow \{0,1\}} when applied to an input vector of weight k {\displaystyle k} . === Weight === The weight of the function can be calculated from its value vector: | f | = ∑ k = 0 n ( n k ) f k {\displaystyle |f|=\sum _{k=0}^{n}{\binom {n}{k}}f_{k}} === Algebraic normal form === The algebraic normal form either contains all monomials of certain order m {\displaystyle m} , or none of them; i.e. the Möbius transform f ^ {\displaystyle {\hat {f}}} of the function is also a symmetric function. It can thus also be described by a simple (n+1) bit vector, the ANF vector f ^ m {\displaystyle {\hat {f}}_{m}} . The ANF and value vectors are related by a Möbius relation: f ^ m = ⨁ k 2 ⊆ m 2 f k {\displaystyle {\hat {f}}_{m}=\bigoplus _{k_{2}\subseteq m_{2}}f_{k}} where k 2 ⊆ m 2 {\displaystyle k_{2}\subseteq m_{2}} denotes all the weights k whose base-2 representation is covered by the base-2 representation of m (a consequence of Lucas’ theorem). Effectively, an n-variable symmetric Boolean function corresponds to a log(n)-variable ordinary Boolean function acting on the base-2 representation of the input weight. For example, for three-variable functions: f ^ 0 = f 0 f ^ 1 = f 0 ⊕ f 1 f ^ 2 = f 0 ⊕ f 2 f ^ 3 = f 0 ⊕ f 1 ⊕ f 2 ⊕ f 3 {\displaystyle {\begin{array}{lcl}{\hat {f}}_{0}&=&f_{0}\\{\hat {f}}_{1}&=&f_{0}\oplus f_{1}\\{\hat {f}}_{2}&=&f_{0}\oplus f_{2}\\{\hat {f}}_{3}&=&f_{0}\oplus f_{1}\oplus f_{2}\oplus f_{3}\end{array}}} So the three variable majority function with value vector (0, 0, 1, 1) has ANF vector (0, 0, 1, 0), i.e.: Maj ( x , y , z ) = x y ⊕ x z ⊕ y z {\displaystyle {\text{Maj}}(x,y,z)=xy\oplus xz\oplus yz} === Unit hypercube polynomial === The coefficients of the real polynomial agreeing with the function on { 0 , 1 } n {\displaystyle \{0,1\}^{n}} are given by: f m ∗ = ∑ k = 0 m ( − 1 ) | k | + | m | ( m k ) f k {\displaystyle f_{m}^{}=\sum _{k=0}^{m}(-1)^{|k|+|m|}{\binom {m}{k}}f_{k}} For example, the three variable majority function polynomial has coefficients (0, 0, 1, -2): Maj ( x , y , z ) = ( x y + x z + y z ) − 2 ( x y z ) {\displaystyle {\text{Maj}}(x,y,z)=(xy+xz+yz)-2(xyz)} == Examples ==

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