AI App Kya Hai In Hindi

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  Logical Machine Corporation

  Logical Machine Corporation (LOMAC) was an American computer company active from the mid-1970s to the 1980s and based in the San Francisco Bay Area. It was founded as John Peers and Company by the British entrepreneur John Peers in 1974. LOMAC developed the ADAM, a minicomputer which ran a specialized compiler for the company's natural English programming language. Throughout the late 1970s, the company acquired several technology firms, including Byte, Inc., the owner of the Byte Shop retail chain. Despite its unique approach to computing and earning $5 million in revenue in 1977, LOMAC struggled as the industry began to standardize around the IBM Personal Computer (IBM PC). Following Peers's departure in 1980, the company rebranded as Logical Business Machines, Inc. (LBM, or simply Logical), and attempted to pivot toward IBM PC–compatible hardware. However, financial difficulties led to the company filing for Chapter 11 bankruptcy in 1984. After emerging from bankruptcy in 1985 with new investment, Logical ceased hardware manufacturing to focus exclusively on software development and value-added reselling. == History == John Peers (born 1942) founded Logical Machine Corporation as John Peers and Company in September 1974. The company originally occupied a 4,500-square-foot office in Burlingame, California. The company was Peers' fourth; he had recently sold off Allied Business Systems of London to Trafalgar House in 1974. Peers sought to set up manufacturing in an agricultural zone in Ukiah, California. Following a delay, caused in part by concerned residents, a 30,000-square-foot plant was raised in Burke Hill, three miles south of Ukiah. The Ukiah plant was built to mass manufacture the company's ADAM minicomputer. The ADAM computer ran a specialized compiler for the company's natural English programming language; that is to say, the programming language attempted to closely emulate English syntax. Prototypes of the ADAM were built in May 1974, based on specifications devised in October 1973. Peers had yet to patent the technology as of June 1975. The ADAM's central processing unit was bolted onto an 7-by-6-foot L-shaped desk, on which rested its terminal. Twenty units of the ADAM were installed between April 1975 and February 1976, out of a backlog of orders for 3,500 from 500 clients, manufactured out of the company's Burlingame headquarters. It cost US$40,000. A controversial print advertisement featuring a naked woman seated at an ADAM terminal—as a pastiche of Adam and Eve—was recalled in early 1976 as a result of outcry from the National Organization for Women. The company changed its name to Logical Machine Corporation (LOMAC) in October 1976 and moved its headquarters to a 26,000-square-foot building in Sunnyvale, California, in anticipation of a ramping up of orders for the ADAM. The company originally occupied half of the building; they later purchased the other half from the tenant in July 1977 to double its manufacturing output. For fiscal year 1977, the company earned $5 million in revenue. In December 1977, LOMAC acquired Byte, Inc.—the proprietor of The Byte Shop, the first computer retail chain—from Paul Terrell and Boyd Wilson for an unspecified amount. The Byte Shop had 65 locations in the San Francisco Bay Area in 1978; it catered mainly to hobbyists with low cost microcomputer kits, in contrast to the high cost of LOMAC's ADAM. By July 1978, however, LOMAC were able to reduce the price of the ADAM down to $15,000. The company by that point had shipped their 50th ADAM and expanded to 14 countries. Also in 1978, LOMAC acquired Mass Memory—a high-tech optical storage company based in Phoenix, Arizona, whose products had storage capacities on the order gigabytes and terabytes—and Centigram, makers of the Mike—a computer with speech recognition. Later that year, the company introduced Tina, a low-cost version of the ADAM. LOMAC suffered losses that year and appointed Jerry Brandt to the board of directions, naming him chief operating officer, in August 1978. Brandt had Logical absorb Mass Memory and Centigram into the parent operations, shutting down their respective plants in the process, converted 10 Byte Shops to franchises and opened 25 more franchised Byte locations, and stopped direct sales of LOMAC's business computer products. By the beginning of 1979, LOMAC was profitable once more, and Brandt was let go from LOMAC. Peers left LOMAC in 1980, following a slump in the company's sales. He became an executive director of the United States Robotics Society, a consortium for industrial automation companies, that year. Following Peers' departure, LOMAC changed its name to Logical Business Machines, adopting the name of its European subsidiary. In 1983, the company announced a 16-bit clone of the IBM PC, called the Logical L-XT, which featured a 10-MB hard drive, 320-KB floppy drive and 192 KB of RAM, and a real-time clock, and came shipped with various software (including MS-DOS, a word processor, and a spreadsheet application) and an amber CRT monitor. The following year, the company introduced L-NET, a local area network system based on the L-XT that could link up to 64 computers. L-NET came shipped with a natural programming language, Diplomat—a descendant of the programming language used on the ADAM. In June 1983, Logical sued Coleco Industries over trademark infringement with the latter's to-be-released Adam microcomputer. Logical cited confusion from their existing ADAM customer base caused by the announcement of the Coleco Adam as the basis for the suit. Coleco challenged Logical in the press, writing that Logical's rights to the Adam trademark for use in computers had lapsed earlier in the year. The two settled out of court, with Coleco agreeing to license the Adam name from Logical in exchange for unlimited rights to the Adam trademark. Logical halted development of the L-XT when they filed for Chapter 11 bankruptcy in July 1984. The company had been $4 million in debt. They emerged from bankruptcy in September 1985, after being infused with $2 million from Carat Ltd. The latter immediately received a little less than 50 percent ownership in Logical—this stake set to grow to over 50 percent over the next six months. As part of the terms of exiting bankruptcy, Logical stopped manufacturing hardware and strictly became a software development company and value-added reseller of computer systems.

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  Sieve of Eratosthenes

  In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. Once all the multiples of each discovered prime have been marked as composites, the remaining unmarked numbers are primes. The earliest known reference to the sieve (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) is in Nicomachus of Gerasa's Introduction to Arithmetic, an early 2nd-century CE book which attributes it to Eratosthenes of Cyrene, a 3rd-century BCE Greek mathematician, though describing the sieving by odd numbers instead of by primes. One of a number of prime number sieves, it is one of the most efficient ways to find all of the smaller primes. It may be used to find primes in arithmetic progressions. == Overview == A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes's method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number. Enumerate the multiples of p by counting in increments of p from 2p to n, and mark them in the list (these will be 2p, 3p, 4p, ...; the p itself should not be marked). Find the smallest number in the list greater than p that is not marked. If there was no such number, stop. Otherwise, let p now equal this new number (which is the next prime), and repeat from step 3. When the algorithm terminates, the numbers remaining not marked in the list are all the primes below n. The main idea here is that every value given to p will be prime, because if it were composite it would be marked as a multiple of some other, smaller prime. Note that some of the numbers may be marked more than once (e.g., 15 will be marked both for 3 and 5). The key property of the sieve is that only additions are needed, no multiplications or divisions are used. As a refinement, it is sufficient to mark the numbers in step 3 starting from p2, as all the smaller multiples of p will have already been marked at that point. This means that the algorithm is allowed to terminate in step 4 when p2 is greater than n. Another refinement is to initially list odd numbers only, (3, 5, ..., n), and count in increments of 2p in step 3, thus marking only odd multiples of p. This actually appears in the original algorithm. This can be generalized with wheel factorization, forming the initial list only from numbers coprime with the first few primes and not just from odds (i.e., numbers coprime with 2), and counting in the correspondingly adjusted increments so that only such multiples of p are generated that are coprime with those small primes, in the first place. === Example === To find all the prime numbers less than or equal to 30, proceed as follows. First, generate a list of natural numbers from 2 to 30: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The first number in the list is 2; cross out every 2nd number in the list after 2 by counting up from 2 in increments of 2 (these will be all the multiples of 2 in the list): 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The next number in the list after 2 is 3; cross out every 3rd number in the list after 3 by counting up from 3 in increments of 3 (these will be all the multiples of 3 in the list): 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The next number not yet crossed out in the list after 3 is 5; cross out every 5th number in the list after 5 by counting up from 5 in increments of 5 (i.e. all the multiples of 5): 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The next number not yet crossed out in the list after 5 is 7; the next step would be to cross out every 7th number in the list after 7, but they are all already crossed out at this point, as these numbers (14, 21, 28) are also multiples of smaller primes because 7 × 7 is greater than 30. The numbers not crossed out at this point in the list are all the prime numbers below 30: 2 3 5 7 11 13 17 19 23 29 == Algorithm and variants == === Pseudocode === The sieve of Eratosthenes can be expressed in pseudocode, as follows: algorithm Sieve of Eratosthenes is input: an integer n > 1. output: all prime numbers from 2 through n. let A be an array of Boolean values, indexed by integers 2 to n, initially all set to true. for i = 2, 3, 4, ..., not exceeding √n do if A[i] is true for j = i2, i2+i, i2+2i, i2+3i, ..., not exceeding n do set A[j] := false return all i such that A[i] is true. This algorithm produces all primes not greater than n. It includes a common optimization, which is to start enumerating the multiples of each prime i from i2. The time complexity of this algorithm is O(n log log n), provided the array update is an O(1) operation, as is usually the case. === Segmented sieve === As Sorenson notes, the problem with the sieve of Eratosthenes is not the number of operations it performs but rather its memory requirements. For large n, the range of primes may not fit in memory; worse, even for moderate n, its cache use is highly suboptimal. The algorithm walks through the entire array A, exhibiting almost no locality of reference. A solution to these problems is offered by segmented sieves, where only portions of the range are sieved at a time. These have been known since the 1970s, and work as follows: Divide the range 2 through n into segments of some size Δ ≥ √n. Find the primes in the first (i.e. the lowest) segment, using the regular sieve. For each of the following segments, in increasing order, with m being the segment's topmost value, find the primes in it as follows: Set up a Boolean array of size Δ. Mark as non-prime the positions in the array corresponding to the multiples of each prime p ≤ √m found so far, by enumerating its multiples in steps of p starting from the lowest multiple of p between m - Δ and m. The remaining non-marked positions in the array correspond to the primes in the segment. It is not necessary to mark any multiples of these primes, because all of these primes are larger than √m, as for k ≥ 1, one has ( k Δ + 1 ) 2 > ( k + 1 ) Δ {\displaystyle (k\Delta +1)^{2}>(k+1)\Delta } . If Δ is chosen to be √n, the space complexity of the algorithm is O(√n), while the time complexity is the same as that of the regular sieve. For ranges with upper limit n so large that the sieving primes below √n as required by the page segmented sieve of Eratosthenes cannot fit in memory, a slower but much more space-efficient sieve like the pseudosquares prime sieve, developed by Jonathan P. Sorenson, can be used instead. === Incremental sieve === An incremental formulation of the sieve generates primes indefinitely (i.e., without an upper bound) by interleaving the generation of primes with the generation of their multiples (so that primes can be found in gaps between the multiples), where the multiples of each prime p are generated directly by counting up from the square of the prime in increments of p (or 2p for odd primes). The generation must be initiated only when the prime's square is reached, to avoid adverse effects on efficiency. It can be expressed symbolically under the dataflow paradigm as primes = [2, 3, ...] \ [[p², p²+p, ...] for p in primes], using list comprehension notation with \ denoting set subtraction of arithmetic progressions of numbers. Primes can also be produced by iteratively sieving out the composites through divisibility testing by sequential primes, one prime at a time. It is not the sieve of Eratosthenes but is often confused with it, even though the sieve of Eratosthenes directly generates the composites instead of testing for them. Trial division has worse theoretical complexity than that of the sieve of Eratosthenes in generating ranges of primes. When testing each prime, the optimal trial division algorithm uses all prime numbers not exceeding its square root, whereas the sieve of Eratosthenes produces each composite from its prime factors only, and gets the primes "for free", between the composites. The widely known 1975 functional sieve code by David Turner is often presented as an example of the sieve of Eratosthenes but is actually a sub-optimal trial division sieve. == Algorithmic complexity == The sieve of Eratosthenes is a popular way to benchmark computer performance. The time complexity of calculating all primes below n in the random access machine model is O(n log log n) ope

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  System of record

  A system of record (SOR) or source system of record (SSoR) is a data management term for an information storage system (commonly implemented on a computer system running a database management system) that is the authoritative data source for a given data element or piece of information, like for example a row (or record) in a table. In data vault it is referred to as the record source. == Background == The need to identify systems of record can become acute in organizations where management information systems have been built by taking output data from multiple source systems, re-processing this data, and then re-presenting the result for a new business use. In these cases, multiple information systems may disagree about the same piece of information. These disagreements may stem from semantic differences, differences in opinion, use of different sources, differences in the timing of the extract, transform, load processes that create the data they report against, or may simply be the result of bugs. == Use == The integrity and validity of any data set is open to question when there is no traceable connection to a good source, and listing a source system of record is a solution to this. Where the integrity of the data is vital, if there is an agreed system of record, the data element must either be linked to, or extracted directly from it. In other cases, the provenance and estimated data quality should be documented. The "system of record" approach is a good fit for environments where both: there is a single authority over all data consumers, and all consumers have similar needs == Trade-offs == In diverse environments, one instead needs to support the presence of multiple opinions. Consumers may accept different authorities or may differ on what constitutes an authoritative source—researchers may prefer carefully vetted data, while tactical military systems may require the most recent credible report.

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  Principles for a Data Economy

  The Principles for a Data Economy – Data Rights and Transactions is a transatlantic legal project carried out jointly by the American Law Institute (ALI) and the European Law Institute (ELI). The Principles for a Data Economy deals with a range of different legal questions that arise in the data economy. Since data is different from other tradeable items, the Principles draw up legal rules for data transactions and data rights that take into account the interests of different stakeholders involved in the data economy. The Principles are designed to facilitate contractual relations as well as the drafting of model agreements and can guide courts and legislators worldwide. The project proposes a set of principles that can be implemented in any legal system and is designed to work in conjunction with any kind of data privacy/data protection law, intellectual property law or trade secret law. The Principles do not address or seek to change any of the substantive rules of these bodies of law. The Project Team consists of Neil B Cohen and Christiane Wendehorst (as Project Reporters) and Lord John Thomas as well as Steven O. Weise (as Project Chairs). == Characteristics of data == The law governing trades in commerce has historically focused on trade in items that are tangible like goods or on intangible assets, such as shares or licenses. However, data does not fit into any of these traditional categories, nor does it qualify as a service. It is often unclear how traditional legal rules and doctrines can apply to data, as data is different from other assets in many ways. For example, data can be multiplied at basically no cost and can be used in parallel for a variety of different purposes by many different people at the same time (data is a “non-rivalrous” resource). Uncertainty regarding the applicable rules to govern the data economy may inhibit innovation and growth and trouble stakeholders like data-driven industries, start-ups, and consumers. == Stakeholders in the data economy == The Principles have taken the basic types of players and relations which can be found in data ecosystems as a starting point to provide guidance in different situations. The central actors in the data economy are data controllers (also called “data holders”). They are in a position to access the data and decide for which purposes and means this data should be processed. A controller may exercise control all by itself or share it with co-controllers, such as under a data pooling arrangement. Data processors provide the processing of data on a controller’s behalf as a service. Another important group of stakeholders includes those that contribute to the generation of data (e.g. data subjects). Other players in the data economy include data assemblers or data intermediaries (e.g. data trusts). == History of the project and timeline == Before the official adoption of the project by ALI and ELI bodies in 2018, the project team carried out a Feasibility Study from October 2016 to February 2018. In the following years, the project team produced a number of drafts (e.g. “Preliminary Drafts” No. 1 to 4, “Tentative Draft No. 1”) and project progress were regularly discussed with advisory bodies and members of both the ALI and the ELI. The project reporters also included feedback and insights from industry stakeholders and experts that was gained after several meetings and workshops, hosted, inter alia by UNCITRAL, UNIDROIT and several national governmental institutions. Tentative Draft No. 2 was presented at the ALI Annual Meeting in May 2021 and approved by ALI membership. The latest draft ("Final Council Draft") was also approved by the ELI Council and ELI Membership. The Principles for a Data Economy were presented at an international conference with representatives from institutions such as the Uniform Law Commission (ULC), the European Commission, UNIDROIT, the OECD, the International Chamber of Commerce (ICC) and the World Economic Forum (WEF) in October 2021. == Project structure == The current draft (“Tentative Draft No. 2”) of the Principles consists of five Parts that each governs different aspects of the data economy: General Provisions, Data Contracts, Data Rights, Third Party Aspects of Data Activities, and Multi-State Issues. === General Provisions === Part I includes general provisions that apply to all other Parts of the Principles for a Data Economy. This Part sets out the purpose of the Principles: they aim to make existing law in the field of the data economy more coherent and support the development of the law in this field by courts and legislators worldwide. It is also clarified that the Principles have a wide scope of application and can be used in a variety of ways by stakeholders in the data economy. The Principles may, for example, serve private parties as a basis for contract formation, guide the deliberations of arbitral tribunals or inspire national legislation. Part I then defines several key terms, such as ‘digital data’ and ‘data right’. The scope of the Principles is limited to matters where information is recorded as an asset, resource or tradeable commodity and where large amounts of data, rather than single pieces of information, are concerned. This Part also clarifies that remedies with respect to data contracts and data rights are left to the applicable national law. === Data Contracts === Part II lists different types of contracts that often occur in the data economy and establishes two broad categories, namely contracts for the supply and sharing of data and contracts for services with regard to data. Contracts for the supply and sharing of data include, e.g. data transfer contracts or data pooling arrangements, while contracts for services with regard to data cover contracts for the processing of data or data intermediary contracts. The Principles provide default terms for each contract type, on issues such as the manner in which data should supply or which characteristics the data supplied should meet. These default terms 'automatically' become part of the contract unless the parties agree otherwise. === Data Rights === Part III governs legally protected interests of players in the data economy that stem from the characteristics of data as a resource (e.g. its non-rivalrous nature) or from public interest considerations. Such data rights may include the right to data access, the right to require the controller to desist from data activities or to correct incorrect/incomplete data, or even to receive an economic share in profits derived from the use of data. For example, the Principles deal with data rights of stakeholders that had a share in the co-generation of data and identify different factors to be considered in determining whether to afford a party a data right. The underlying idea that parties who have contributed to the generation of data should have some rights in the utilization of the data is also recognized by governmental institutions, such as by the Japanese Ministry of Economy, Trade and Industry (METI), and the term co-generated data, which was coined by the Principles for a Data Economy, has been adopted, inter alia by the European Commission, the German Data Ethics Commission and the Global Partnership on Artificial Intelligence (GPAI). This Part also deals with data rights for the public interest, such as data sharing rights in the field of innovation. === Third Party Aspects === Part IV governs different situations in which data transactions interfere with the rights of third parties. Such rights include intellectual property rights or rights derived from data privacy or data protection law. This Part sets out under which circumstances data activities should be considered wrongful vis à vis another party. For example, a data activity (like data processing or the onward supply of data) could be considered wrongful, if a controller interferes with the rights of data subjects that are protected by data-protection law. A data activity could also be wrongful if the controller is non-compliant with contractual limitations on data activities, enforceable by the protected party (e.g. a controller may only process data for a certain purpose). If someone obtained access to data by unauthorized means (i.e. data “theft”) this could also be considered wrongful. The Part on Third-Party Aspects also takes a detailed look at the effects of the onward supply of data can have on third parties, while balancing the protection of third parties on the one hand, with the interests of data recipients and the desire to encourage data sharing on the other. === Multi-State Issues === As transactions in the data economy are international by nature and hardly occur within one legal system alone, the Part V of the Principles also briefly touches upon the applicability of the rules and doctrines of private international law to such transactions. == Links == Website of the “Principles for a Data Economy – Data Rights and Transaction

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  GNU social

  GNU social (and its predecessor StatusNet) is a largely defunct free and open-source microblogging social networking service that implements the OStatus and ActivityPub standards for interoperability between installations. While offering similar functionality to social networks such as Twitter, GNU social seeks to provide the ability for open and federated communication between different microblogging communities, known as 'instances'. Both enterprises and individuals can install and control their own instances and user data. At its peak in popularity, GNU social had been deployed on hundreds of interconnected instances, however has since fallen into disuse as competing software like Mastodon and Pleroma have taken its position as the dominant federated microblogging services. Later on in its lifespan, the project split into two separate branches, with "v2" being a continuation of the original codebase for maintenance of existing instances, with "v3" being a complete redesign of the project meant to integrate further ActivityPub support and modernization of the user experience and its technological back-end. As of August 15, 2022, there had been no new commits to the v2 branch, with the v3 branch also no longer being actively developed not long after by November 25, 2022, with the project essentially abandoned. Despite its modern obsolescence and dated design compared to modern platforms, GNU social and StatusNet is regarded to be the origin of the Fediverse network and has had a major influence on the design of more modern decentralized social networks that succeeded it. == History == While being the main project within its lineage, GNU social originally began as a fork of StatusNet. The software was first developed for a service called identi.ca from Evan Prodromou, which offered free microblogging accounts to the public. The software quickly became one of the first popular examples of a decentralized social network, as identi.ca allowed any other server that was running the software to communicate with it, something which had not previously been attempted before in social media at such a large scale. === StatusNet === Originally, StatusNet (named Laconica at the time) was launched with a communication protocol designed specifically for the project called OpenMicroBlogging (OMB). With version 0.8.1, the name of the software was changed to StatusNet. Version 0.9.0 was released soon after in March 3, 2010, with the developers implementing a newly designed protocol dubbed OStatus, with support for OMB being dropped not long after. Compared to OpenMicroBlogging, OStatus could handle and federate more events and actions than the basic plaintext communication that OMB provided and was based on a variety of other web technologies, allowing for easier adoption of new implementations of the protocol for servers and clients compared to the fully custom architecture of OMB. With the StatusNet name change, the company developing both the software and OStatus as well as managing identi.ca rebranded from Control Yourself to StatusNet Inc. In August 2010, the company raised a new round of venture capital funds to establish a hosting service under the status.net domain from sources such as First Mark Capital, BOLDstart Ventures, iNovia Capital and Montreal Start Up, raising over $2.3 million in funding up to that point. The hosting service allowed anyone to establish their own StatusNet instance without maintaining a server, similar to WordPress.com and other blogging platforms. New registrations on identi.ca along with the ability to create new status.net instances was disabled in December 2012, in preparation for a migration to pump.io that has since been named by users of StatusNet and OStatus as "the Pumpocalypse". pump.io was a brand new software package like StatusNet, but with a new protocol designed for general purpose activity streams outside of microblogging and ease-of-use for developers building on the technology, much like the transition from OMB to OStatus. The announcement was seen as unexpected among identi.ca users, who were concerned about the possibility of their statuses being deleted with the transition. At the same time, server administrators running third-party instances and their users who were left behind on StatusNet were also worried, as it was unclear at the time whether future development of the software would be picked up by a new maintainer. The transition for identi.ca users to pump.io was completed on 12 July 2013. ==== Previous names ==== The original name of StatusNet was Laconica, a reference to the Laconic phrase; a particularly brief statement commonly attributed to the leaders of Sparta (Laconia being the Greek region containing Sparta). In microblogging, all messages are designed to be very short due to the traditional 140-character limit on message size, a limitation imported from SMS. Beginning with version 0.8.1, the name was changed to StatusNet. The developers said that the new name "simply reflects what our software does: send status updates into your social network." === GNU social === GNU social originally began as a side project of GNU FM (Libre.fm) maintainer Matt Lee, with the goal of being able to federate messages between Last.fm and other instances of GNU FM using StatusNet plugins. Around the same time, a developer named Mikael Nordfeldth forked StatusNet with the intention of maintaining it as a personal project, dubbing it "Free Social". However, following identi.ca's transition to pump.io and its developers' sudden abandonment of StatusNet, the projects received more attention from server administrators and other users looking for an actively updated alternative. Shortly after LibrePlanet 2012, a plan was formed to merge all three projects into a single service. On June 8, 2013, it was announced that along with Free Social, StatusNet would be merged into the GNU social project and stewarded by the Free Software Foundation, with the project since becoming the dominant variant of StatusNet. During GNU social's lifespan, a popular theme for the user interface named Quitter was used, which was similar to an earlier Twitter interface. Many instances were made specifically using the name Quitter such as Quitter.se, an instance created by the developer of the theme. Before the establishment of Mastodon's popularity and dominance within the network, Quitter was noted as a frequent location for users of Twitter to migrate to when users disagreed with moderation policies or feature updates, such as when an algorithmic feed was added to Twitter. A fork of GNU social was made called postActiv, which planned to rewrite the backend and user interface of GNU social, as well as to add compatibility for Diaspora's protocol. == Features == A basic GNU social instance takes the form of a microblogging service with a reverse chronological timeline that features status updates and small messages from followed accounts, similar to other services such as Twitter or Weibo. While users could see their own customized timeline, they could access another timeline that showcased every message that the instance knows of, including from other instances that were connected to each other if someone on the instance followed an account from it. Users could also create and join groups, which allows for discussion and collaboration on specific topics. Administrators can also customize their server via the plugin system, which allows developers to create new features or modify existing plugins to suit the needs of the instance via PHP. A notable plugin built for GNU social was Quitter, a revamp of the user interface that resembles an earlier version of Twitter's user interface.

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  Mathematical knowledge management

  Mathematical knowledge management (MKM) is the study of how society can effectively make use of the vast and growing literature on mathematics. It studies approaches such as databases of mathematical knowledge, automated processing of formulae and the use of semantic information, and artificial intelligence. Mathematics is particularly suited to a systematic study of automated knowledge processing due to the high degree of interconnectedness between different areas of mathematics.

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  Digital artifact

  Digital artifact in information science, is any undesired or unintended alteration in data introduced in a digital process by an involved technique and/or technology. Digital artifact can be of any content types including text, audio, video, image, animation or a combination. == Information science == In information science, digital artifacts result from: Hardware malfunction: In computer graphics, visual artifacts may be generated whenever a hardware component such as the processor, memory chip, cabling malfunctions, etc., corrupts data. Examples of malfunctions include physical damage, overheating, insufficient voltage and GPU overclocking. Common types of hardware artifacts are texture corruption and T-vertices in 3D graphics, and pixelization in MPEG compressed video. Software malfunction: Artifacts may be caused by algorithm flaws such as decoding/encoding audio or video, or a poor pseudo-random number generator that would introduce artifacts distinguishable from the desired noise into statistical models. Compression: Controlled amounts of unwanted information may be generated as a result of the use of lossy compression techniques. One example is the artifacts seen in JPEG and MPEG compression algorithms that produce compression artifacts. Quantization: Digital imprecision generated in the process of converting analog information into digital space, is due to the limited granularity of digital numbering space. In computer graphics, quantization is seen as pixelation. Aliasing: As a consequence of sampling or sample-rate conversion, energy from frequencies outside of the signal frequency band of interest are folded across multiples of the Nyquist frequency. This is typically mitigated by using an anti-aliasing filter. Filtering: The process of filtering a signal, such as using an anti-aliasing filter, causes undesired alterations to the signal due to imperfections in the frequency response magnitude and phase, and due to the time domain impulse response. Rolling shutter, the line scanning of an object that is moving too fast for the image sensor to capture a unitary image. Error diffusion: poorly-weighted kernel coefficients result in undesirable visual artifacts.

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  Recommender system

  A recommender system, also called a recommendation algorithm, recommendation engine, or recommendation platform, is a type of information filtering system that suggests items most relevant to a particular user. The value of these systems becomes particularly evident in scenarios where users must select from a large number of options, such as products, media, or content. Major social media platforms and streaming services rely on recommender systems that employ machine learning to analyze user behavior and preferences, thereby enabling personalized content feeds. Typically, the suggestions refer to a variety decision-making processes, including the selection of a product, musical selection, or online news source to read. The implementation of recommender systems is pervasive, with commonly recognised examples including the generation of playlist for video and music services, the provision of product recommendations for e-commerce platforms, and the recommendation of content on social media platforms and the open web. These systems can operate using a single type of input, such as music, or multiple inputs from diverse platforms, including news, books and search queries. Additionally, popular recommender systems have been developed for specific topics, such as restaurants and online dating services. Recommender systems have also been developed to explore research articles and experts, collaborators, and financial services. A content discovery platform is a software recommendation platform that employs recommender system tools. It utilizes user metadata in order to identify and suggest relevant content, whilst reducing ongoing maintenance and development costs. A content discovery platform delivers personalized content to websites, mobile devices, and set-top boxes. A large range of content discovery platforms currently exist for various forms of content ranging from news articles and academic journal articles to television. As operators compete to serve as the gateway to home entertainment, personalized television emerges as a key service differentiator. Academic content discovery has recently become another area of interest, the emergence of numerous companies dedicated to assisting academic researchers in keeping up to date with relevant academic content and facilitating serendipitous discovery of new content. == Overview == Recommender systems usually make use of either or both collaborative filtering and content-based filtering, as well as other systems such as knowledge-based systems. Collaborative filtering approaches build a model from a user's past behavior (e.g., items previously purchased or selected and/or numerical ratings given to those items) as well as similar decisions made by other users. This model is then used to predict items (or ratings for items) that the user may have an interest in. Content-based filtering approaches utilize a series of discrete, pre-tagged characteristics of an item in order to recommend additional items with similar properties. === Example === The differences between collaborative and content-based filtering can be demonstrated by comparing two early music recommender systems, Last.fm and Pandora Radio. We can also look at how these methods are applied in e-commerce, for example, on platforms like Amazon. Last.fm creates a "station" of recommended songs by observing what bands and individual tracks the user has listened to on a regular basis and comparing those against the listening behavior of other users. Last.fm will play tracks that do not appear in the user's library, but are often played by other users with similar interests. As this approach leverages the behavior of users, it is an example of a collaborative filtering technique. Pandora uses the properties of a song or artist (a subset of the 450 attributes provided by the Music Genome Project) to seed a "station" that plays music with similar properties. User feedback is used to refine the station's results, deemphasizing certain attributes when a user "dislikes" a particular song and emphasizing other attributes when a user "likes" a song. This is an example of a content-based approach. In e-commerce, Amazon's well-known "customers who bought X also bought Y" feature is a prime example of collaborative filtering. It also uses content-based filtering when it recommends a book by the same author you've previously read or a pair of shoes in a similar style to ones you've viewed. Each type of system has its strengths and weaknesses. In the above example, Last.fm requires a large amount of information about a user to make accurate recommendations. This is an example of the cold start problem, and is common in collaborative filtering systems. Whereas Pandora needs very little information to start, it is far more limited in scope (for example, it can only make recommendations that are similar to the original seed). === Alternative implementations === Recommender systems are a useful alternative to search algorithms since they help users discover items they might not have found otherwise. Of note, recommender systems are often implemented using search engines indexing non-traditional data. In some cases, like in the Gonzalez v. Google Supreme Court case, may argue that search and recommendation algorithms are different technologies. Recommender systems have been the focus of several granted patents, and there are more than 50 software libraries that support the development of recommender systems including LensKit, RecBole, ReChorus and RecPack. == History == Elaine Rich created the first recommender system in 1979, called Grundy. She looked for a way to recommend users books they might like. Her idea was to create a system that asks users specific questions and classifies them into classes of preferences, or "stereotypes", depending on their answers. Depending on users' stereotype membership, they would then get recommendations for books they might like. Another early recommender system, called a "digital bookshelf", was described in a 1990 technical report by Jussi Karlgren at Columbia University, and implemented at scale and worked through in technical reports and publications from 1994 onwards by Jussi Karlgren, then at SICS, and research groups led by Pattie Maes at MIT, Will Hill at Bellcore, and Paul Resnick, also at MIT, whose work with GroupLens was awarded the 2010 ACM Software Systems Award. Montaner provided the first overview of recommender systems from an intelligent agent perspective. Adomavicius provided a new, alternate overview of recommender systems. Herlocker provides an additional overview of evaluation techniques for recommender systems, and Beel et al. discussed the problems of offline evaluations. Beel et al. have also provided literature surveys on available research paper recommender systems and existing challenges. == Approaches == === Collaborative filtering === One approach to the design of recommender systems that has wide use is collaborative filtering. Collaborative filtering is based on the assumption that people who agreed in the past will agree in the future, and that they will like similar kinds of items as they liked in the past. The system generates recommendations using only information about rating profiles for different users or items. By locating peer users/items with a rating history similar to the current user or item, they generate recommendations using this neighborhood. This approach is a cornerstone for e-commerce sites that analyze the purchasing patterns of thousands of users to suggest what you might like. Collaborative filtering methods are classified as memory-based and model-based. A well-known example of memory-based approaches is the user-based algorithm, while that of model-based approaches is matrix factorization (recommender systems). A key advantage of the collaborative filtering approach is that it does not rely on machine analyzable content and therefore it is capable of accurately recommending complex items such as movies without requiring an "understanding" of the item itself. Many algorithms have been used in measuring user similarity or item similarity in recommender systems. For example, the k-nearest neighbor (k-NN) approach and the Pearson Correlation as first implemented by Allen. When building a model from a user's behavior, a distinction is often made between explicit and implicit forms of data collection. Examples of explicit data collection include the following: Asking a user to rate an item on a sliding scale. Asking a user to search. Asking a user to rank a collection of items from favorite to least favorite. Presenting two items to a user and asking him/her to choose the better one of them. Asking a user to create a list of items that he/she likes (see Rocchio classification or other similar techniques). Examples of implicit data collection include the following: Observing the items that a user views in an online store, media library, or other repository of med

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  Environmental impact of AI

  The environmental impact of the design, training, deployment and use of artificial intelligence includes the greenhouse gas emissions from generating electricity for data centres and computing hardware, operational and upstream water use, and material impacts from hardware manufacturing, mining and electronic waste. Estimating AI's environmental effects can be difficult because results depend on how impacts are measured, including whether accounting includes only model computation or also data-centre overhead, idle capacity, hardware manufacture, and local electricity supply. As these issues have received greater attention, governments and regulators have increasingly considered data-centre reporting requirements, energy-efficiency standards, and broader transparency measures for AI-related resource use. == Carbon footprint and energy use == AI-related energy use arises at multiple stages, including model training, fine-tuning, inference, storage, networking, and supporting infrastructure such as cooling and power conversion. === Individual level === Published estimates of energy use per AI request vary widely across models, tasks and measurement methods. A benchmark study presented at the 2024 ACM Conference on Fairness, Accountability, and Transparency found substantial differences between task types, with lower energy use for some text tasks and much higher energy use for image generation in the study's test conditions. In that benchmark, simple classification tasks consumed about 0.002–0.007 Wh per prompt on average (about 9% of a smartphone charge for 1,000 prompts), while text generation and text summarisation each used about 0.05 Wh per prompt; image generation averaged 2.91 Wh per prompt, and the least efficient image model in the study used 11.49 Wh per image (roughly equivalent to half a smartphone charge). First-party measurements in production environments have also been published. A 2025 Google study on Gemini assistant serving reported median per-prompt energy, emissions, and water-use estimates under the authors' accounting framework, while noting that different system boundaries can produce substantially different results. The study reported a median text-prompt estimate of about 0.24 Wh, which is roughly as much energy as watching nine seconds of television. The study also stated that software and infrastructure improvements reduced energy use by a factor of 33 and carbon emissions by a factor of 44 for a typical prompt over one year within the authors' framework. Researchers at the University of Michigan measured the energy consumption of various Meta Llama 3.1 models released in 2024 and found that smaller language models (8 billion parameters) use about 114 joules (0.03167 Wh) per response, while larger models (405 billion parameters) require up to 6,700 joules (1.861 Wh) per response. This corresponds to the energy needed to run a microwave oven for roughly one-tenth of a second and eight seconds, respectively. Comparisons between AI systems and human labour for specific tasks have produced mixed results and remain sensitive to assumptions about output quality, workload and system boundaries. A 2024 study in Scientific Reports reported 130 to 2900 times lower estimated carbon emissions for selected AI systems than for human writers and illustrators under its assumptions. A later Scientific Reports paper reported a counterexample for programming tasks under its assumptions, finding 5 to 19 times higher estimated emissions for the evaluated AI system than for human programmers on the benchmark used in that study. === System level === ==== Energy use and efficiency ==== AI electricity intensity depends not only on model architecture but also on hardware and facility efficiency. Data-centre operators commonly report Power usage effectiveness (PUE), which measures the ratio of total facility energy to IT equipment energy; a lower PUE indicates less overhead energy for cooling and other supporting infrastructure. Operators may also publish metrics and case studies on hardware efficiency, cooling systems and power sourcing. In its 2024 environmental report, Google stated that its 2023 total greenhouse gas emissions increased 13% year over year, primarily because of increased data-centre energy consumption and supply-chain emissions, while also reporting lower PUE than industry averages for its own facilities. The International Energy Agency has also reported that data centres remain a relatively small share of global electricity use overall, but that their local effects can be much more pronounced because demand is geographically concentrated. ==== Carbon footprint ==== At system level, AI contributes to rising electricity demand in data centres and related infrastructure. The International Energy Agency estimated that data centres used about 415 TWh of electricity in 2024, or around 1.5% of global electricity consumption, and projected that data-centre electricity use could rise to about 945 TWh by 2030, with AI identified as the main driver of that growth alongside other digital services. The carbon footprint of AI systems depends strongly on electricity sources, hardware efficiency, utilisation rates, and what stages are included in the accounting. Training large models can require substantial electricity, while total lifecycle impacts also depend on deployment scale and the amount of inference performed after training. Early analyses of frontier-model development reported rapid historical growth in training compute for selected systems, although later trends have depended on changes in model design, hardware and efficiency gains. Accounting methods that include upstream or embodied impacts, such as hardware manufacture and facilities construction, can materially affect estimates of AI-related emissions. === Decisions and strategies by individual companies === Large technology companies have reported that the expansion of AI and cloud infrastructure affects their sustainability targets, electricity demand, and resource use. Google, for example, attributed part of its emissions growth in 2023 to increased data-centre energy consumption and supply-chain emissions in its 2024 environmental report. Cloud and AI companies have also announced measures intended to reduce environmental impacts, including investment in more efficient hardware, low-carbon electricity procurement, alternative cooling systems, and water stewardship programmes. The extent, comparability, and third-party verification of such disclosures vary between firms and jurisdictions. == Water usage == Data centres can use water directly for cooling and indirectly through the water used in electricity generation, depending on the local energy mix. Public reporting on data-centre water use has often been inconsistent, making comparisons between operators and regions difficult. To standardise operational reporting, The Green Grid proposed the metric water usage effectiveness (WUE), defined as annual site water use divided by IT equipment energy use. WUE does not by itself measure local water stress, source sustainability, or all upstream water impacts. Studies of AI water use also distinguish between water withdrawal and water consumption. Research on AI-specific water use has argued that the water footprint of AI systems can be difficult to observe and may vary substantially by location, cooling design, and electricity source. A 2025 Communications of the ACM article summarised methods for estimating AI water footprints and emphasised the distinction between water withdrawal and water consumption. Li and colleagues estimated that global AI water withdrawal could reach 4.2–6.6 billion cubic metres in 2027 under the scenarios examined in their article. Using GPT-3, released by OpenAI in 2020, as an example, they estimated that training the model in Microsoft's U.S. data centres could consume about 700,000 litres of onsite water and about 5.4 million litres in total when offsite electricity-related water use was included; they also estimated that 10–50 medium-length GPT-3 responses could consume about 500 mL of water, depending on when and where the model was deployed. Published prompt-level estimates have also varied by system and accounting framework: the 2025 Google study on Gemini assistant serving reported a median text-prompt estimate of about 0.26 mL under its framework. Location can materially affect the significance of data-centre water use. Research on U.S. data centres found that one-fifth of servers' direct water footprint came from moderately to highly water-stressed watersheds, while nearly half of servers were fully or partially powered by plants located in water-stressed regions. A 2025 Reuters report, citing data from Verisk Maplecroft and NatureFinance, said that an average mid-sized data centre uses about 1.4 million litres of water per day for cooling and that Phoenix would experience a 32% increase in annual water stress if currently pl

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  Behavior selection algorithm

  In artificial intelligence, a behavior selection algorithm, or action selection algorithm, is an algorithm that selects appropriate behaviors or actions for one or more intelligent agents. In game artificial intelligence, it selects behaviors or actions for one or more non-player characters. Common behavior selection algorithms include: Finite-state machines Hierarchical finite-state machines Decision trees Behavior trees Hierarchical task networks Hierarchical control systems Utility systems Dialogue tree (for selecting what to say) == Related concepts == In application programming, run-time selection of the behavior of a specific method is referred to as the strategy design pattern.

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  Wiki survey

  Wiki surveys or wikisurveys are a software-based survey method that crowdsource discussions and help participants to find areas of agreement. Other names include bridging systems and collective response systems. The approach, inspired by Wikipedia, is to open up surveys where participants can shape the questions, instead of traditional 'closed' surveys where participants can only respond to the questions asked. Wiki surveys have been used for purposes including facilitating deliberative democracy, crowdsourcing opinions from experts and figuring out common beliefs on a given topic. A notable usage of wiki surveys is in Taiwan's government system, where citizens can participate in crowdsourced lawmaking through Pol.is wiki surveys. == Implementations == === All Our Ideas === All Our Ideas founders coined the term "wiki survey," explaining how they took inspiration from the organic evolution of Wikipedia and hoped to create something similar for surveys. They hosted 5000 surveys between 2010 and 2014. A 2020 survey using the tool found 3 of its top 10 findings were user-generated. === Decidim === Decidim has been used by governments throughout Spain and Europe to help with participatory budgeting and other public policy decisions. === Polis === Polis (also known as Pol.is) was developed in 2012. The focus of Polis is to project participants into an 'opinion space' where they can see how their voting behavior compares to other participants. The opinion space clusters participants into groups of similar opinion and is designed in a way to avoid tyranny of the majority by being able to include groups that have small numbers of participants. The questions participants are presented with are agree/disagree/pass on a single 'comment' submitted by a participant. The code for Polis is free and open-source software under the GNU AGPL. === Remesh === Remesh was founded in 2013 and has partnered with the United Nations and Alliance for Middle East Peace efforts to bring peaceful resolutions to conflicts. Participants are anonymous and the algorithm can be fine-tuned to better understand local dialects in specific regions. == Examples == PlaNYC used All Our Ideas to gather ideas on how to establish New York City's sustainability plan vTaiwan, a citizen-lead government process in Taiwan, uses Polis for enabling large amounts of citizens to deliberate and consequently provide input on Taiwan's legislative decisions OECD used All Our Ideas to gather ideas from the public prior to meeting for a forum and meeting on which skills are most important to invest in for the 21st century March On, an offshoot of the Women's March Movement, used Polis to understand the opinions of people wanting to support the movement Residents of Harrogate use Polis to debate issues in their community, with the results being released publicly to everyone == Characteristics == Wiki surveys often have these three characteristics: === Collaborativeness === Wiki surveys allow participants to contribute questions, as well as answer questions created by its participants. === Adaptivity === Wiki surveys adapt to elicit the most useful information from its participants. One example involves changing the ordering of questions based on the voting behavior of previous participants so as to maximize consensus. The heuristic determining the ordering of questions highly values showing the comments that have been voted on the least. === 'Greediness' === In the context of wiki surveys, 'greediness' simply means making full use of information that participants are willing to provide. Wiki surveys do not require participants to answer a fixed amount of questions, so participants can answer as little or as much as they want. This is intended to be more efficient in capturing participants' preferences by allowing more organic sharing of their perspectives. == Traditional survey methods vs. wiki surveys == Questions in traditional survey methods fall into two categories: Open and closed questions. Open questions ask the person taking the survey to write an open response while closed questions give a fixed set of responses to select from. Wiki surveys are like a hybrid of the two, enabling insightful consensus in certain situations where traditional survey methods may lack. Closed questions are easy to analyze quantitively, but the limited options to select from for a given question may cause bias. Open questions are not as subject to bias, but are difficult to analyze quantitatively at scale. Wiki surveys allow for open responses by the users' contribution of survey questions (also called 'items'), and uses machine learning techniques to (at least partially) automate the quantitative analysis of the responses to those questions.

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  Berlekamp–Rabin algorithm

  In number theory, Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials over the field F p {\displaystyle \mathbb {F} _{p}} with p {\displaystyle p} elements. The method was discovered by Elwyn Berlekamp in 1970 as an auxiliary to the algorithm for polynomial factorization over finite fields. The algorithm was later modified by Rabin for arbitrary finite fields in 1979. The method was also independently discovered before Berlekamp by other researchers. == History == The method was proposed by Elwyn Berlekamp in his 1970 work on polynomial factorization over finite fields. His original work lacked a formal correctness proof and was later refined and modified for arbitrary finite fields by Michael Rabin. In 1986 René Peralta proposed a similar algorithm for finding square roots in F p {\displaystyle \mathbb {F} _{p}} . In 2000 Peralta's method was generalized for cubic equations. == Statement of problem == Let p {\displaystyle p} be an odd prime number. Consider the polynomial f ( x ) = a 0 + a 1 x + ⋯ + a n x n {\textstyle f(x)=a_{0}+a_{1}x+\cdots +a_{n}x^{n}} over the field F p ≃ Z / p Z {\displaystyle \mathbb {F} _{p}\simeq \mathbb {Z} /p\mathbb {Z} } of remainders modulo p {\displaystyle p} . The algorithm should find all λ {\displaystyle \lambda } in F p {\displaystyle \mathbb {F} _{p}} such that f ( λ ) = 0 {\textstyle f(\lambda )=0} in F p {\displaystyle \mathbb {F} _{p}} . == Algorithm == === Randomization === Let f ( x ) = ( x − λ 1 ) ( x − λ 2 ) ⋯ ( x − λ n ) {\textstyle f(x)=(x-\lambda _{1})(x-\lambda _{2})\cdots (x-\lambda _{n})} . Finding all roots of this polynomial is equivalent to finding its factorization into linear factors. To find such factorization it is sufficient to split the polynomial into any two non-trivial divisors and factorize them recursively. To do this, consider the polynomial f z ( x ) = f ( x − z ) = ( x − λ 1 − z ) ( x − λ 2 − z ) ⋯ ( x − λ n − z ) {\textstyle f_{z}(x)=f(x-z)=(x-\lambda _{1}-z)(x-\lambda _{2}-z)\cdots (x-\lambda _{n}-z)} where z {\displaystyle z} is some element of F p {\displaystyle \mathbb {F} _{p}} . If one can represent this polynomial as the product f z ( x ) = p 0 ( x ) p 1 ( x ) {\displaystyle f_{z}(x)=p_{0}(x)p_{1}(x)} then in terms of the initial polynomial it means that f ( x ) = p 0 ( x + z ) p 1 ( x + z ) {\displaystyle f(x)=p_{0}(x+z)p_{1}(x+z)} , which provides needed factorization of f ( x ) {\displaystyle f(x)} . === Classification of === F p {\displaystyle \mathbb {F} _{p}} elements Due to Euler's criterion, for every monomial ( x − λ ) {\displaystyle (x-\lambda )} exactly one of following properties holds: The monomial is equal to x {\displaystyle x} if λ = 0 {\displaystyle \lambda =0} , The monomial divides g 0 ( x ) = ( x ( p − 1 ) / 2 − 1 ) {\textstyle g_{0}(x)=(x^{(p-1)/2}-1)} if λ {\displaystyle \lambda } is quadratic residue modulo p {\displaystyle p} , The monomial divides g 1 ( x ) = ( x ( p − 1 ) / 2 + 1 ) {\textstyle g_{1}(x)=(x^{(p-1)/2}+1)} if λ {\displaystyle \lambda } is quadratic non-residual modulo p {\displaystyle p} . Thus if f z ( x ) {\displaystyle f_{z}(x)} is not divisible by x {\displaystyle x} , which may be checked separately, then f z ( x ) {\displaystyle f_{z}(x)} is equal to the product of greatest common divisors gcd ( f z ( x ) ; g 0 ( x ) ) {\displaystyle \gcd(f_{z}(x);g_{0}(x))} and gcd ( f z ( x ) ; g 1 ( x ) ) {\displaystyle \gcd(f_{z}(x);g_{1}(x))} . === Berlekamp's method === The property above leads to the following algorithm: Explicitly calculate coefficients of f z ( x ) = f ( x − z ) {\displaystyle f_{z}(x)=f(x-z)} , Calculate remainders of x , x 2 , x 2 2 , x 2 3 , x 2 4 , … , x 2 ⌊ log 2 ⁡ p ⌋ {\textstyle x,x^{2},x^{2^{2}},x^{2^{3}},x^{2^{4}},\ldots ,x^{2^{\lfloor \log _{2}p\rfloor }}} modulo f z ( x ) {\displaystyle f_{z}(x)} by squaring the current polynomial and taking remainder modulo f z ( x ) {\displaystyle f_{z}(x)} , Using exponentiation by squaring and polynomials calculated on the previous steps calculate the remainder of x ( p − 1 ) / 2 {\textstyle x^{(p-1)/2}} modulo f z ( x ) {\textstyle f_{z}(x)} , If x ( p − 1 ) / 2 ≢ ± 1 ( mod f z ( x ) ) {\textstyle x^{(p-1)/2}\not \equiv \pm 1{\pmod {f_{z}(x)}}} then gcd {\displaystyle \gcd } mentioned below provide a non-trivial factorization of f z ( x ) {\displaystyle f_{z}(x)} , Otherwise all roots of f z ( x ) {\displaystyle f_{z}(x)} are either residues or non-residues simultaneously and one has to choose another z {\displaystyle z} . If f ( x ) {\displaystyle f(x)} is divisible by some non-linear primitive polynomial g ( x ) {\displaystyle g(x)} over F p {\displaystyle \mathbb {F} _{p}} then when calculating gcd {\displaystyle \gcd } with g 0 ( x ) {\displaystyle g_{0}(x)} and g 1 ( x ) {\displaystyle g_{1}(x)} one will obtain a non-trivial factorization of f z ( x ) / g z ( x ) {\displaystyle f_{z}(x)/g_{z}(x)} , thus algorithm allows to find all roots of arbitrary polynomials over F p {\displaystyle \mathbb {F} _{p}} . === Modular square root === Consider equation x 2 ≡ a ( mod p ) {\textstyle x^{2}\equiv a{\pmod {p}}} having elements β {\displaystyle \beta } and − β {\displaystyle -\beta } as its roots. Solution of this equation is equivalent to factorization of polynomial f ( x ) = x 2 − a = ( x − β ) ( x + β ) {\textstyle f(x)=x^{2}-a=(x-\beta )(x+\beta )} over F p {\displaystyle \mathbb {F} _{p}} . In this particular case problem it is sufficient to calculate only gcd ( f z ( x ) ; g 0 ( x ) ) {\displaystyle \gcd(f_{z}(x);g_{0}(x))} . For this polynomial exactly one of the following properties will hold: GCD is equal to 1 {\displaystyle 1} which means that z + β {\displaystyle z+\beta } and z − β {\displaystyle z-\beta } are both quadratic non-residues, GCD is equal to f z ( x ) {\displaystyle f_{z}(x)} which means that both numbers are quadratic residues, GCD is equal to ( x − t ) {\displaystyle (x-t)} which means that exactly one of these numbers is quadratic residue. In the third case GCD is equal to either ( x − z − β ) {\displaystyle (x-z-\beta )} or ( x − z + β ) {\displaystyle (x-z+\beta )} . It allows to write the solution as β = ( t − z ) ( mod p ) {\textstyle \beta =(t-z){\pmod {p}}} . === Example === Assume we need to solve the equation x 2 ≡ 5 ( mod 11 ) {\textstyle x^{2}\equiv 5{\pmod {11}}} . For this we need to factorize f ( x ) = x 2 − 5 = ( x − β ) ( x + β ) {\displaystyle f(x)=x^{2}-5=(x-\beta )(x+\beta )} . Consider some possible values of z {\displaystyle z} : Let z = 3 {\displaystyle z=3} . Then f z ( x ) = ( x − 3 ) 2 − 5 = x 2 − 6 x + 4 {\displaystyle f_{z}(x)=(x-3)^{2}-5=x^{2}-6x+4} , thus gcd ( x 2 − 6 x + 4 ; x 5 − 1 ) = 1 {\displaystyle \gcd(x^{2}-6x+4;x^{5}-1)=1} . Both numbers 3 ± β {\displaystyle 3\pm \beta } are quadratic non-residues, so we need to take some other z {\displaystyle z} . Let z = 2 {\displaystyle z=2} . Then f z ( x ) = ( x − 2 ) 2 − 5 = x 2 − 4 x − 1 {\displaystyle f_{z}(x)=(x-2)^{2}-5=x^{2}-4x-1} , thus gcd ( x 2 − 4 x − 1 ; x 5 − 1 ) ≡ x − 9 ( mod 11 ) {\textstyle \gcd(x^{2}-4x-1;x^{5}-1)\equiv x-9{\pmod {11}}} . From this follows x − 9 = x − 2 − β {\textstyle x-9=x-2-\beta } , so β ≡ 7 ( mod 11 ) {\displaystyle \beta \equiv 7{\pmod {11}}} and − β ≡ − 7 ≡ 4 ( mod 11 ) {\textstyle -\beta \equiv -7\equiv 4{\pmod {11}}} . A manual check shows that, indeed, 7 2 ≡ 49 ≡ 5 ( mod 11 ) {\textstyle 7^{2}\equiv 49\equiv 5{\pmod {11}}} and 4 2 ≡ 16 ≡ 5 ( mod 11 ) {\textstyle 4^{2}\equiv 16\equiv 5{\pmod {11}}} . == Correctness proof == The algorithm finds factorization of f z ( x ) {\displaystyle f_{z}(x)} in all cases except for ones when all numbers z + λ 1 , z + λ 2 , … , z + λ n {\displaystyle z+\lambda _{1},z+\lambda _{2},\ldots ,z+\lambda _{n}} are quadratic residues or non-residues simultaneously. According to theory of cyclotomy, the probability of such an event for the case when λ 1 , … , λ n {\displaystyle \lambda _{1},\ldots ,\lambda _{n}} are all residues or non-residues simultaneously (that is, when z = 0 {\displaystyle z=0} would fail) may be estimated as 2 − k {\displaystyle 2^{-k}} where k {\displaystyle k} is the number of distinct values in λ 1 , … , λ n {\displaystyle \lambda _{1},\ldots ,\lambda _{n}} . In this way even for the worst case of k = 1 {\displaystyle k=1} and f ( x ) = ( x − λ ) n {\displaystyle f(x)=(x-\lambda )^{n}} , the probability of error may be estimated as 1 / 2 {\displaystyle 1/2} and for modular square root case error probability is at most 1 / 4 {\displaystyle 1/4} . == Complexity == Let a polynomial have degree n {\displaystyle n} . We derive the algorithm's complexity as follows: Due to the binomial theorem ( x − z ) k = ∑ i = 0 k ( k i ) ( − z ) k − i x i {\textstyle (x-z)^{k}=\sum \limits _{i=0}^{k}{\binom {k}{i}}(-z)^{k-i}x^{i}} , we may transition from f ( x ) {\displaystyle f(x)} to f ( x − z ) {\displaystyle f(x-z)} in O ( n 2 ) {\displaystyle O(n^{2})} time. Polynomial multiplication a

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  JAUS Tool Set

  The JAUS Tool Set (JTS) is a software engineering tool for the design of software services used in a distributed computing environment. JTS provides a graphical user interface (GUI) and supporting tools for the rapid design, documentation, and implementation of service interfaces that adhere to the Society of Automotive Engineers' standard AS5684A, the JAUS Service Interface Design Language (JSIDL). JTS is designed to support the modeling, analysis, implementation, and testing of the protocol for an entire distributed system. == Overview == The JAUS Tool Set (JTS) is a set of open source software specification and development tools accompanied by an open source software framework to develop Joint Architecture for Unmanned Systems (JAUS) designs and compliant interface implementations for simulations and control of robotic components per SAE-AS4 standards. JTS consists of the components: GUI based Service Editor: The Service Editor (referred to as the GUI in this document) provides a user friendly interface with which a system designer can specify and analyze formal specifications of Components and Services defined using the JAUS Service Interface Definition Language (JSIDL). Validator: A syntactic and semantic validator provides on-the-fly validation of specifications entered (or imported) by the user with respect to JSIDL syntax and semantics is integrated into the GUI. Specification Repository: A repository (or database) that is integrated into the GUI that allows for the storage of and encourages the reuse of existing formal specifications. C++ Code Generator: The Code Generator automatically generates C++ code that has a 1:1 mapping to the formal specifications. The generated code includes all aspects of the service, including the implementations of marshallers and unmarshallers for messages, and implementations of finite-state machines for protocol behavior that are effectively decoupled from application behavior. Document Generator: The Document Generator automatically generates documentation for sets of Service Definitions. Documents may be generated in several formats. Software Framework: The software framework implements the transport layer specification AS5669A, and provides the interfaces necessary to integrate the auto-generated C++ code with the transport layer implementation. Present transport options include UDP and TCP in wired or wireless networks, as well as serial connections. The transport layer itself is modular, and allows end-users to add additional support as needed. Wireshark Plugin: The Wireshark plugin implements a plugin to the popular network protocol analyzer called Wireshark. This plugin allows for the live capture and offline analysis of JAUS message-based communication at runtime. A built-in repository facilitates easy reuse of service interfaces and implementations traffic across the wire. The JAUS Tool Set can be downloaded from www.jaustoolset.org User documentation and community forum are also available at the site. == Release history == Following a successful Beta test, Version 1.0 of the JAUS Tool Set was released in July 2010. The initial offering focused on core areas of User Interface, HTML document generation, C++ code generation, and the software framework. The Version 1.1 update was released in October 2010. In addition to bug fixes and UI improvements, this version offered several important upgrades including enhancement to the Validator, Wireshark plug-in, and generated code. The JTS 2.0 release is scheduled for the second quarter of 2011 and further refines the Tool Set functionality: Protocol Validation: Currently, JTS provides validation for message creation, to ensure users cannot create invalid messages specifications. That capability does not currently exist for protocol definitions, but is being added. This will help ensure that users create all necessary elements of a service definition, and reduce user error. C# and Java Code Generation: Currently, JTS generates cross-platform C++ code. However, other languages including Java and C# are seeing a dramatic increase in their use in distributed systems, particularly in the development of graphical clients to embedded services. MS Word Document Generation: HTML and JSIDL output is supported, but native Office-Open-XML (OOXML) based MS Word generation has advantages in terms of output presentation, and ease of use for integration with other documents. Therefore, we plan to integrate MS Word service document generation. In addition, the development team has several additional goals that are not-yet-scheduled for a particular release window: Protocol Verification: This involves converting the JSIDL definition of a service into a PROMELA model, for validation by the SPIN model checking tool. Using PROMELA to model client and server interfaces will allow developers to formally validate JAUS services. End User Experience: We plan to conduct formal User Interface testing. This involves defining a set of tasks and use cases, asking users with various levels of JAUS experience to accomplish those tasks, and measuring performance and collecting feedback, to look for areas where the overall user experience can be improved. Improved Service Re-Use: JSIDL allows for inheritance of protocol descriptions, much like object-oriented programming languages allow child classes to re-use and extend behaviors defined by the parent class. At present, the generated code 'flattens' these state machines into a series of nested states which gives the correct interface behavior, but only if each single leaf (child) service is generated within its own component. This limits service re-use and can lead to a copy-and-paste of the same implementation across multiple components. The team is evaluating other inheritance solutions that would allow for multiple leaf (child) services to share access to a common parent, but at present the approach is sufficient to address the requirements of the JAUS Core Service Set. == Domains and application == The JAUS Tool Set is based on the JAUS Service Interface Definition Language (JSIDL), which was originally developed for application within the unmanned systems, or robotics, communities. As such, JTS has quickly gained acceptance as a tool for generation of services and interfaces compliant with the SAE AS-4 "JAUS" publications. Although usage statistics are not available, the Tool Set has been downloaded by representatives of US Army, Navy, Marines, and numerous defense contractors. It was also used in a commercial product called the JAUS Expansion Module sold by DeVivo AST, Inc. Since the JSIDL schema is independent of the data being exchanged, however, the Tool Set can be used for the design and implementation of a Service Oriented Architecture for any distributed systems environment that uses binary encoded message exchange. JSIDL is built on a two-layered architecture that separates the application layer and the transport layer, effectively decoupling the data being exchanges from the details of how that data moves from component to component. Furthermore, since the schema itself is widely generic, it's possible to define messages for any number of domains including but not limited to industrial control systems, remote monitoring and diagnostics, and web-based applications. == Licensing == JTS is released under the open source BSD license. The JSIDL Standard is available from the SAE. The Jr Middleware on which the Software Framework (Transport Layer) is based is open source under LGPL. Other packages distributed with JTS may have different licenses. == Sponsors == Development of the JAUS Tool Set was sponsored by several United States Department of Defense organizations: Office of Under Secretary of Defense for Acquisition, Technology & Logistics / Unmanned Warfare. Navy Program Executive Officer Littoral and Mine Navy Program Executive Officer Unmanned Aviation and Strike Weapons Office of Naval Research Air Force Research Lab

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  Visual Peer Review

  == Development and history == Visual Peer Review was first described in a 2017 classroom study by Friedman and Rosen, which examined how students evaluate peer-produced data visualizations using structured rubrics. Developed within the broader fields of data visualization, information visualization, and educational technology, the system emphasized clear labeling, visual integrity, and reduction of chartjunk. Students assigned rubric scores and provided written explanations, aligning the activity with established principles of peer review. Follow-up research expanded both the methodological and analytic dimensions of the framework. Friedman and colleagues applied natural language processing (NLP) to peer-review text to analyze part-of-speech patterns, sentence complexity, and comment length. These analyses offered insight into how students expressed critique and engaged with core design principles. Later studies incorporated advanced statistical modeling to evaluate system-level behavior, including peer review networks and reviewer typologies. Between 2021 and 2024, the framework underwent iterative refinement through a series of studies that explored interface design, behavioral nudges, reviewer engagement, and social network dynamics. The system was influenced by earlier work in computer-supported peer review—particularly My Reviewers, a rubric-based writing assessment platform developed by Joe Moxley at the University of South Florida. While Moxley's platform focused on text-based feedback, Visual Peer Review adapted its core structure to support critique of DataVis and visual analytics. To guide structured analysis and feedback, Friedman and Rosen also drew on the “what, why, and how” framework introduced by Liu and Stasko (2010), which emphasizes understanding a visualization's purpose, task alignment, and encoding strategy. == Framework and components == Visual Peer Review is designed to support critique, reflection, and learning in courses focusing on data visualization, visual analytics, and related fields in educational technology. The system consists of interconnected component. Core components include: Visual Artifacts: Students generate original visualizations using software such as R (e.g., ggplot2), Tableau, Python, or Adobe Illustrator. These artifacts may include statistical graphics, dashboards, or design-oriented infographics. Rubric-Based Assessment: Peer reviewers evaluate submitted visualizations using structured rubrics grounded in visualization theory and design heuristics. Rubric dimensions typically include: Use of labeling and axis scales Minimalization of chartjunk and clutter (following Tufte's principles) Optimization of the data–ink ratio Preservation of visual integrity through accurate representation (lie factor) Written Peer Comments: In addition to scoring, reviewers provide narrative feedback explaining their reasoning. These comments aim to improve design literacy, strengthen visual reasoning, and support the learning process common to peer review across educational contexts. Instructor Analytics Dashboard: Instructors access an analytics dashboard that displays peer-review activity across the course. Metrics include comment length, rubric coverage, participation patterns, and potential indicators of disengagement. These features position the framework within the domain of learning analytics, where visualized data helps instructors monitor student progress and identify support needs. == Ongoing development == Current work focuses on enhancing rubric structure, integrating principles from human–computer interaction, DataVis and expanding learning-analytics capabilities. Ongoing studies investigate how interface design, reviewer behavior, and classroom context influence the quality of feedback and overall engagement. Continuing development positions Visual Peer Review at the intersection of data visualization education, peer assessment, and educational technology.

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  Reverse data management

  Reverse data management describes a branch and set of research questions in relational database theory that aim to reverse the common focus of standard data management. Instead of focusing on the "forward" transformation of an input databases (a set of relational tables) to an output table, which is the main focus of standard query evaluation, reverse data management reverses that focus and studies the possible input database transformations that would achieve a desired output. Usually the objective is to find an intervention (a deletion, addition, or change of tuples) of minimal size, in order to achieve a particular change in the output. The problem has been studied at least since the 1980s, but has received renewed attention due to an influential paper in the early 2000s that made a connection between provenance and view propagation. The term was coined in a VLDB 2011 vision paper. The problem has been receiving significant attention in recent years due to its connection to computational fairness. == Topics in reverse data management problems == Example topics in reverse data management include: Deletion propagation with source side-effects: Find a minimal number of tuples to delete in the database in order to delete a particular tuple in the output. Deletion propagation with view side-effects: Find a set of tuples to delete in the database in order to delete a particular tuple in the output, while removing the minimal number of other output tuples. Causal responsibility: Find a minimal number of tuples to delete in the database in order to make a particular input tuple counterfactual. This notion is inspired by the notions of actual cause and causal responsibility from the work of Halpern and Pearl. Resilience: Find a minimal number of tuples to delete in the database in order to make a Boolean query false. The complexity of this problem is identical to the problem of deletion propagation with source-side effects over a different database. Smallest witness problem: Find a minimal number of tuples to keep in the a database (or equivalently, delete a maximal number of tuples) while keeping a particular tuple in the output. Minimum repair: Given a database that violates certain integrity constraints, find a minimal number of tuples to delete in the database in order to fulfill all constraints (also called to "repair" the database).

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