AI Chat UI Design

AI Chat UI Design — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Wide-column store

  A wide-column store (or extensible record store) is a type of NoSQL database. It uses tables, rows, and columns, but unlike a relational database, the names and format of the columns can vary from row to row in the same table. A wide-column store can be interpreted as a two-dimensional key–value store. Google's Bigtable is one of the prototypical examples of a wide-column store. == Wide-column stores versus columnar databases == Wide-column stores such as Bigtable and Apache Cassandra are not column stores in the original sense of the term, since their two-level structures do not use a columnar data layout. In genuine column stores, a columnar data layout is adopted such that each column is stored separately on disk. Wide-column stores do often support the notion of column families that are stored separately. However, each such column family typically contains multiple columns that are used together, similar to traditional relational database tables. Within a given column family, all data is stored in a row-by-row fashion, such that the columns for a given row are stored together, rather than each column being stored separately. Wide-column stores that support column families are also known as column family databases. == Notable examples == Notable wide-column stores include: Apache Accumulo Apache Cassandra Apache HBase Bigtable DataStax Enterprise (uses Apache Cassandra) DataStax Astra DB (uses Apache Cassandra) Hypertable Azure Tables ScyllaDB

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  Virtual directory

  In computing, the term virtual directory has a couple of meanings. It may simply designate (for example in IIS) a folder which appears in a path but which is not actually a subfolder of the preceding folder in the path. However, this article will discuss the term in the context of directory services and identity management. A virtual directory or virtual directory server (VDS) in this context is a software layer that delivers a single access point for identity management applications and service platforms. A virtual directory operates as a high-performance, lightweight abstraction layer that resides between client applications and disparate types of identity-data repositories, such as proprietary and standard directories, databases, web services, and applications. A virtual directory receives queries and directs them to the appropriate data sources by abstracting and virtualizing data. The virtual directory integrates identity data from multiple heterogeneous data stores and presents it as though it were coming from one source. This ability to reach into disparate repositories makes virtual directory technology ideal for consolidating data stored in a distributed environment. As of 2011, virtual directory servers most commonly use the LDAP protocol, but more sophisticated virtual directories can also support SQL as well as DSML and SPML. Industry experts have heralded the importance of the virtual directory in modernizing the identity infrastructure. According to Dave Kearns of Network World, "Virtualization is hot and a virtual directory is the building block, or foundation, you should be looking at for your next identity management project." In addition, Gartner analyst, Bob Blakley said that virtual directories are playing an increasingly vital role. In his report, “The Emerging Architecture of Identity Management,” Blakley wrote: “In the first phase, production of identities will be separated from consumption of identities through the introduction of a virtual directory interface.” == Capabilities == Virtual directories can have some or all of the following capabilities: Aggregate identity data across sources to create a single point of access. Create high-availability for authoritative data stores. Act as identity firewall by preventing denial-of-service attacks on the primary data stores through an additional virtual layer. Support a common searchable namespace for centralized authentication. Present a unified virtual view of user information stored across multiple systems. Delegate authentication to backend sources through source-specific security means. Virtualize data sources to support migration from legacy data stores without modifying the applications that rely on them. Enrich identities with attributes pulled from multiple data stores, based on a link between user entries. Some advanced identity virtualization platforms can also: Enable application-specific, customized views of identity data without violating internal or external regulations governing identity data. Reveal contextual relationships between objects through hierarchical directory structures. Develop advanced correlation across diverse sources using correlation rules. Build a global user identity by correlating unique user accounts across various data stores, and enrich identities with attributes pulled from multiple data stores, based on a link between user entries. Enable constant data refresh for real-time updates through a persistent cache. == Advantages == Virtual directories: Enable faster deployment because users do not need to add and sync additional application-specific data sources Leverage existing identity infrastructure and security investments to deploy new services Deliver high availability of data sources Provide application-specific views of identity data which can help avoid the need to develop a master enterprise schema Allow a single view of identity data without violating internal or external regulations governing identity data Act as identity firewalls by preventing denial-of-service attacks on the primary data-stores and providing further security on access to sensitive data Can reflect changes made to authoritative sources in real-time Leverages existing update processes of authoritative sources, so no separate (sometimes manual) process to update a central directory is needed Present a unified virtual view of user information from multiple systems so that it appears to reside in a single system Can secure all backend storage locations with a single security policy == Disadvantages == An original disadvantage is public perception of "push & pull technologies" which is the general classification of "virtual directories" depending on the nature of their deployment. Virtual directories were initially designed and later deployed with "push technologies" in mind, which also contravened with privacy laws of the United States. This is no longer the case. There are, however, other disadvantages in the current technologies. The classical virtual directory based on proxy cannot modify underlying data structures or create new views based on the relationships of data from across multiple systems. So if an application requires a different structure, such as a flattened list of identities, or a deeper hierarchy for delegated administration, a virtual directory is limited. Many virtual directories cannot correlate same-users across multiple diverse sources in the case of duplicate users Virtual directories without advanced caching technologies cannot scale to heterogeneous, high-volume environments. == Sample terminology == Unify metadata: Extract schemas from the local data source, map them to a common format, and link the same identities from different data silos based on a unique identifier. Namespace joining: Create a single large directory by bringing multiple directories together at the namespace level. For instance, if one directory has the namespace "ou=internal,dc=domain,dc=com" and a second directory has the namespace "ou=external,dc=domain,dc=com," then creating a virtual directory with both namespaces is an example of namespace joining. Identity joining: Enrich identities with attributes pulled from multiple data stores, based on a link between user entries. For instance if the user joeuser exists in a directory as "cn=joeuser,ou=users" and in a database with a username of "joeuser" then the "joeuser" identity can be constructed from both the directory and the database. Data remapping: The translation of data inside of the virtual directory. For instance, mapping “uid” to “samaccountname,” so a client application that only supports a standard LDAP-compliant data source is able to search an Active Directory namespace, as well. Query routing: Route requests based on certain criteria, such as “write operations going to a master, while read operations are forwarded to replicas.” Identity routing: Virtual directories may support the routing of requests based on certain criteria (such as write operations going to a master while read operations being forwarded to replicas). Authoritative source: A "virtualized" data repository, such as a directory or database, that the virtual directory can trust for user data. Server groups: Group one or more servers containing the same data and functionality. A typical implementation is the multi-master, multi-replica environment in which replicas process "read" requests and are in one server group, while masters process "write" requests and are in another, so that servers are grouped by their response to external stimuli, even though all share the same data. == Use cases == The following are sample use cases of virtual directories: Integrating multiple directory namespaces to create a central enterprise directory. Supporting infrastructure integrations after mergers and acquisitions. Centralizing identity storage across the infrastructure, making identity information available to applications through various protocols (including LDAP, JDBC, and web services). Creating a single access point for web access management (WAM) tools. Enabling web single sign-on (SSO) across varied sources or domains. Supporting role-based, fine-grained authorization policies Enabling authentication across different security domains using each domain’s specific credential checking method. Improving secure access to information both inside and outside of the firewall.

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  Whitehead's algorithm

  Whitehead's algorithm is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The algorithm is based on a classic 1936 paper of J. H. C. Whitehead. It is still unknown (except for the case n = 2) if Whitehead's algorithm has polynomial time complexity. == Statement of the problem == Let F n = F ( x 1 , … , x n ) {\displaystyle F_{n}=F(x_{1},\dots ,x_{n})} be a free group of rank n ≥ 2 {\displaystyle n\geq 2} with a free basis X = { x 1 , … , x n } {\displaystyle X=\{x_{1},\dots ,x_{n}\}} . The automorphism problem, or the automorphic equivalence problem for F n {\displaystyle F_{n}} asks, given two freely reduced words w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} whether there exists an automorphism φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} such that φ ( w ) = w ′ {\displaystyle \varphi (w)=w'} . Thus the automorphism problem asks, for w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} whether Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} . For w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} one has Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} if and only if Out ⁡ ( F n ) [ w ] = Out ⁡ ( F n ) [ w ′ ] {\displaystyle \operatorname {Out} (F_{n})[w]=\operatorname {Out} (F_{n})[w']} , where [ w ] , [ w ′ ] {\displaystyle [w],[w']} are conjugacy classes in F n {\displaystyle F_{n}} of w , w ′ {\displaystyle w,w'} accordingly. Therefore, the automorphism problem for F n {\displaystyle F_{n}} is often formulated in terms of Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} -equivalence of conjugacy classes of elements of F n {\displaystyle F_{n}} . For an element w ∈ F n {\displaystyle w\in F_{n}} , | w | X {\displaystyle |w|_{X}} denotes the freely reduced length of w {\displaystyle w} with respect to X {\displaystyle X} , and ‖ w ‖ X {\displaystyle \|w\|_{X}} denotes the cyclically reduced length of w {\displaystyle w} with respect to X {\displaystyle X} . For the automorphism problem, the length of an input w {\displaystyle w} is measured as | w | X {\displaystyle |w|_{X}} or as ‖ w ‖ X {\displaystyle \|w\|_{X}} , depending on whether one views w {\displaystyle w} as an element of F n {\displaystyle F_{n}} or as defining the corresponding conjugacy class [ w ] {\displaystyle [w]} in F n {\displaystyle F_{n}} . == History == The automorphism problem for F n {\displaystyle F_{n}} was algorithmically solved by J. H. C. Whitehead in a classic 1936 paper, and his solution came to be known as Whitehead's algorithm. Whitehead used a topological approach in his paper. Namely, consider the 3-manifold M n = # i = 1 n S 2 × S 1 {\displaystyle M_{n}=\#_{i=1}^{n}\mathbb {S} ^{2}\times \mathbb {S} ^{1}} , the connected sum of n {\displaystyle n} copies of S 2 × S 1 {\displaystyle \mathbb {S} ^{2}\times \mathbb {S} ^{1}} . Then π 1 ( M n ) ≅ F n {\displaystyle \pi _{1}(M_{n})\cong F_{n}} , and, moreover, up to a quotient by a finite normal subgroup isomorphic to Z 2 n {\displaystyle \mathbb {Z} _{2}^{n}} , the mapping class group of M n {\displaystyle M_{n}} is equal to Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} ; see. Different free bases of F n {\displaystyle F_{n}} can be represented by isotopy classes of "sphere systems" in M n {\displaystyle M_{n}} , and the cyclically reduced form of an element w ∈ F n {\displaystyle w\in F_{n}} , as well as the Whitehead graph of [ w ] {\displaystyle [w]} , can be "read-off" from how a loop in general position representing [ w ] {\displaystyle [w]} intersects the spheres in the system. Whitehead moves can be represented by certain kinds of topological "swapping" moves modifying the sphere system. Subsequently, Rapaport, and later, based on her work, Higgins and Lyndon, gave a purely combinatorial and algebraic re-interpretation of Whitehead's work and of Whitehead's algorithm. The exposition of Whitehead's algorithm in the book of Lyndon and Schupp is based on this combinatorial approach. Culler and Vogtmann, in their 1986 paper that introduced the Outer space, gave a hybrid approach to Whitehead's algorithm, presented in combinatorial terms but closely following Whitehead's original ideas. == Whitehead's algorithm == Our exposition regarding Whitehead's algorithm mostly follows Ch.I.4 in the book of Lyndon and Schupp, as well as. === Overview === The automorphism group Aut ⁡ ( F n ) {\displaystyle \operatorname {Aut} (F_{n})} has a particularly useful finite generating set W {\displaystyle {\mathcal {W}}} of Whitehead automorphisms or Whitehead moves. Given w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} the first part of Whitehead's algorithm consists of iteratively applying Whitehead moves to w , w ′ {\displaystyle w,w'} to take each of them to an "automorphically minimal" form, where the cyclically reduced length strictly decreases at each step. Once we find automorphically these minimal forms u , u ′ {\displaystyle u,u'} of w , w ′ {\displaystyle w,w'} , we check if ‖ u ‖ X = ‖ u ′ ‖ X {\displaystyle \|u\|_{X}=\|u'\|_{X}} . If ‖ u ‖ X ≠ ‖ u ′ ‖ X {\displaystyle \|u\|_{X}\neq \|u'\|_{X}} then w , w ′ {\displaystyle w,w'} are not automorphically equivalent in F n {\displaystyle F_{n}} . If ‖ u ‖ X = ‖ u ′ ‖ X {\displaystyle \|u\|_{X}=\|u'\|_{X}} , we check if there exists a finite chain of Whitehead moves taking u {\displaystyle u} to u ′ {\displaystyle u'} so that the cyclically reduced length remains constant throughout this chain. The elements w , w ′ {\displaystyle w,w'} are not automorphically equivalent in F n {\displaystyle F_{n}} if and only if such a chain exists. Whitehead's algorithm also solves the search automorphism problem for F n {\displaystyle F_{n}} . Namely, given w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} , if Whitehead's algorithm concludes that Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} , the algorithm also outputs an automorphism φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} such that φ ( w ) = w ′ {\displaystyle \varphi (w)=w'} . Such an element φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} is produced as the composition of a chain of Whitehead moves arising from the above procedure and taking w {\displaystyle w} to w ′ {\displaystyle w'} . === Whitehead automorphisms === A Whitehead automorphism, or Whitehead move, of F n {\displaystyle F_{n}} is an automorphism τ ∈ Aut ⁡ ( F n ) {\displaystyle \tau \in \operatorname {Aut} (F_{n})} of F n {\displaystyle F_{n}} of one of the following two types: There is a permutation σ ∈ S n {\displaystyle \sigma \in S_{n}} of { 1 , 2 , … , n } {\displaystyle \{1,2,\dots ,n\}} such that for i = 1 , … , n {\displaystyle i=1,\dots ,n} τ ( x i ) = x σ ( i ) ± 1 {\displaystyle \tau (x_{i})=x_{\sigma (i)}^{\pm 1}} Such τ {\displaystyle \tau } is called a Whitehead automorphism of the first kind. There is an element a ∈ X ± 1 {\displaystyle a\in X^{\pm 1}} , called the multiplier, such that for every x ∈ X ± 1 {\displaystyle x\in X^{\pm 1}} τ ( x ) ∈ { x , x a , a − 1 x , a − 1 x a } . {\displaystyle \tau (x)\in \{x,xa,a^{-1}x,a^{-1}xa\}.} Such τ {\displaystyle \tau } is called a Whitehead automorphism of the second kind. Since τ {\displaystyle \tau } is an automorphism of F n {\displaystyle F_{n}} , it follows that τ ( a ) = a {\displaystyle \tau (a)=a} in this case. Often, for a Whitehead automorphism τ ∈ Aut ⁡ ( F n ) {\displaystyle \tau \in \operatorname {Aut} (F_{n})} , the corresponding outer automorphism in Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} is also called a Whitehead automorphism or a Whitehead move. ==== Examples ==== Let F 4 = F ( x 1 , x 2 , x 3 , x 4 ) {\displaystyle F_{4}=F(x_{1},x_{2},x_{3},x_{4})} . Let τ : F 4 → F 4 {\displaystyle \tau :F_{4}\to F_{4}} be a homomorphism such that τ ( x 1 ) = x 2 x 1 , τ ( x 2 ) = x 2 , τ ( x 3 ) = x 2 x 3 x 2 − 1 , τ ( x 4 ) = x 4 {\displaystyle \tau (x_{1})=x_{2}x_{1},\quad \tau (x_{2})=x_{2},\quad \tau (x_{3})=x_{2}x_{3}x_{2}^{-1},\quad \tau (x_{4})=x_{4}} Then τ {\displaystyle \tau } is actually an automorphism of F 4 {\displaystyle F_{4}} , and, moreover, τ {\displaystyle \tau } is a Whitehead automorphism of the second kind, with the multiplier a = x 2 − 1 {\displaystyle a=x_{2}^{-1}} . Let τ ′ : F 4 → F 4 {\displaystyle \tau ':F_{4}\to F_{4}} be a homomorphism such that τ ′ ( x 1 ) = x 1 , τ ′ ( x 2 ) = x 1 − 1 x 2 x 1 , τ ′ ( x 3 ) = x 1 − 1 x 3 x 1 , τ ′ ( x 4 ) = x 1 − 1 x 4 x 1 {\displaystyle \tau '(x_{1})=x_{1},\quad \tau '(x_{2})=x_{1}^{-1}x_{2}x_{1},\quad \tau '(x_{3})=x_{1}^{-1}x_{3}x_{1},\quad \tau '(x_{4})=x_{1}^{-1}x_{4}x_{1}} Then τ ′ {\displaystyle \tau '} is actually an inner automorphism of F 4 {\displaystyle F_{4}} given by conjugation by x 1 {\displaystyle x_{1}} , and, moreover, τ ′ {\displaystyle \

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  Long division

  In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. It enables computations involving arbitrarily large numbers to be performed by following a series of simple steps. The abbreviated form of long division is called short division, which is almost always used instead of long division when the divisor has only one digit. == History == Related algorithms have existed since the 12th century. Al-Samawal al-Maghribi (1125–1174) performed calculations with decimal numbers that essentially require long division, leading to infinite decimal results, but without formalizing the algorithm. Caldrini (1491) is the earliest printed example of long division, known as the Danda method in medieval Italy, and it became more practical with the introduction of decimal notation for fractions by Pitiscus (1608). The specific algorithm in modern use was introduced by Henry Briggs c. 1600. == Education == Inexpensive calculators and computers have become the most common tools for performing division in educational and professional contexts worldwide, reducing reliance on traditional paper-and-pencil techniques. Internally, these devices implement various division algorithms, many of which rely on iterative approximations and multiplication to improve computational efficiency. Educational approaches to teaching division vary across countries and regions, reflecting differing curricular priorities. In North America, long division has been de-emphasized or, in some cases, removed from portions of the curriculum as part of reform mathematics, which emphasizes conceptual understanding and the use of technology. In contrast, many education systems in Europe and Asia continue to emphasize mastery of standard algorithms, including long division, as a foundational arithmetic skill. For example, curricula in countries such as Japan and Germany typically introduce and reinforce long division during primary education, often alongside mental arithmetic strategies and problem-solving techniques. International assessments such as the Trends in International Mathematics and Science Study (TIMSS) highlight these differences, showing variation in how procedural fluency and conceptual understanding are balanced across educational systems. These differing approaches reflect broader educational philosophies regarding the balance between procedural fluency, conceptual understanding, and the role of technology in mathematics education. == Method == In English-speaking countries, long division does not use the division slash ⟨∕⟩ or division sign ⟨÷⟩ symbols but instead constructs a tableau. The divisor is separated from the dividend by a right parenthesis ⟨)⟩ or vertical bar ⟨|⟩; the dividend is separated from the quotient by a vinculum (i.e., an overbar). The combination of these two symbols is sometimes known as a long division symbol, division bracket, or even a bus stop. It developed in the 18th century from an earlier single-line notation separating the dividend from the quotient by a left parenthesis. The process is begun by dividing the left-most digit of the dividend by the divisor. The quotient (rounded down to an integer) becomes the first digit of the result, and the remainder is calculated (this step is notated as a subtraction). This remainder carries forward when the process is repeated on the following digit of the dividend (notated as 'bringing down' the next digit to the remainder). When all digits have been processed and no remainder is left, the process is complete. An example is shown below, representing the division of 500 by 4 (with a result of 125). 125 (Explanations) 4)500 4 ( 4 × 1 = 4) 10 ( 5 - 4 = 1) 8 ( 4 × 2 = 8) 20 (10 - 8 = 2) 20 ( 4 × 5 = 20) 0 (20 - 20 = 0) A more detailed breakdown of the steps goes as follows: Find the shortest sequence of digits starting from the left end of the dividend, 500, that the divisor 4 goes into at least once. In this case, this is simply the first digit, 5. The largest number that the divisor 4 can be multiplied by without exceeding 5 is 1, so the digit 1 is put above the 5 to start constructing the quotient. Next, the 1 is multiplied by the divisor 4, to obtain the largest whole number that is a multiple of the divisor 4 without exceeding the 5 (4 in this case). This 4 is then placed under and subtracted from the 5 to get the remainder, 1, which is placed under the 4 under the 5. Afterwards, the first as-yet unused digit in the dividend, in this case the first digit 0 after the 5, is copied directly underneath itself and next to the remainder 1, to form the number 10. At this point the process is repeated enough times to reach a stopping point: The largest number by which the divisor 4 can be multiplied without exceeding 10 is 2, so 2 is written above as the second leftmost quotient digit. This 2 is then multiplied by the divisor 4 to get 8, which is the largest multiple of 4 that does not exceed 10; so 8 is written below 10, and the subtraction 10 minus 8 is performed to get the remainder 2, which is placed below the 8. The next digit of the dividend (the last 0 in 500) is copied directly below itself and next to the remainder 2 to form 20. Then the largest number by which the divisor 4 can be multiplied without exceeding 20, which is 5, is placed above as the third leftmost quotient digit. This 5 is multiplied by the divisor 4 to get 20, which is written below and subtracted from the existing 20 to yield the remainder 0, which is then written below the second 20. At this point, since there are no more digits to bring down from the dividend and the last subtraction result was 0, we can be assured that the process finished. If the last remainder when we ran out of dividend digits had been something other than 0, there would have been two possible courses of action: We could just stop there and say that the dividend divided by the divisor is the quotient written at the top with the remainder written at the bottom, and write the answer as the quotient followed by a fraction that is the remainder divided by the divisor. We could extend the dividend by writing it as, say, 500.000... and continue the process (using a decimal point in the quotient directly above the decimal point in the dividend), in order to get a decimal answer, as in the following example. 31.75 4)127.00 12 (12 ÷ 4 = 3) 07 (0 remainder, bring down next figure) 4 (7 ÷ 4 = 1 r 3) 3.0 (bring down 0 and the decimal point) 2.8 (7 × 4 = 28, 30 ÷ 4 = 7 r 2) 20 (an additional zero is brought down) 20 (5 × 4 = 20) 0 In this example, the decimal part of the result is calculated by continuing the process beyond the units digit, "bringing down" zeros as being the decimal part of the dividend. This example also illustrates that, at the beginning of the process, a step that produces a zero can be omitted. Since the first digit 1 is less than the divisor 4, the first step is instead performed on the first two digits 12. Similarly, if the divisor were 13, one would perform the first step on 127 rather than 12 or 1. === Basic procedure for long division of n ÷ m === Find the location of all decimal points in the dividend n and divisor m. If necessary, simplify the long division problem by moving the decimals of the divisor and dividend by the same number of decimal places, to the right (or to the left), so that the decimal of the divisor is to the right of the last digit. When doing long division, keep the numbers lined up straight from top to bottom under the tableau. After each step, be sure the remainder for that step is less than the divisor. If it is not, there are three possible problems: the multiplication is wrong, the subtraction is wrong, or a greater quotient is needed. In the end, the remainder, r, is added to the growing quotient as a fraction, r⁄m. === Invariant property and correctness === The basic presentation of the steps of the process (above) focuses on what steps are to be performed, rather than the properties of those steps that ensure the result will be correct (specifically, that q × m + r = n, where q is the final quotient and r the final remainder). A slight variation of presentation requires more writing, and requires that we change, rather than just update, digits of the quotient, but can shed more light on why these steps actually produce the right answer by allowing evaluation of q × m + r at intermediate points in the process. This illustrates the key property used in the derivation of the algorithm (below). Specifically, we amend the above basic procedure so that we fill the space after the digits of the quotient under construction with 0's, to at least the 1's place, and include those 0's in the numbers we write below the division bra

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  GPT-5

  GPT-5 is a multimodal large language model developed by OpenAI and the fifth in its series of generative pre-trained transformer (GPT) foundation models. Preceded in the series by GPT-4, it was launched on August 7, 2025. It is publicly accessible to users of the chatbot products ChatGPT and Microsoft Copilot as well as to developers through the OpenAI API. == Background == On April 14, 2023, Sam Altman, the chief executive officer of OpenAI, spoke at an event at the Massachusetts Institute of Technology and said that the company was not training GPT-5 at that time. He stated that OpenAI was "prioritizing GPT-4 development" and that "we are not and won't for some time" release GPT-5. On July 18, OpenAI filed for a "GPT-5" trademark in the United States. On November 13, Altman confirmed to the Financial Times that the company was working to develop GPT-5. According to The Information, "[f]or much of the second half of 2024, OpenAI was developing a model known internally as Orion and intended to become GPT-5", "[b]ut the Orion effort failed to produce a better model, and the company instead released it as GPT-4.5 in February [2025]." By late July 2025, OpenAI was widely anticipated as planning to release GPT-5 in early August. On July 30, The Verge reported that "Microsoft is getting ready for GPT-5" as "sources familiar with Microsoft's AI plans" told an editor that the company was testing a new mode for its Copilot chatbot that would offer a model that "thinks deeply or quickly based on the task". On August 5, in the leadup to the release of GPT-5, OpenAI released GPT-OSS, a set of two open-weight models that have reasoning capabilities. GPT-5 was then unveiled during a livestream event on August 7. == Capabilities == At the time of its release, GPT-5 had state-of-the-art performance on benchmarks that test mathematics, programming, finance, and multimodal understanding. According to OpenAI, improvements over its predecessor models include faster response times, better coding and writing skills, more accurate answers to health questions, and lower levels of hallucination. Also, compared to previous models, GPT-5 aims to give safe, high-level responses to potentially harmful queries rather than outright declining them, an approach that OpenAI refers to as "safe completions", aiming to result "in GPT-5 being able to refuse more unsafe questions, while offering fewer rejections to users seeking harmless information." In addition, GPT-5 was trained to give more critical, "less effusively agreeable" answers compared to its predecessor models. Days before the launch of GPT-5, two early testers of the model stated that they were "impressed" by its ability to code and to solve mathematical and scientific problems. They suggested that the model shows great improvement from GPT-4, but not as large of a gain as from GPT-3 to GPT-4. A day prior to the release of GPT-5, during a press briefing, Sam Altman, the chief executive officer of OpenAI, called GPT-5 "a significant step along the path to AGI", referring to artificial general intelligence, the hypothetical level of intelligence that OpenAI defines as the ability to perform any economically valuable task that a human can. According to Altman, GPT-5 is "significantly better" than its predecessors, offering "PhD-level" abilities across a wide range of tasks. The exact energy consumption of GPT-5 use has not been disclosed by OpenAI. Researchers at the University of Rhode Island estimated that a medium-length response consumes slightly over 18 watt-hours, equivalent to using an incandescent bulb for 18 minutes. === Architecture === GPT-5 is a system that contains a fast, high-throughput model, a deeper reasoning model, and a real-time router that decides which model to use based on conversation type, complexity, tool needs, and explicit user intent. Altman had previously criticized the manual model picker for being overly complex, suggesting a need for unification. GPT-5 also includes agentic functionality through which it can set up its own desktop and can use its browser to search autonomously for sources that relate to its task. The GPT-5 system card defines two fast, high-throughput models – gpt-5-main and gpt-5-main-mini – and two thinking models – gpt-5-thinking and gpt-5-thinking-mini. In the OpenAI API, developers can access the thinking model, its mini version, and gpt-5-thinking-nano, an even smaller and faster nano version of the thinking model. The version of GPT-5 that is accessible via the API has adjustable reasoning effort (low, medium, high, or minimal) and verbosity (low, medium, or high). Additionally, ChatGPT provides access to gpt-5-thinking with a setting that makes use of parallel test-time compute, referred to as gpt-5-thinking-pro. == Limitations == === Safety === Neuraltrust, a security research company, claimed to have successfully compromised GPT-5 within its first day of testing the model. According to its report, it enabled GPT-5 to generate detailed instructions for manufacturing explosive devices. SPLX, another company, conducted similar tests and came to similar conclusions about GPT-5's security. Their assessments suggest that GPT-5 has significant security gaps, potentially rendering it as being unsafe for use in a corporate environment. == Training == According to AIMultiple, GPT-5 is natively multimodal, meaning that it was trained from scratch on multiple modalities (like text and images) at once without relying on already-trained language or vision models. Its training process involved three stages: unsupervised pretraining, supervised fine-tuning, and reinforcement learning from human feedback. Pretraining used a large-scale multilingual dataset of books, articles, web pages, academic papers, and licensed sources. GPT-5's visual and text capabilities were described as having been developed alongside each other throughout training, unlike with GPT-4. == Use == GPT-5 is used in ChatGPT. Although GPT-5 is free for all ChatGPT users, Plus users get higher use limits while Pro users get unlimited access to GPT-5 as well as limited access to GPT-5 Pro. Standard limits for lower-tier users on responses per hour still apply. Additionally, with the introduction of GPT-5, ChatGPT's "Advanced Voice Mode" was replaced by "ChatGPT Voice", which is supposed to enable more natural-sounding conversations. OpenAI stated that "Standard Voice Mode retires on September 9, 2025, unifying all users on ChatGPT Voice". On November 24, 2025, the feature of shopping research was added to ChatGPT, claimed to be a mini model post-trained on gpt-5-thinking-mini. GPT-5 is also available in Microsoft Copilot, and Microsoft stated that it will incorporate GPT-5 into a wide variety of its products. According to 9to5Mac, Apple Inc. is planning to integrate the model into the Apple Intelligence feature in its iOS 26, iPadOS 26, and macOS Tahoe operating systems. It is also accessible via the OpenAI API. A number of American companies were reported as having received access to GPT-5 ahead of its launch. OpenAI stated that the private health insurance company Oscar Health was checking applications from its policyholders with the model. In addition, Uber was using GPT-5 for its customer support system; GitLab, Windsurf, and Cursor were using the model for software development; and the Spanish bank BBVA was using it for financial analysis. Other companies that OpenAI listed as having used GPT-5 pre-release include Amgen, Lowe's, and Notion. == Reception == === Critical reviews === Grace Huckins in MIT Technology Review found that, "[w]hereas o1 was a major technological advancement, GPT-5 is, above all else, a refined product." In response to claims that Sam Altman, the chief executive officer of OpenAI, had made about the model, she stated that "GPT-5 will furnish a more pleasant and seamless user experience. That's not nothing, but it falls far short of the transformative AI future that Altman has spent much of the past year hyping." In response to Altman's claim that GPT-5 is "a significant step along the path" to artificial general intelligence, she noted: "[M]aybe he's right—but if so, it's a very small step." In The Information, Stephanie Palazzolo praised GPT-5's coding capabilities. According to Matteo Wong in The Atlantic, GPT-5 "is intuitive, fast, and efficient; adapts to human preferences and intentions; and is easy to personalize." He stated: "At this stage of the AI boom, when every major chatbot is legitimately helpful in numerous ways, benchmarks, science, and rigor feel almost insignificant. What matters is how the chatbot feels [...]". John Herrman from the New York magazine wrote: "Casual users who encounter GPT-5 through ChatGPT aren't likely to feel like they're using a completely different product [...] while people who use it for software development or in a corporate context are more likely to notice a major change." Mashable's Christian de Looper found that "GPT-5

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  BuildingSMART Data Dictionary

  buildingSMART Data Dictionary (bSDD) is a service provided by buildingSMART which offers free data dictionaries for the international standardization of construction planning. The structure of bSDD was defined by the Nonprofit organization Buildingsmart and is used to describe objects and their attributes in a BIM process. == Aim == The aim of bSDD is to enable architects and planners to exchange and share building data across different specialists and language boundaries and thus avoid misunderstandings caused by different interpretations of terms. The bSDD standard extends the more general IFC. Software developers can access and use the dictionaries. In May 2025 over 300 dictionaries are available, including IFC, extensions to it such as Airport Domain IFC extension module or classification systems like Uniclass. == Structure == The main structural parts of bSDD are: Dictionary: A dictionary is a collection of classes: Class: A class describes the various object types, such as Bag drop or Baggage conveyor in airport planning. A class contains properties: Property: A property describes a part of a class, e.g. color or weight. Related properties are organized in a group: GroupOfProperties: A group organizes related properties, e.g. environmental properties or electrical properties. == Creating and managing a directory == Every dictionary in bSDD must be published in the name of a registered organization. As soon as the content is activated, it receives an unchangeable URI. This means that the content remains permanently in bSDD and cannot be deleted - this ensures stable use of the dictionary. It is only possible to change the status to inactive if it is no longer to be used - however, the dictionary remains permanently.

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  Data drilling

  Data drilling (also drilldown) refers to any of various operations and transformations on tabular, relational, and multidimensional data. The term has widespread use in various contexts, but is primarily associated with specialized software designed specifically for data analysis. == Common data drilling operations == There are certain operations that are common to applications that allow data drilling. Among them are: Query operations: tabular query pivot query === Tabular query === Tabular query operations consist of standard operations on data tables. Among these operations are: search sort filter (by value) filter (by extended function or condition) transform (e.g., by adding or removing columns) Consider the following example: Fred and Wilma table (Fig 001): gender, fname, lname, home male, fred, chopin, Poland male, fred, flintstone, bedrock male, fred, durst, usa female, wilma, flintstone, bedrock female, wilma, rudolph, usa female, wilma, webb, usa male, fred, johnson, usa The preceding is an example of a simple flat file table formatted as comma-separated values. The table includes first name, last name, gender and home country for various people named fred or wilma. Although the example is formatted this way, it is important to emphasize that tabular query operations (as well as all data drilling operations) can be applied to any conceivable data type, regardless of the underlying formatting. The only requirement is that the data be readable by the software application in use. === Pivot query === A pivot query allows multiple representations of data according to different dimensions. This query type is similar to tabular query, except it also allows data to be represented in summary format, according to a flexible user-selected hierarchy. This class of data drilling operation is formally, (and loosely) known by different names, including crosstab query, pivot table, data pilot, selective hierarchy, intertwingularity and others. To illustrate the basics of pivot query operations, consider the Fred and Wilma table (Fig 001). A quick scan of the data reveals that the table has redundant information. This redundancy could be consolidated using an outline or a tree structure or in some other way. Moreover, once consolidated, the data could have many different alternate layouts. Using a simple text outline as output, the following alternate layouts are all possible with a pivot query: Summarize by gender (Fig 001): female flintstone, wilma rudolph, wilma webb, wilma male chopin, fred flintstone, fred durst, fred johnson, fred (Dimensions = gender; Tabular fields = lname, fname;) Summarize by home, lname (Fig 001): bedrock flintstone fred wilma Poland chopin fred usa ... (Dimensions = home, lname; Tabular fields = fname;) ==== Uses ==== Pivot query operations are useful for summarizing a corpus of data in multiple ways, thereby illustrating different representations of the same basic information. Although this type of operation appears prominently in spreadsheets and desktop database software, its flexibility is arguably under-utilized. There are many applications that allow only a 'fixed' hierarchy for representing data, and this represents a substantial limitation. == Drillup == Drillup is the opposite of drilldown. For example, if you drilldown to see the revenue of one product, then you might want to drillup to see the revenue of all products.

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  Physical schema

  A physical data model (or database design) is a representation of a data design as implemented, or intended to be implemented, in a database management system. In the lifecycle of a project it typically derives from a logical data model, though it may be reverse-engineered from a given database implementation. A complete physical data model will include all the database artifacts required to create relationships between tables or to achieve performance goals, such as indexes, constraint definitions, linking tables, partitioned tables or clusters. Analysts can usually use a physical data model to calculate storage estimates; it may include specific storage allocation details for a given database system. As of 2012 seven main databases dominate the commercial marketplace: Informix, Oracle, Postgres, SQL Server, Sybase, IBM Db2 and MySQL. Other RDBMS systems tend either to be legacy databases or used within academia such as universities or further education colleges. Physical data models for each implementation would differ significantly, not least due to underlying operating-system requirements that may sit underneath them. For example: SQL Server runs only on Microsoft Windows operating-systems (Starting with SQL Server 2017, SQL Server runs on Linux. It's the same SQL Server database engine, with many similar features and services regardless of your operating system), while Oracle and MySQL can run on Solaris, Linux and other UNIX-based operating-systems as well as on Windows. This means that the disk requirements, security requirements and many other aspects of a physical data model will be influenced by the RDBMS that a database administrator (or an organization) chooses to use. == Physical schema == Physical schema is a term used in data management to describe how data is to be represented and stored (files, indices, etc.) in secondary storage using a particular database management system (DBMS) (e.g., Oracle RDBMS, Sybase SQL Server, etc.). In the ANSI/SPARC Architecture three schema approach, the internal schema is the view of data that involved data management technology. This is as opposed to an external schema that reflects an individual's view of the data, or the conceptual schema that is the integration of a set of external schemas. The logical schema was the way data were represented to conform to the constraints of a particular approach to database management. At that time the choices were hierarchical and network. Describing the logical schema, however, still did not describe how physically data would be stored on disk drives. That is the domain of the physical schema. Now logical schemas describe data in terms of relational tables and columns, object-oriented classes, and XML tags. A single set of tables, for example, can be implemented in numerous ways, up to and including an architecture where table rows are maintained on computers in different countries.

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  Multi-armed bandit

  In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is named from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. More generally, it is a problem in which a decision maker iteratively selects one of multiple fixed choices (i.e., arms or actions) when the properties of each choice are only partially known at the time of allocation, and may become better understood as time passes. A fundamental aspect of bandit problems is that choosing an arm does not affect the properties of the arm or other arms. Instances of the multi-armed bandit problem include the task of iteratively allocating a fixed, limited set of resources between competing (alternative) choices in a way that minimizes the regret. A notable alternative setup for the multi-armed bandit problem includes the "best arm identification (BAI)" problem where the goal is instead to identify the best choice by the end of a finite number of rounds. The multi-armed bandit problem is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. In contrast to general reinforcement learning, the selected actions in bandit problems do not affect the reward distribution of the arms. The multi-armed bandit problem also falls into the broad category of stochastic scheduling. In the problem, each machine provides a random reward from a probability distribution specific to that machine, that is not known a priori. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between "exploitation" of the machine that has the highest expected payoff and "exploration" to get more information about the expected payoffs of the other machines. The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company. In early versions of the problem, the gambler begins with no initial knowledge about the machines. Herbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward. == Empirical motivation == The multi-armed bandit problem models an agent that simultaneously attempts to acquire new knowledge (called "exploration") and optimize their decisions based on existing knowledge (called "exploitation"). The agent attempts to balance these competing tasks in order to maximize their total value over the period of time considered. There are many practical applications of the bandit model, for example: clinical trials investigating the effects of different experimental treatments while minimizing patient losses, adaptive routing efforts for minimizing delays in a network, financial portfolio design In these practical examples, the problem requires balancing reward maximization based on the knowledge already acquired with attempting new actions to further increase knowledge. This is known as the exploitation vs. exploration tradeoff in machine learning. The model has also been used to control dynamic allocation of resources to different projects, answering the question of which project to work on, given uncertainty about the difficulty and payoff of each possibility. Originally considered by Allied scientists in World War II, it proved so intractable that, according to Peter Whittle, the problem was proposed to be dropped over Germany so that German scientists could also waste their time on it. The version of the problem now commonly analyzed was formulated by Herbert Robbins in 1952. == The multi-armed bandit model == The multi-armed bandit (short: bandit or MAB) can be seen as a set of real distributions B = { R 1 , … , R K } {\displaystyle B=\{R_{1},\dots ,R_{K}\}} , each distribution being associated with the rewards delivered by one of the K ∈ N + {\displaystyle K\in \mathbb {N} ^{+}} levers. Let μ 1 , … , μ K {\displaystyle \mu _{1},\dots ,\mu _{K}} be the mean values associated with these reward distributions. The gambler iteratively plays one lever per round and observes the associated reward. The objective is to maximize the sum of the collected rewards. The horizon H {\displaystyle H} is the number of rounds that remain to be played. The bandit problem is formally equivalent to a one-state Markov decision process. The regret ρ {\displaystyle \rho } after T {\displaystyle T} rounds is defined as the expected difference between the reward sum associated with an optimal strategy and the sum of the collected rewards: ρ = T μ ∗ − ∑ t = 1 T r ^ t {\displaystyle \rho =T\mu ^{}-\sum _{t=1}^{T}{\widehat {r}}_{t}} , where μ ∗ {\displaystyle \mu ^{}} is the maximal reward mean, μ ∗ = max k { μ k } {\displaystyle \mu ^{}=\max _{k}\{\mu _{k}\}} , and r ^ t {\displaystyle {\widehat {r}}_{t}} is the reward in round t {\displaystyle t} . A zero-regret strategy is a strategy whose average regret per round ρ / T {\displaystyle \rho /T} tends to zero with probability 1 when the number of played rounds tends to infinity. Intuitively, zero-regret strategies are guaranteed to converge to a (not necessarily unique) optimal strategy if enough rounds are played. == Variations == A common formulation is the Binary multi-armed bandit or Bernoulli multi-armed bandit, which issues a reward of one with probability p {\displaystyle p} , and otherwise a reward of zero. Another formulation of the multi-armed bandit has each arm representing an independent Markov machine. Each time a particular arm is played, the state of that machine advances to a new one, chosen according to the Markov state evolution probabilities. There is a reward depending on the current state of the machine. In a generalization called the "restless bandit problem", the states of non-played arms can also evolve over time. There has also been discussion of systems where the number of choices (about which arm to play) increases over time. Computer science researchers have studied multi-armed bandits under worst-case assumptions, obtaining algorithms to minimize regret in both finite and infinite (asymptotic) time horizons for both stochastic and non-stochastic arm payoffs. === Best arm identification === An important variation of the classical regret minimization problem in multi-armed bandits is best arm identification (BAI), also known as pure exploration. This problem is crucial in various applications, including clinical trials, adaptive routing, recommendation systems, and A/B testing. In BAI, the objective is to identify the arm having the highest expected reward. An algorithm in this setting is characterized by a sampling rule, a decision rule, and a stopping rule, described as follows: Sampling rule: ( a t ) t ≥ 1 {\displaystyle (a_{t})_{t\geq 1}} is a sequence of actions at each time step Stopping rule: τ {\displaystyle \tau } is a (random) stopping time which suggests when to stop collecting samples Decision rule: a ^ τ {\displaystyle {\hat {a}}_{\tau }} is a guess on the best arm based on the data collected up to time τ {\displaystyle \tau } There are two predominant settings in BAI: Fixed budget setting: Given a time horizon T ≥ 1 {\displaystyle T\geq 1} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} minimizing probability of error δ {\displaystyle \delta } . Fixed confidence setting: Given a confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} with the least possible amount of trials and with probability of error P ( a ^ τ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau }\neq a^{\star })\leq \delta } . For example using a decision rule, we could use m 1 {\displaystyle m_{1}} where m {\displaystyle m} is the machine no.1 (you can use a different variable respectively) and 1 {\displaystyle 1} is the amount for each time an attempt is made at pulling the lever, where ∫ ∑ m 1 , m 2 , ( . . . ) = M {\displaystyle \int \sum m_{1},m_{2},(...)=M} , identify M {\displaystyle M} as the sum of each attempts m 1 + m 2 {\displaystyle m_{1}+m_{2}} , (...) as needed, and from there you can get a ratio, sum or mean as quantitative probability and sample your formulation for each slots. You can also do ∫ ∑ k ∝ i N − (

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  Virtual facility

  A Virtual Facility (VF) is a highly realistic digital representation of a data center, used to model all relevant aspects of a physical data center with a high degree of precision. The term "virtual" in Virtual Facility refers to its use of virtual reality, rather than the abstraction of computer resources as seen in platform virtualization. The VF mirrors the characteristics of a physical facility over time and allows for detailed analysis and modeling. == VF Model features == A standard VF model includes: Three-dimensional physical facility layout Network connectivity of facility equipment Full inventory of facility equipment, including electronics and electrical systems such as power distribution units (PDUs) and uninterruptible power supplies (UPSs) Full air conditioning system (ACUs) and controls within the room The term Virtual Facility was introduced to address the emerging environmental problems facing modern Mission Critical Facilities (MCFs). This concept combines virtual reality (VR), computer simulation, and expert systems applied to the domain of facilities. The VF type of computer simulation allows for detailed analysis and prototyping of airflow in the data center using computational fluid dynamics (CFD) techniques. This enables the visualization and numerical analysis of airflow and temperatures within the facility, helping to predict real-world outcomes. == VF applications == The VF model can be used to assist with the following: Greenfield design Asset management Troubleshooting existing data centers Making existing data centers more resilient Making existing data centers more energy efficient Cost prediction Staff training Capacity planning Load growth management Many organizations use VF models to virtually assess scenarios before committing resources to physical changes. This allows for better decision-making regarding the addition or modification of equipment, helping to avoid logistical or thermal problems.

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  Enterprise information integration

  Enterprise information integration (EII) is the ability to support a unified view of data and information for an entire organization. The goal of EII is to get a large set of heterogeneous data sources to appear to a user or system as a single, homogeneous data source. In a data virtualization application of EII, there is a process of information integration, using data abstraction to provide a unified interface (known as uniform data access) for viewing all the data within an organization, and a single set of structures and naming conventions (known as uniform information representation) to represent this data. == Overview == Data within an enterprise can be stored in heterogeneous formats, including relational databases (which themselves come in a large number of varieties), text files, XML files, spreadsheets and a variety of proprietary storage methods, each with their own indexing and data access methods. Standardized data access APIs have emerged that offer a specific set of commands to retrieve and modify data from a generic data source. Many applications exist that implement these APIs' commands across various data sources, most notably relational databases. Such APIs include ODBC, JDBC, XQJ, OLE DB, and more recently ADO.NET. There are also standard formats for representing data within a file that are very important to information integration. The best-known of these is XML, which has emerged as a standard universal representation format. There are also more specific XML "grammars" defined for specific types of data such as Geography Markup Language for expressing geographical features and Directory Service Markup Language for holding directory-style information. In addition, non-XML standard formats exist such as iCalendar for representing calendar information and vCard for business card information. Enterprise Information Integration (EII) applies data integration commercially. Despite the theoretical problems described above, the private sector shows more concern with the problems of data integration as a viable product. EII emphasizes neither correctness nor tractability, but speed and simplicity. === Uniform data access === Uniform data access means connectivity and controllability across numerous target data sources. Necessary to fields such as EII and Electronic Data Interchange (EDI), it is most often used regarding analysis of disparate data types and data sources, which must be rendered into a uniform information representation, and generally must appear homogenous to the analysis tools—when the data being analyzed is typically heterogeneous and widely varying in size, type, and original representation. === Uniform information representation === Uniform information representation allows information from several realms or disciplines to be displayed and worked with as if it came from the same realm or discipline. It takes information from a number of sources, which may have used different methodologies and metrics in their data collection, and builds a single large collection of information, where some records may be more complete than others across all fields of data Uniform information representation is particularly important in EII and Electronic Data Interchange (EDI), where different departments of a large organization may have collected information for different purposes, with different labels and units, until one department realized that data already collected by those other departments could be re-purposed for their own needs—saving the enterprise the effort and cost of re-collecting the same information. === Combining disparate data sets === Each data source is disparate and as such is not designed to support EII. Therefore, data virtualization as well as data federation depends upon accidental data commonality to support combining data and information from disparate data sets. Because of this lack of data value commonality across data sources, the return set may be inaccurate, incomplete, and impossible to validate. One solution is to recast disparate databases to integrate these databases without the need for ETL. The recast databases support commonality constraints where referential integrity may be enforced between databases. The recast databases provide designed data access paths with data value commonality across databases. === Simplicity of deployment === Even if recognized as a solution to a problem, EII as of 2009 currently takes time to apply and offers complexities in deployment. Proposed schema-less solutions include "Lean Middleware". === Handling higher-order information === Analysts experience difficulty—even with a functioning information integration system—in determining whether the sources in the database will satisfy a given application. Answering these kinds of questions about a set of repositories requires semantic information like metadata and/or ontologies. == Applications == EII products enable loose coupling between homogeneous-data consuming client applications and services and heterogeneous-data stores. Such client applications and services include Desktop Productivity Tools (spreadsheets, word processors, presentation software, etc.), development environments and frameworks (Java EE, .NET, Mono, SOAP or RESTful Web services, etc.), business intelligence (BI), business activity monitoring (BAM) software, enterprise resource planning (ERP), Customer relationship management (CRM), business process management (BPM and/or BPEL) Software, and web content management (CMS). == Data access technologies == Service Data Objects (SDO) for Java, C++ and .Net clients and any type of data source XQuery and XQuery API for Java

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  BRS/Search

  BRS/Search is a full-text database and information retrieval system. BRS/Search uses a fully inverted indexing system to store, locate, and retrieve unstructured data. It was the search engine that in 1977 powered Bibliographic Retrieval Services (BRS) commercial operations with 20 databases (including the first national commercial availability of MEDLINE); it has changed ownership several times during its development and is currently sold as Livelink ECM Discovery Server by Open Text Corporation. == Early development == Development on what was to become BRS began as Biomedical Communications Network (BCN) at the State University of New York at Albany (SUNY). BCN, which went online in 1968, provided on-line access to nine databases, including MEDLINE and BIOSIS Previews, to large universities and medical schools primarily in the Northeast of the USA. State funding for the project was withdrawn in 1975, and Bibliographic Retrieval Services (BRS) was formed as a non-profit concern the following year. It was incorporated in May 1976 as a for-profit corporation with Ron Quake as president, Jan Egeland as vice president in charge of marketing and training, and Lloyd Palmer as vice president of systems. == BRS commercial operations == In December 1976, the First BRS User Meeting was held in Syracuse, New York, and by January 1977 BRS started commercial operations with 20 databases (including the first national commercial availability of MEDLINE) and 9 million records, using modified IBM STAIRS (STorage And Information Retrieval System) software, Telenet for telecommunications, and timesharing mainframe computers of Carrier Corporation. In October 1980 BRS was sold by Egeland and Quake to Indian Head, Inc., a subsidiary of the Dutch company Thyssen-Bornemisza Group. == 1989–1993 == In 1989 Robert Maxwell acquired BRS and the BRS/Search software; he announced the planned incorporation of the ORBIT Search Service and BRS Information Technologies and renamed the whole group Maxwell Online, Inc. At that time BRS Information Technologies was serving the medical and academic library marketplace with over 150 databases. Maxwell later bought the publishing company Macmillan and put Maxwell Online under Macmillan. In the same year BRS/LINK (hypertext connection of databases; first application delivering full text) was announced. The initial BRS/LINK application "relates the citation in a bibliographic database to its full-text article in a second database," and "eliminates the need to re-execute a search strategy in the second database in order to find the corresponding full-text article." Initially BRS/LINK supported linking only selected bibliographic databases: MEDLINE, Health Planning and Administration, and MEDLINE References on AIDS to the full-text Comprehensive Core Medical Library. At the time of Robert Maxwell’s death in 1991, Macmillan brought in Andrew Gregory to represent the company during the 2 years that Maxwell’s affairs were being settled and to prepare Maxwell Online to be able to sell the components. Maxwell Online shortly thereafter underwent yet another name change, this time to InfoPro Technologies. == Dataware Technologies ownership of BRS/SEARCH == Early in 1994, InfoPro Technologies, a subsidiary of MHC Inc. (holding company for Macmillan Inc.), the former Maxwell Online service, sold off all its subsidiaries. ORBIT Search Services went to the French-owned Questel, the dial-up BRS Search Services to CD Plus Technologies (later to become OVID), and BRS Software Products (including BRS/SEARCH) to Dataware Technologies. Almost up to the end of InfoPro Technologies, BRS Software had been the fastest growing segment of the company. At the 14th BRS North American Users Group Conference in 1999, Dave Schubmehl of Dataware Technologies presented a paper in which he stated "The purpose of this presentation is to update BRS users on upcoming releases of BRS/Search, NetAnswer, and other Dataware products. BRS/Search 7.0 will include features specifically requested by customers, as well as other enhancements. Earlier this year, Dataware acquired Sovereign Hill Software, makers of InQuery. In light of that acquisition, and Dataware's other development projects, we'll look at Dataware's plans for all products, including BRS/Search and NetAnswer." == Open Text acquisition of BRS/Search == In 2001 BRS/Search was acquired by Open Text and became LiveLink ECM Discovery Server. It is now referred to as Open Text Discovery Server. Open Text still supports both BRS/Search and NetAnswer. The core BRS/Search technology in the Open Text portfolio was augmented with other capabilities through various acquisitions. For example, Dataware's acquisition of Sovereign-Hill brought InQuery, “a probabilistic information retrieval system using an inference network”, which was developed by the University of Massachusetts Amherst Center for Intelligent Information Retrieval] out of the UMass CIIR and into the marketplace. A product re-branding table shows the range of products, their old names and their new names. InQuery is a concept search engine that uses noun phrases, parts of speech and other co-occurrence relationships in overlapping passages of text rather than single term inverted indexes of single words in documents. Open Text's portfolio has grown to include Hummingbird Content Management, and has always included BASIS. == 2003 == BRS/Search North America User's Group (BRSNAUG) website with a June 8, 2003 date listed the following features for BRS/Search. The BRSNAUG also disincorporated in 2003. Cross-references to BRS/Search on the World Wide Web point to Open Text Livelink. Engine features include: Rapid query response time. Numerical data handling and elementary statistical processing (sum, avg, min, max) Search results weighting and relevancy ranking Left- and right-truncation and expansion of search terms Superior data compression – loaded databases typically use only about 1.5 times the input stream size in disk space Large capacity databases – up to 100 million documents, each with up to 65,000 paragraphs Fine control of indexing and searching – right down to the word, sentence, and paragraph level Fine control over data security. Document access can be controlled at the database, document, and paragraph level International language support for all 7/8 bit characters sets and customizable language tables Flexible and customizable stop word lists ANSI-compatible thesauri Hypertext links within and between documents and databases (R6.x) Support for natural language parsing of queries Automatic document summarization tools Client/Server development Programming interfaces for World-Wide Web (HTTP, HTML) access to databases

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  Excalidraw

  Excalidraw is an open-source, web-based virtual whiteboard and diagramming application. It is used to create diagrams, wireframes, and sketches within a web browser without requiring account registration. The software features a characteristic hand-drawn visual style and supports real-time multi-user collaboration using client-side end-to-end encryption. Excalidraw is released under the MIT License and is maintained by Excalidraw s.r.o., a company based in Brno, Czech Republic. == History == Excalidraw was created on 1 January 2020 by Christopher Chedeau, a software engineer at Meta Platforms. Chedeau, who previously co-created React Native and Prettier, initially developed the application as a personal project before registering the domain on 3 January 2020. Within its first months, the project attracted open-source contributors who assisted in expanding its features and rewriting the codebase into TypeScript and React. By early 2021, day-to-day operations moved to Czech developers David Luzar and Milos Vetesnik. In May 2021, the team incorporated Excalidraw s.r.o. in Brno and launched a commercial cloud-based version named Excalidraw+ to fund the open-source project's development. By May 2026, the main open-source repository on GitHub had accumulated over 123,000 stars. == Features and architecture == The application provides an infinite canvas for geometric shapes, lines, arrows, text, and freehand drawing. Its visual presentation relies on Rough.js, a JavaScript graphics library that alters standard vector paths to mimic irregular, hand-drawn lines. Excalidraw operates as a Progressive web application (PWA), allowing local installation and offline usage, saving data natively to local browser storage. Files use a native, JSON-based extension format (.excalidraw), and canvases can be exported to PNG or SVG formats. Real-time collaboration sessions are executed using Socket.IO via a relay server. Data transmission uses the browser's native Web Cryptography API to achieve end-to-end encryption. A symmetric AES key is generated on the client side and appended to the sharing URL as a fragment identifier (following the # character). Because web browsers do not transmit URL fragments to HTTP servers, the data remains unreadable to the distribution server. == Ecosystem == Excalidraw is distributed as an npm package, allowing third-party developers to embed the whiteboard component directly into external React web applications. Community-developed extensions integrate the application's file format into text editors and note-taking systems, including Visual Studio Code and Obsidian. The platform also has native integrations in commercial platforms such as Notion and HackerRank. == Reception == Google's developer relations team published a technical case study on Excalidraw as a reference implementation for Progressive Web Apps. The analysis highlighted the software's adoption of advanced web platform capabilities, specifically its utilization of the File System Access API and native Clipboard API to replicate desktop software behavior within a web browser environment.

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  Semantic translation

  Semantic translation is the process of using semantic information to aid in the translation of data in one representation or data model to another representation or data model. Semantic translation takes advantage of semantics that associate meaning with individual data elements in one dictionary to create an equivalent meaning in a second system. An example of semantic translation is the conversion of XML data from one data model to a second data model using formal ontologies for each system such as the Web Ontology Language (OWL). This is frequently required by intelligent agents that wish to perform searches on remote computer systems that use different data models to store their data elements. The process of allowing a single user to search multiple systems with a single search request is also known as federated search. Semantic translation should be differentiated from data mapping tools that do simple one-to-one translation of data from one system to another without actually associating meaning with each data element. Semantic translation requires that data elements in the source and destination systems have "semantic mappings" to a central registry or registries of data elements. The simplest mapping is of course where there is equivalence. There are three types of Semantic equivalence: Class Equivalence - indicating that class or "concepts" are equivalent. For example: "Person" is the same as "Individual" Property Equivalence - indicating that two properties are equivalent. For example: "PersonGivenName" is the same as "FirstName" Instance Equivalence - indicating that two individual instances of objects are equivalent. For example: "Dan Smith" is the same person as "Daniel Smith" Semantic translation is very difficult if the terms in a particular data model do not have direct one-to-one mappings to data elements in a foreign data model. In that situation, an alternative approach must be used to find mappings from the original data to the foreign data elements. This problem can be alleviated by centralized metadata registries that use the ISO-11179 standards such as the National Information Exchange Model (NIEM).

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  Knowledge organization

  Knowledge organization (KO), organization of knowledge, organization of information, or information organization is an intellectual discipline concerned with activities such as document description, indexing, and classification that serve to provide systems of representation and order for knowledge and information objects. According to The Organization of Information by Joudrey and Taylor, information organization: examines the activities carried out and tools used by people who work in places that accumulate information resources (e.g., books, maps, documents, datasets, images) for the use of humankind, both immediately and for posterity. It discusses the processes that are in place to make resources findable, whether someone is searching for a single known item or is browsing through hundreds of resources just hoping to discover something useful. Information organization supports a myriad of information-seeking scenarios. Issues related to knowledge sharing can be said to have been an important part of knowledge management for a long time. Knowledge sharing has received a lot of attention in research and business practice both within and outside organizations and its different levels. Sharing knowledge is not only about giving it to others, but it also includes searching, locating, and absorbing knowledge. Unawareness of the employees' work and duties tends to provoke the repetition of mistakes, the waste of resources, and duplication of the same projects. Motivating co-workers to share their knowledge is called knowledge enabling. It leads to trust among individuals and encourages a more open and proactive relationship that grants the exchange of information easily. Knowledge sharing is part of the three-phase knowledge management process which is a continuous process model. The three parts are knowledge creation, knowledge implementation, and knowledge sharing. The process is continuous, which is why the parts cannot be fully separated. Knowledge creation is the consequence of individuals' minds, interactions, and activities. Developing new ideas and arrangements alludes to the process of knowledge creation. Using the knowledge which is present at the company in the most effective manner stands for the implementation of knowledge. Knowledge sharing, the most essential part of the process for our topic, takes place when two or more people benefit by learning from each other. Traditional human-based approaches performed by librarians, archivists, and subject specialists are increasingly challenged by computational (big data) algorithmic techniques. KO as a field of study is concerned with the nature and quality of such knowledge-organizing processes (KOP) (such as taxonomy and ontology) as well as the resulting knowledge organizing systems (KOS). == Theoretical approaches == === Traditional approaches === Among the major figures in the history of KO are Melvil Dewey (1851–1931) and Henry Bliss (1870–1955). Dewey's goal was an efficient way to manage library collections; not an optimal system to support users of libraries. His system was meant to be used in many libraries as a standardized way to manage collections. The first version of this system was created in 1876. An important characteristic in Henry Bliss' (and many contemporary thinkers of KO) was that the sciences tend to reflect the order of Nature and that library classification should reflect the order of knowledge as uncovered by science: The implication is that librarians, in order to classify books, should know about scientific developments. This should also be reflected in their education: Again from the standpoint of the higher education of librarians, the teaching of systems of classification ... would be perhaps better conducted by including courses in the systematic encyclopedia and methodology of all the sciences, that is to say, outlines which try to summarize the most recent results in the relation to one another in which they are now studied together. ... (Ernest Cushing Richardson, quoted from Bliss, 1935, p. 2) Among the other principles, which may be attributed to the traditional approach to KO are: Principle of controlled vocabulary Cutter's rule about specificity Hulme's principle of literary warrant (1911) Principle of organizing from the general to the specific Today, after more than 100 years of research and development in LIS, the "traditional" approach still has a strong position in KO and in many ways its principles still dominate. === Facet analytic approaches === The date of the foundation of this approach may be chosen as the publication of S. R. Ranganathan's colon classification in 1933. The approach has been further developed by, in particular, the British Classification Research Group. The best way to explain this approach is probably to explain its analytico-synthetic methodology. The meaning of the term "analysis" is: breaking down each subject into its basic concepts. The meaning of the term synthesis is: combining the relevant units and concepts to describe the subject matter of the information package in hand. Given subjects (as they appear in, for example, book titles) are first analyzed into a few common categories, which are termed "facets". Ranganathan proposed his PMEST formula: Personality, Matter, Energy, Space and Time: Personality is the distinguishing characteristic of a subject. Matter is the physical material of which a subject may be composed. Energy is any action that occurs with respect to the subject. Space is the geographic component of the location of a subject. Time is the period associated with a subject. === The information retrieval tradition (IR) === Important in the IR-tradition have been, among others, the Cranfield experiments, which were founded in the 1950s, and the TREC experiments (Text Retrieval Conferences) starting in 1992. It was the Cranfield experiments, which introduced the measures "recall" and "precision" as evaluation criteria for systems efficiency. The Cranfield experiments found that classification systems like UDC and facet-analytic systems were less efficient compared to free-text searches or low level indexing systems ("UNITERM"). The Cranfield I test found, according to Ellis (1996, 3–6) the following results: Although these results have been criticized and questioned, the IR-tradition became much more influential while library classification research lost influence. The dominant trend has been to regard only statistical averages. What has largely been neglected is to ask: Are there certain kinds of questions in relation to which other kinds of representation, for example, controlled vocabularies, may improve recall and precision? === User-oriented and cognitive views === The best way to define this approach is probably by method: Systems based upon user-oriented approaches must specify how the design of a system is made on the basis of empirical studies of users. User studies demonstrated very early that users prefer verbal search systems as opposed to systems based on classification notations. This is one example of a principle derived from empirical studies of users. Adherents of classification notations may, of course, still have an argument: That notations are well-defined and that users may miss important information by not considering them. Folksonomies is a recent kind of KO based on users' rather than on librarians' or subject specialists' indexing. === Bibliometric approaches === These approaches are primarily based on using bibliographical references to organize networks of papers, mainly by bibliographic coupling (introduced by Kessler 1963) or co-citation analysis ( independently suggested by Marshakova 1973 and Small 1973). In recent years it has become a popular activity to construe bibliometric maps as structures of research fields. Two considerations are important in considering bibliometric approaches to KO: The level of indexing depth is partly determined by the number of terms assigned to each document. In citation indexing this corresponds to the number of references in a given paper. On the average, scientific papers contain 10–15 references, which provide quite a high level of depth. The references, which function as access points, are provided by the highest subject-expertise: The experts writing in the leading journals. This expertise is much higher than that which library catalogs or bibliographical databases typically are able to draw on. === The domain analytic approach === Domain analysis is a sociological-epistemological standpoint that advocates that the indexing of a given document should reflect the needs of a given group of users or a given ideal purpose. In other words, any description or representation of a given document is more or less suited to the fulfillment of certain tasks. A description is never objective or neutral, and the goal is not to standardize descriptions or make one description once and for all for different target groups. The develo

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