AI Data Flow Diagram Generator

AI Data Flow Diagram Generator — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Contrast-to-noise ratio

  Contrast-to-noise ratio (CNR) is a measure used to determine image quality. CNR is similar to the metric signal-to-noise ratio (SNR), but subtracts a term before taking the ratio. This is important when there is a significant bias in an image, such as from haze. As can be seen in the picture at right, the intensity is rather high even though the features of the image are washed out by the haze. Thus this image may have a high SNR metric, but will have a low CNR metric. One way to define contrast-to-noise ratio is: C = | S A − S B | σ o {\displaystyle C={\frac {|S_{A}-S_{B}|}{\sigma _{o}}}} where SA and SB are signal intensities for signal producing structures A and B in the region of interest and σo is the standard deviation of the pure image noise.

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  Flajolet–Martin algorithm

  The Flajolet–Martin algorithm is an algorithm for approximating the number of distinct elements in a stream with a single pass and space-consumption logarithmic in the maximal number of possible distinct elements in the stream (the count-distinct problem). The algorithm was introduced by Philippe Flajolet and G. Nigel Martin in their 1984 article "Probabilistic Counting Algorithms for Data Base Applications". Later it has been refined in "LogLog counting of large cardinalities" by Marianne Durand and Philippe Flajolet, and "HyperLogLog: The analysis of a near-optimal cardinality estimation algorithm" by Philippe Flajolet et al. In their 2010 article "An optimal algorithm for the distinct elements problem", Daniel M. Kane, Jelani Nelson and David P. Woodruff give an improved algorithm, which uses nearly optimal space and has optimal O(1) update and reporting times. == The algorithm == Assume that we are given a hash function h a s h ( x ) {\displaystyle \mathrm {hash} (x)} that maps input x {\displaystyle x} to integers in the range [ 0 ; 2 L − 1 ] {\displaystyle [0;2^{L}-1]} , and where the outputs are sufficiently uniformly distributed. Note that the set of integers from 0 to 2 L − 1 {\displaystyle 2^{L}-1} corresponds to the set of binary strings of length L {\displaystyle L} . For any non-negative integer y {\displaystyle y} , define b i t ( y , k ) {\displaystyle \mathrm {bit} (y,k)} to be the k {\displaystyle k} -th bit in the binary representation of y {\displaystyle y} , such that: y = ∑ k ≥ 0 b i t ( y , k ) 2 k . {\displaystyle y=\sum _{k\geq 0}\mathrm {bit} (y,k)2^{k}.} We then define a function ρ ( y ) {\displaystyle \rho (y)} that outputs the position of the least-significant set bit in the binary representation of y {\displaystyle y} , and L {\displaystyle L} if no such set bit can be found as all bits are zero: ρ ( y ) = { min { k ≥ 0 ∣ b i t ( y , k ) ≠ 0 } y > 0 L y = 0 {\displaystyle \rho (y)={\begin{cases}\min\{k\geq 0\mid \mathrm {bit} (y,k)\neq 0\}&y>0\\L&y=0\end{cases}}} Note that with the above definition we are using 0-indexing for the positions, starting from the least significant bit. For example, ρ ( 13 ) = ρ ( 1101 2 ) = 0 {\displaystyle \rho (13)=\rho (1101_{2})=0} , since the least significant bit is a 1 (0th position), and ρ ( 8 ) = ρ ( 1000 2 ) = 3 {\displaystyle \rho (8)=\rho (1000_{2})=3} , since the least significant set bit is at the 3rd position. At this point, note that under the assumption that the output of our hash function is uniformly distributed, then the probability of observing a hash output ending with 2 k {\displaystyle 2^{k}} (a one, followed by k {\displaystyle k} zeroes) is 2 − ( k + 1 ) {\displaystyle 2^{-(k+1)}} , since this corresponds to flipping k {\displaystyle k} heads and then a tail with a fair coin. Now the Flajolet–Martin algorithm for estimating the cardinality of a multiset M {\displaystyle M} is as follows: Initialize a bit-vector BITMAP to be of length L {\displaystyle L} and contain all 0s. For each element x {\displaystyle x} in M {\displaystyle M} : Calculate the index i = ρ ( h a s h ( x ) ) {\displaystyle i=\rho (\mathrm {hash} (x))} . Set B I T M A P [ i ] = 1 {\displaystyle \mathrm {BITMAP} [i]=1} . Let R {\displaystyle R} denote the smallest index i {\displaystyle i} such that B I T M A P [ i ] = 0 {\displaystyle \mathrm {BITMAP} [i]=0} . Estimate the cardinality of M {\displaystyle M} as 2 R / ϕ {\displaystyle 2^{R}/\phi } , where ϕ ≈ 0.77351 {\displaystyle \phi \approx 0.77351} . The idea is that if n {\displaystyle n} is the number of distinct elements in the multiset M {\displaystyle M} , then B I T M A P [ 0 ] {\displaystyle \mathrm {BITMAP} [0]} is accessed approximately n / 2 {\displaystyle n/2} times, B I T M A P [ 1 ] {\displaystyle \mathrm {BITMAP} [1]} is accessed approximately n / 4 {\displaystyle n/4} times and so on. Consequently, if i ≫ log 2 ⁡ n {\displaystyle i\gg \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} is almost certainly 0, and if i ≪ log 2 ⁡ n {\displaystyle i\ll \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} is almost certainly 1. If i ≈ log 2 ⁡ n {\displaystyle i\approx \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} can be expected to be either 1 or 0. The correction factor ϕ ≈ 0.77351 {\displaystyle \phi \approx 0.77351} (OEIS: A244256) is found by calculations, which can be found in the original article. == Improving accuracy == A problem with the Flajolet–Martin algorithm in the above form is that the results vary significantly. A common solution has been to run the algorithm multiple times with k {\displaystyle k} different hash functions and combine the results from the different runs. One idea is to take the mean of the k {\displaystyle k} results together from each hash function, obtaining a single estimate of the cardinality. The problem with this is that averaging is very susceptible to outliers (which are likely here). A different idea is to use the median, which is less prone to be influences by outliers. The problem with this is that the results can only take form 2 R / ϕ {\displaystyle 2^{R}/\phi } , where R {\displaystyle R} is integer. A common solution is to combine both the mean and the median: Create k ⋅ l {\displaystyle k\cdot l} hash functions and split them into k {\displaystyle k} distinct groups (each of size l {\displaystyle l} ). Within each group use the mean for aggregating together the l {\displaystyle l} results, and finally take the median of the k {\displaystyle k} group estimates as the final estimate. The 2007 HyperLogLog algorithm splits the multiset into subsets and estimates their cardinalities, then it uses the harmonic mean to combine them into an estimate for the original cardinality.

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  Algorithmic paradigm

  An algorithmic paradigm or algorithm design paradigm is a generic model or framework which underlies the design of a class of algorithms. An algorithmic paradigm is an abstraction higher than the notion of an algorithm, just as an algorithm is an abstraction higher than a computer program. == List of well-known paradigms == === General === Backtracking Branch and bound Brute-force search Divide and conquer Dynamic programming Greedy algorithm Recursion Prune and search === Parameterized complexity === Kernelization Iterative compression === Computational geometry === Sweep line algorithms Rotating calipers Randomized incremental construction

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  Query language

  A query language, also known as data query language or database query language (DQL), is a computer language used to make queries in databases and information systems. In database systems, query languages rely on strict theory to retrieve information. A well known example is the Structured Query Language (SQL). == Types == Broadly, query languages can be classified according to whether they are database query languages or information retrieval query languages. The difference is that a database query language attempts to give factual answers to factual questions, while an information retrieval query language attempts to find documents containing information that is relevant to an area of inquiry. Other types of query languages include: Full-text. The simplest query language is treating all terms as bag of words that are to be matched with the postings in the inverted index and where subsequently ranking models are applied to retrieve the most relevant documents. Only tokens are defined in the CFG. Web search engines often use this approach. Boolean. A query language that also supports the use of the Boolean operators AND, OR, NOT. Structured. A language that supports searching within (a combination of) fields when a document is structured and has been indexed using its document structure. Natural language. A query language that supports natural language by parsing the natural language query to a form that can be best used to retrieve relevant documents, for example with Question answering systems or conversational search. == Examples == Attempto Controlled English is a query language that is also a controlled natural language. AQL is a query language for the ArangoDB native multi-model database system. .QL is a proprietary object-oriented query language for querying relational databases; successor of Datalog. CodeQL is the analysis engine used by developers to automate security checks, and by security researchers to perform variant analysis on GitHub. Contextual Query Language (CQL) a formal language for representing queries to information retrieval systems such as web indexes or bibliographic catalogues. Cypher is a query language for the Neo4j graph database. DMX is a query language for data mining models. Datalog is a query language for deductive databases. F-logic is a declarative object-oriented language for deductive databases and knowledge representation. FQL enables you to use a SQL-style interface to query the data exposed by the Graph API. It provides advanced features not available in the Graph API. Gellish English is a language that can be used for queries in Gellish English Databases, for dialogues (requests and responses) as well as for information modeling and knowledge modeling. Gremlin is an Apache Software Foundation graph traversal language for OLTP and OLAP graph systems. GraphQL is a data query language developed by Facebook as an alternate to REST and ad-hoc webservice architectures. HTSQL is a query language that translates HTTP queries to SQL. ISBL is a query language for PRTV, one of the earliest relational database management systems. Jaql is a functional data processing and query language most commonly used for JSON query processing. JPQL is a query language defined as part of Jakarta Persistence (used in Java applications to make queries to a relational DB using entity objects instead of DB tables). jq is a functional programming language often used for processing queries against one or more JSON documents, including very large ones. JSONiq is a declarative query language designed for collections of JSON documents. KQL (Kusto Query Language), a query language by Microsoft used in Azure Data Explorer LDAP is an application protocol for querying and modifying directory services running over TCP/IP. LogiQL is a variant of Datalog and is the query language for the LogicBlox system. M Formula language, a mashup query language used in Microsoft's Power Query. MQL is a cheminformatics query language for a substructure search allowing beside nominal properties also numerical properties. MDX is a query language for OLAP databases. N1QL is a Couchbase's query language finding data in Couchbase Servers. Object Query Language OCL (Object Constraint Language). Despite its name, OCL is also an object query language and an OMG standard. OPath, intended for use in querying WinFS Stores. Poliqarp Query Language is a special query language designed to analyze annotated text. Used in the Poliqarp search engine. PQL is a special-purpose programming language for managing process models based on information about scenarios that these models describe. PRQL PRQL (Pipelined Relational Query Language) is a modern language for transforming data. Consists of a curated set of orthogonal transformations, which are combined together to form a pipeline. PTQL based on relational queries over program traces, allowing programmers to write expressive, declarative queries about program behavior. QUEL is a relational database access language, similar in most ways to SQL. RDQL is a RDF query language. SMARTS is the cheminformatics standard for a substructure search. SPARQL is a query language for RDF graphs. SQL is a well-known query language and data manipulation language for relational databases. XQuery is a query language for XML data sources. XPath is a declarative language for navigating XML documents. YQL is an SQL-like query language created by Yahoo!. Search engine query languages, e.g., as used by Google. or Bing

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  Voice user interface

  A voice user interface (VUI) enables spoken human interaction with computers, using speech recognition to understand spoken commands and answer questions, and typically text to speech to play a reply. A voice command device is a device controlled with a voice user interface. Voice user interfaces have been added to automobiles, home automation systems, computer operating systems, home appliances like washing machines and microwave ovens, and television remote controls. They are the primary way of interacting with virtual assistants on smartphones and smart speakers. Older automated attendants (which route phone calls to the correct extension) and interactive voice response systems (which conduct more complicated transactions over the phone) can respond to the pressing of keypad buttons via DTMF tones, but those with a full voice user interface allow callers to speak requests and responses without having to press any buttons. Newer voice command devices are speaker-independent, so they can respond to multiple voices, regardless of accent or dialectal influences. They are also capable of responding to several commands at once, separating vocal messages, and providing appropriate feedback, accurately imitating a natural conversation. == Overview == A VUI is the interface to any speech application. Only a short time ago, controlling a machine by simply talking to it was only possible in science fiction. Until recently, this area was considered to be artificial intelligence. However, advances in technologies like text-to-speech, speech-to-text, natural language processing, and cloud services contributed to the mass adoption of these types of interfaces. VUIs have become more commonplace, and people are taking advantage of the value that these hands-free, eyes-free interfaces provide in many situations. VUIs rely on the ability to process input reliably, inconsistent performance often leads to decreased user engagement and negative feedback. Designing a good VUI requires interdisciplinary talents of computer science, linguistics and human factors such as psychology. Even with advanced development tools, constructing an effective VUI requires understanding of both the tasks to be performed, as well as the target audience that will use the final system. The closer the VUI matches the user's mental model of the task, the easier it will be to use with little or no training, resulting in both higher efficiency and higher user satisfaction. A VUI designed for the general public should emphasize ease of use and provide a lot of help and guidance for first-time callers. In contrast, a VUI designed for a small group of power users (including field service workers), should focus more on productivity and less on help and guidance. Such applications should streamline the call flows, minimize prompts, eliminate unnecessary iterations and allow elaborate "mixed initiative dialogs", which enable callers to enter several pieces of information in a single utterance and in any order or combination. In short, speech applications have to be carefully crafted for the specific business process that is being automated. Not all business processes render themselves equally well for speech automation. In general, the more complex the inquiries and transactions are, the more challenging they will be to automate, and the more likely they will be to fail with the general public. In some scenarios, automation is simply not applicable, so live agent assistance is the only option. A legal advice hotline, for example, would be very difficult to automate. On the flip side, speech is perfect for handling quick and routine transactions, like changing the status of a work order, completing a time or expense entry, or transferring funds between accounts. == History == Early applications for VUI included voice-activated dialing of phones, either directly or through a (typically Bluetooth) headset or vehicle audio system. In 2007, a CNN business article reported that voice command was over a billion dollar industry and that companies like Google and Apple were trying to create speech recognition features. In the years since the article was published, the world has witnessed a variety of voice command devices. Additionally, Google has created a speech recognition engine called Pico TTS and Apple released Siri. Voice command devices are becoming more widely available, and innovative ways for using the human voice are always being created. For example, Business Week suggests that the future remote controller is going to be the human voice. Currently Xbox Live allows such features and Jobs hinted at such a feature on the new Apple TV. == Voice command software products on computing devices == Both Apple Mac and Windows PC provide built in speech recognition features for their latest operating systems. === Microsoft Windows === Two Microsoft operating systems, Windows 7 and Windows Vista, provide speech recognition capabilities. Microsoft integrated voice commands into their operating systems to provide a mechanism for people who want to limit their use of the mouse and keyboard, but still want to maintain or increase their overall productivity. ==== Windows Vista ==== With Windows Vista voice control, a user may dictate documents and emails in mainstream applications, start and switch between applications, control the operating system, format documents, save documents, edit files, efficiently correct errors, and fill out forms on the Web. The speech recognition software learns automatically every time a user uses it, and speech recognition is available in English (U.S.), English (U.K.), German (Germany), French (France), Spanish (Spain), Japanese, Chinese (Traditional), and Chinese (Simplified). In addition, the software comes with an interactive tutorial, which can be used to train both the user and the speech recognition engine. ==== Windows 7 ==== In addition to all the features provided in Windows Vista, Windows 7 provides a wizard for setting up the microphone and a tutorial on how to use the feature. ==== Mac OS X ==== All Mac OS X computers come pre-installed with the speech recognition software. The software is user-independent, and it allows for a user to, "navigate menus and enter keyboard shortcuts; speak checkbox names, radio button names, list items, and button names; and open, close, control, and switch among applications." However, the Apple website recommends a user buy a commercial product called Dictate. === Commercial products === If a user is not satisfied with the built in speech recognition software or a user does not have a built speech recognition software for their OS, then a user may experiment with a commercial product such as Braina Pro or DragonNaturallySpeaking for Windows PCs, and Dictate, the name of the same software for Mac OS. == Voice command mobile devices == Any mobile device running Android OS, Microsoft Windows Phone, iOS 9 or later, or Blackberry OS provides voice command capabilities. In addition to the built-in speech recognition software for each mobile phone's operating system, a user may download third party voice command applications from each operating system's application store: Apple App store, Google Play, Windows Phone Marketplace (initially Windows Marketplace for Mobile), or BlackBerry App World. === Android OS === Google has developed an open source operating system called Android, which allows a user to perform voice commands such as: send text messages, listen to music, get directions, call businesses, call contacts, send email, view a map, go to websites, write a note, and search Google. The speech recognition software is available for all devices since Android 2.2 "Froyo", but the settings must be set to English. Google allows for the user to change the language, and the user is prompted when he or she first uses the speech recognition feature if he or she would like their voice data to be attached to their Google account. If a user decides to opt into this service, it allows Google to train the software to the user's voice. Google introduced the Google Assistant with Android 7.0 "Nougat". It is much more advanced than the older version. Amazon.com has the Echo that uses Amazon's custom version of Android to provide a voice interface. === Microsoft Windows === Windows Phone is Microsoft's mobile device's operating system. On Windows Phone 7.5, the speech app is user independent and can be used to: call someone from your contact list, call any phone number, redial the last number, send a text message, call your voice mail, open an application, read appointments, query phone status, and search the web. In addition, speech can also be used during a phone call, and the following actions are possible during a phone call: press a number, turn the speaker phone on, or call someone, which puts the current call on hold. Windows 10 introduces Cortana, a voice control system that replaces the formerly used voice control on Windows

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  Artisto

  Artisto is a video processing application with art and movie effects filters based on neural network algorithms created in 2016 by Mail.ru Group machine learning specialists. At the moment the application can process videos up to 10 seconds long and offers users 21 filters, including those based on the works of famous artists (e.g. Blue Dream — Pablo Picasso), theme-based (Rio-2016 — related to the 2016 Summer Olympics in Rio de Janeiro) and others. The app works with both pre-recorded videos and videos recorded with the application. == History == Information on the application first appeared on Mail.ru Group Vice President Anna Artamonova's FB page on July 29, 2016. At the moment of posting there was only an Android version available. According to Anna, the application's first version only took eight days to develop. On July 31, the application was added to the AppStore for free download. From this moment and continuing into the present, Artisto has been the world's first app that uses neural networks for editing short videos, processing them in the style of famous artworks or any other source image. Prisma (app) application developers promise to deliver similar functionality at any moment. The application soon won recognition and started to attract the attention of both international brands (e.g. Korean auto manufacturer Kia Motors) and popular singers and musicians. According to the independent App Annie analysis system, within the first two weeks on the market the application made it onto the TOP download lists in nine countries. == Technology == The idea of transferring styles from works of famous artists to images was first mentioned in September 2015 after the publication of Leon Gatys's article "A Neural Algorithm of Artistic Style", where he described the algorithm in detail. The major shortcoming of this algorithm is its slow performance, which is up to dozens of seconds depending on the algorithm's settings. In March 2016, Russian researcher Dmitry Ulyanov's article was published, where he invented a way to improve the generation of stylized pictures using additional neuron generator network training. With this approach, stylized images can be generated within just dozens of milliseconds. Seventeen days after Ulyanov's article, Justin Johnson published an article containing an identical idea, the only difference being the structure of the generator network. The Artisto application was developed using these open-source technologies, which Mail.ru Group's machine learning specialists improved for faster video processing and better quality.

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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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  Bartels–Stewart algorithm

  In numerical linear algebra, the Bartels–Stewart algorithm is used to numerically solve the Sylvester matrix equation A X − X B = C {\displaystyle AX-XB=C} . Developed by R.H. Bartels and G.W. Stewart in 1971, it was the first numerically stable method that could be systematically applied to solve such equations. The algorithm works by using the real Schur decompositions of A {\displaystyle A} and B {\displaystyle B} to transform A X − X B = C {\displaystyle AX-XB=C} into a triangular system that can then be solved using forward or backward substitution. In 1979, G. Golub, C. Van Loan and S. Nash introduced an improved version of the algorithm, known as the Hessenberg–Schur algorithm. It remains a standard approach for solving Sylvester equations when X {\displaystyle X} is of small to moderate size. == The algorithm == Let X , C ∈ R m × n {\displaystyle X,C\in \mathbb {R} ^{m\times n}} , and assume that the eigenvalues of A {\displaystyle A} are distinct from the eigenvalues of B {\displaystyle B} . Then, the matrix equation A X − X B = C {\displaystyle AX-XB=C} has a unique solution. The Bartels–Stewart algorithm computes X {\displaystyle X} by applying the following steps: 1.Compute the real Schur decompositions R = U T A U , {\displaystyle R=U^{T}AU,} S = V T B T V . {\displaystyle S=V^{T}B^{T}V.} The matrices R {\displaystyle R} and S {\displaystyle S} are block-upper triangular matrices, with diagonal blocks of size 1 × 1 {\displaystyle 1\times 1} or 2 × 2 {\displaystyle 2\times 2} . 2. Set F = U T C V . {\displaystyle F=U^{T}CV.} 3. Solve the simplified system R Y − Y S T = F {\displaystyle RY-YS^{T}=F} , where Y = U T X V {\displaystyle Y=U^{T}XV} . This can be done using forward substitution on the blocks. Specifically, if s k − 1 , k = 0 {\displaystyle s_{k-1,k}=0} , then ( R − s k k I ) y k = f k + ∑ j = k + 1 n s k j y j , {\displaystyle (R-s_{kk}I)y_{k}=f_{k}+\sum _{j=k+1}^{n}s_{kj}y_{j},} where y k {\displaystyle y_{k}} is the k {\displaystyle k} th column of Y {\displaystyle Y} . When s k − 1 , k ≠ 0 {\displaystyle s_{k-1,k}\neq 0} , columns [ y k − 1 ∣ y k ] {\displaystyle [y_{k-1}\mid y_{k}]} should be concatenated and solved for simultaneously. 4. Set X = U Y V T . {\displaystyle X=UYV^{T}.} === Computational cost === Using the QR algorithm, the real Schur decompositions in step 1 require approximately 10 ( m 3 + n 3 ) {\displaystyle 10(m^{3}+n^{3})} flops, so that the overall computational cost is 10 ( m 3 + n 3 ) + 2.5 ( m n 2 + n m 2 ) {\displaystyle 10(m^{3}+n^{3})+2.5(mn^{2}+nm^{2})} . === Simplifications and special cases === In the special case where B = − A T {\displaystyle B=-A^{T}} and C {\displaystyle C} is symmetric, the solution X {\displaystyle X} will also be symmetric. This symmetry can be exploited so that Y {\displaystyle Y} is found more efficiently in step 3 of the algorithm. == The Hessenberg–Schur algorithm == The Hessenberg–Schur algorithm replaces the decomposition R = U T A U {\displaystyle R=U^{T}AU} in step 1 with the decomposition H = Q T A Q {\displaystyle H=Q^{T}AQ} , where H {\displaystyle H} is an upper-Hessenberg matrix. This leads to a system of the form H Y − Y S T = F {\displaystyle HY-YS^{T}=F} that can be solved using forward substitution. The advantage of this approach is that H = Q T A Q {\displaystyle H=Q^{T}AQ} can be found using Householder reflections at a cost of ( 5 / 3 ) m 3 {\displaystyle (5/3)m^{3}} flops, compared to the 10 m 3 {\displaystyle 10m^{3}} flops required to compute the real Schur decomposition of A {\displaystyle A} . == Software and implementation == The subroutines required for the Hessenberg-Schur variant of the Bartels–Stewart algorithm are implemented in the SLICOT library. These are used in the MATLAB control system toolbox. == Alternative approaches == For large systems, the O ( m 3 + n 3 ) {\displaystyle {\mathcal {O}}(m^{3}+n^{3})} cost of the Bartels–Stewart algorithm can be prohibitive. When A {\displaystyle A} and B {\displaystyle B} are sparse or structured, so that linear solves and matrix vector multiplies involving them are efficient, iterative algorithms can potentially perform better. These include projection-based methods, which use Krylov subspace iterations, methods based on the alternating direction implicit (ADI) iteration, and hybridizations that involve both projection and ADI. Iterative methods can also be used to directly construct low rank approximations to X {\displaystyle X} when solving A X − X B = C {\displaystyle AX-XB=C} .

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  Trustworthy computing

  The term trustworthy computing (TwC) has been applied to computing systems that are inherently secure, available, and reliable. It is particularly associated with the Microsoft initiative of the same name, launched in 2002. == History == Until 1995, there were restrictions on commercial traffic over the Internet. On, May 26, 1995, Bill Gates sent the "Internet Tidal Wave" memorandum to Microsoft executives assigning "...the Internet this highest level of importance..." but Microsoft's Windows 95 was released without a web browser as Microsoft had not yet developed one. The success of the web had caught them by surprise but by mid 1995, they were testing their own web server, and on August 24, 1995, launched a major online service, The Microsoft Network (MSN). The National Research Council recognized that the rise of the Internet simultaneously increased societal reliance on computer systems while increasing the vulnerability of such systems to failure and produced an important report in 1999, "Trust in Cyberspace". This report reviews the cost of un-trustworthy systems and identifies actions required for improvement. == Microsoft and Trustworthy Computing == Bill Gates launched Microsoft's "Trustworthy Computing" initiative with a January 15, 2002 memo, referencing an internal whitepaper by Microsoft CTO and Senior Vice President Craig Mundie. The move was reportedly prompted by the fact that they "...had been under fire from some of its larger customers–government agencies, financial companies and others–about the security problems in Windows, issues that were being brought front and center by a series of self-replicating worms and embarrassing attacks." such as Code Red, Nimda, Klez and Slammer. Four areas were identified as the initiative's key areas: Security, Privacy, Reliability, and Business Integrity, and despite some initial scepticism, at its 10-year anniversary it was generally accepted as having "...made a positive impact on the industry...". The Trustworthy Computing campaign was the main reason why Easter eggs disappeared from Windows, Office and other Microsoft products.

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  Single-source publishing

  Single-source publishing, also known as single-sourcing publishing, is a content management method which allows the same source content to be used across different forms of media and more than one time. The labor-intensive and expensive work of editing need only be carried out once, on only one document; that source document (the single source of truth) can then be stored in one place and reused. This reduces the potential for error, as corrections are only made one time in the source document. The benefits of single-source publishing primarily relate to the editor rather than the user. The user benefits from the consistency that single-sourcing brings to terminology and information. This assumes the content manager has applied an organized conceptualization to the underlying content (A poor conceptualization can make single-source publishing less useful). Single-source publishing is sometimes used synonymously with multi-channel publishing though whether or not the two terms are synonymous is a matter of discussion. == Definition == While there is a general definition of single-source publishing, there is no single official delineation between single-source publishing and multi-channel publishing, nor are there any official governing bodies to provide such a delineation. Single-source publishing is most often understood as the creation of one source document in an authoring tool and converting that document into different file formats or human languages (or both) multiple times with minimal effort. Multi-channel publishing can either be seen as synonymous with single-source publishing, or similar in that there is one source document but the process itself results in more than a mere reproduction of that source. == History == The origins of single-source publishing lie, indirectly, with the release of Windows 3.0 in 1990. With the eclipsing of MS-DOS by graphical user interfaces, help files went from being unreadable text along the bottom of the screen to hypertext systems such as WinHelp. On-screen help interfaces allowed software companies to cease the printing of large, expensive help manuals with their products, reducing costs for both producer and consumer. This system raised opportunities as well, and many developers fundamentally changed the way they thought about publishing. Writers of software documentation did not simply move from being writers of traditional bound books to writers of electronic publishing, but rather they became authors of central documents which could be reused multiple times across multiple formats. The first single-source publishing project was started in 1993 by Cornelia Hofmann at Schneider Electric in Seligenstadt, using software based on Interleaf to automatically create paper documentation in multiple languages based on a single original source file. XML, developed during the mid- to late-1990s, was also significant to the development of single-source publishing as a method. XML, a markup language, allows developers to separate their documentation into two layers: a shell-like layer based on presentation and a core-like layer based on the actual written content. This method allows developers to write the content only one time while switching it in and out of multiple different formats and delivery methods. In the mid-1990s, several firms began creating and using single-source content for technical documentation (Boeing Helicopter, Sikorsky Aviation and Pratt & Whitney Canada) and user manuals (Ford owners manuals) based on tagged SGML and XML content generated using the Arbortext Epic editor with add-on functions developed by a contractor. The concept behind this usage was that complex, hierarchical content that did not lend itself to discrete componentization could be used across a variety of requirements by tagging the differences within a single document using the capabilities built into SGML and XML. Ford, for example, was able to tag its single owner's manual files so that 12 model years could be generated via a resolution script running on the single completed file. Pratt & Whitney, likewise, was able to tag up to 20 subsets of its jet engine manuals in single-source files, calling out the desired version at publication time. World Book Encyclopedia also used the concept to tag its articles for American and British versions of English. Starting from the early 2000s, single-source publishing was used with an increasing frequency in the field of technical translation. It is still regarded as the most efficient method of publishing the same material in different languages. Once a printed manual was translated, for example, the online help for the software program which the manual accompanies could be automatically generated using the method. Metadata could be created for an entire manual and individual pages or files could then be translated from that metadata with only one step, removing the need to recreate information or even database structures. Although single-source publishing is now decades old, its importance has increased urgently as of the 2010s. As consumption of information products rises and the number of target audiences expands, so does the work of developers and content creators. Within the industry of software and its documentation, there is a perception that the choice is to embrace single-source publishing or render one's operations obsolete. == Criticism == Editors using single-source publishing have been criticized for below-standard work quality, leading some critics to describe single-source publishing as the "conveyor belt assembly" of content creation. While heavily used in technical translation, there are risks of error in regard to indexing. While two words might be synonyms in English, they may not be synonyms in another language. In a document produced via single-sourcing, the index will be translated automatically and the two words will be rendered as synonyms. This is because they are synonyms in the source language, while in the target language they are not.

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  ISO 15926

  ISO 15926 is a standard for data integration, sharing, exchange, and hand-over between computer systems. The title, "Industrial automation systems and integration—Integration of life-cycle data for process plants including oil and gas production facilities", is regarded too narrow by the present ISO 15926 developers. Having developed a generic data model and reference data library for process plants, it turned out that this subject is already so wide, that actually any state information may be modelled with it. == History == In 1991 a European Union ESPRIT-, named ProcessBase, started. The focus of this research project was to develop a data model for lifecycle information of a facility that would suit the requirements of the process industries. At the time that the project duration had elapsed, a consortium of companies involved in the process industries had been established: EPISTLE (European Process Industries STEP Technical Liaison Executive). Initially individual companies were members, but later this changed into a situation where three national consortia were the only members: PISTEP (UK), POSC/Caesar (Norway), and USPI-NL (Netherlands). (later PISTEP merged into POSC/Caesar, and USPI-NL was renamed to USPI). EPISTLE took over the work of the ProcessBase project. Initially this work involved a standard called ISO 10303-221 (referred to as "STEP AP221"). In that AP221 we saw, for the first time, an Annex M with a list of standard instances of the AP221 data model, including types of objects. These standard instances would be for reference and would act as a knowledge base with knowledge about the types of objects. In the early nineties EPISTLE started an activity to extend Annex M to become a library of such object classes and their relationships: STEPlib. In the STEPlib activities a group of approx. 100 domain experts from all three member consortia, spread over the various expertises (e.g. Electrical, Piping, Rotating equipment, etc.), worked together to define the "core classes". The development of STEPlib was extended with many additional classes and relationships between classes and published as Open source data. Furthermore, the concepts and relation types from the AP221 and ISO 15926-2 data models were also added to the STEPlib dictionary. This resulted in the development of Gellish English, whereas STEPlib became the Gellish English dictionary. Gellish English is a structured subset of natural English and is a modeling language suitable for knowledge modeling, product modeling and data exchange. It differs from conventional modeling languages (meta languages) as used in information technology as it not only defines generic concepts, but also includes an English dictionary. The semantic expression capability of Gellish English was significantly increased by extending the number of relation types that can be used to express knowledge and information. For modelling-technical reasons POSC/Caesar proposed another standard than ISO 10303, called ISO 15926. EPISTLE (and ISO) supported that proposal, and continued the modelling work, thereby writing Part 2 of ISO 15926. This Part 2 has official ISO IS (International Standard) status since 2003. POSC/Caesar started to put together their own RDL (Reference Data Library). They added many specialized classes, for example for ANSI (American National Standards Institute) pipe and pipe fittings. Meanwhile, STEPlib continued its existence, mainly driven by some members of USPI. Since it was clear that it was not in the interest of the industry to have two libraries for, in essence, the same set of classes, the Management Board of EPISTLE decided that the core classes of the two libraries shall be merged into Part 4 of ISO 15926. This merging process has been finished. Part 4 should act as reference data for part 2 of ISO 15926 as well as for ISO 10303-221 and replaced its Annex M. On June 5, 2007 ISO 15926-4 was signed off as a TS (Technical Specification). In 1999 the work on an earlier version of Part 7 started. Initially this was based on XML Schema (the only useful W3C Recommendation available then), but when Web Ontology Language (OWL) became available it was clear that provided a far more suitable environment for Part 7. Part 7 passed the first ISO ballot by the end of 2005, and an implementation project started. A formal ballot for TS (Technical Specification) was planned for December 2007. However, it was decided then to split Part 7 into more than one part, because the scope was too wide. == Need for ISO15926 == In 2004, the National Institute of Standards and Technology (NIST) released a report on the impact of the lack of digital interoperability in the capital projects industry. The report estimated the cost of inadequate interoperability in the U.S. capital facilities industry to be $15.8 billion per year. This was considered likely to be a conservative figure. == The standard == ISO 15926 has thirteen parts (as of February 2022): Part 1 - Overview and fundamental principles Part 2 - Data model Part 3 - Reference data for geometry and topology Part 4 - Reference Data, the terms used within facilities for the process industry Part 6 - Methodology for the development and validation of reference data (under development) Part 7 - Template methodology Part 8 - OWL/RDF implementation Part 9 - Implementation standards, with the focus on standard web servers, web services, and security (under development) Part 10 - Conformance testing Part 11 - Methodology for simplified industrial usage of reference data (under development) Part 12 - Life cycle integration ontology in Web Ontology Language (OWL2) Part 13 - Integrated lifecycle asset planning === Description === The model and the library are suitable for representing lifecycle information about technical installations and their components. They can also be used for defining the terms used in product catalogs in e-commerce. Another, more limited, use of the standard is as a reference classification for harmonization purposes between shared databases and product catalogues that are not based on ISO 15926. The purpose of ISO 15926 is to provide a Lingua Franca for computer systems, thereby integrating the information produced by them. Although set up for the process industries with large projects involving many parties, and involving plant operations and maintenance lasting decades, the technology can be used by anyone willing to set up a proper vocabulary of reference data in line with Part 4. In Part 7 the concept of Templates is introduced. These are semantic constructs, using Part 2 entities, that represent a small piece of information. These constructs then are mapped to more efficient classes of n-ary relations that interlink the Nodes that are involved in the represented information. In Part 8 the Part 7 Templates are defined in OWL and instantiated in RDF. For validation and reasoning purposes all are represented in First-Order Logic as well. In Part 9 these Node and Template instances are stored in an RDF triple store, set up to a standard schema and an API. Each participating computer system maps its data from its internal format to such ISO-standard Node and Template instances. Data can be "handed over" from one triple store to another in cases where data custodianship is handed over (e.g. from a contractor to a plant owner, or from a manufacturer to the owners of the manufactured goods). Hand-over can be for a part of all data, whilst maintaining full referential integrity. Documents are user-definable. They are defined in XML Schema and they are, in essence, only a structure containing cells that make reference to instances of Templates. This represents a view on all lifecycle data: since the data model is a 4D (space-time) model, it is possible to present the data that was valid at any given point in time, thus providing a true historical record. It is expected that this will be used for Knowledge Mining. Data can be queried by means of SPARQL. In any implementation a restricted number of triple stores can be involved, with different access rights. This is done by means of creating a CPF Server (= Confederation of Participating Façades). An Ontology Browser allows for access to one or more triple stores in a given CPF, depending on the access rights. == Projects and applications == There are a number of projects working on the extension of the ISO 15926 standard in different application areas. === Capital-intensive projects === Within the application of Capital Intensive projects, some cooperating implementation projects are running: The DEXPI project: The objective of DEXPI is to develop and promote a general standard for the process industry covering all phases of the lifecycle of a (petro-)chemical plant, ranging from specification of functional requirements to assets in operation. Finalised projects include: The EDRC Project of FIATECH Capturing Equipment Data Requirements Using ISO 15926 and Assessing Conforma

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  Randomized rounding

  In computer science and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). For such problems, randomized rounding can be used to design fast (polynomial time) approximation algorithms—that is, algorithms that are guaranteed to return an approximately optimal solution given any input. The basic idea of randomized rounding is to convert an optimal solution of a relaxation of the problem into an approximately-optimal solution to the original problem. The resulting algorithm is usually analyzed using the probabilistic method. == Overview == The basic approach has three steps: Formulate the problem to be solved as an integer linear program (ILP). Compute an optimal fractional solution x {\displaystyle x} to the linear programming relaxation (LP) of the ILP. Round the fractional solution x {\displaystyle x} of the LP to an integer solution x ′ {\displaystyle x'} of the ILP. (Although the approach is most commonly applied with linear programs, other kinds of relaxations are sometimes used. For example, see Goemans' and Williamson's semidefinite programming-based Max-Cut approximation algorithm.) In the first step, the challenge is to choose a suitable integer linear program. Familiarity with linear programming, in particular modelling using linear programs and integer linear programs, is required. For many problems, there is a natural integer linear program that works well, such as in the Set Cover example below. (The integer linear program should have a small integrality gap; indeed randomized rounding is often used to prove bounds on integrality gaps.) In the second step, the optimal fractional solution can typically be computed in polynomial time using any standard linear programming algorithm. In the third step, the fractional solution must be converted into an integer solution (and thus a solution to the original problem). This is called rounding the fractional solution. The resulting integer solution should (provably) have cost not much larger than the cost of the fractional solution. This will ensure that the cost of the integer solution is not much larger than the cost of the optimal integer solution. The main technique used to do the third step (rounding) is to use randomization, and then to use probabilistic arguments to bound the increase in cost due to the rounding (following the probabilistic method from combinatorics). Therein, probabilistic arguments are used to show the existence of discrete structures with desired properties. In this context, one uses such arguments to show the following: Given any fractional solution x {\displaystyle x} of the LP, with positive probability the randomized rounding process produces an integer solution x ′ {\displaystyle x'} that approximates x {\displaystyle x} according to some desired criterion. Finally, to make the third step computationally efficient, one either shows that x ′ {\displaystyle x'} approximates x {\displaystyle x} with high probability (so that the step can remain randomized) or one derandomizes the rounding step, typically using the method of conditional probabilities. The latter method converts the randomized rounding process into an efficient deterministic process that is guaranteed to reach a good outcome. == Example: the set cover problem == The following example illustrates how randomized rounding can be used to design an approximation algorithm for the set cover problem. Fix any instance ⟨ c , S ⟩ {\displaystyle \langle c,{\mathcal {S}}\rangle } of set cover over a universe U {\displaystyle {\mathcal {U}}} . === Computing the fractional solution === For step 1, let IP be the standard integer linear program for set cover for this instance. For step 2, let LP be the linear programming relaxation of IP, and compute an optimal solution x ∗ {\displaystyle x^{}} to LP using any standard linear programming algorithm. This takes time polynomial in the input size. The feasible solutions to LP are the vectors x {\displaystyle x} that assign each set s ∈ S {\displaystyle s\in {\mathcal {S}}} a non-negative weight x s {\displaystyle x_{s}} , such that, for each element e ∈ U {\displaystyle e\in {\mathcal {U}}} , x ′ {\displaystyle x'} covers e {\displaystyle e} —the total weight assigned to the sets containing e {\displaystyle e} is at least 1, that is, ∑ s ∋ e x s ≥ 1. {\displaystyle \sum _{s\ni e}x_{s}\geq 1.} The optimal solution x ∗ {\displaystyle x^{}} is a feasible solution whose cost ∑ s ∈ S c ( S ) x s ∗ {\displaystyle \sum _{s\in {\mathcal {S}}}c(S)x_{s}^{}} is as small as possible. Note that any set cover C {\displaystyle {\mathcal {C}}} for S {\displaystyle {\mathcal {S}}} gives a feasible solution x {\displaystyle x} (where x s = 1 {\displaystyle x_{s}=1} for s ∈ C {\displaystyle s\in {\mathcal {C}}} , x s = 0 {\displaystyle x_{s}=0} otherwise). The cost of this C {\displaystyle {\mathcal {C}}} equals the cost of x {\displaystyle x} , that is, ∑ s ∈ C c ( s ) = ∑ s ∈ S c ( s ) x s . {\displaystyle \sum _{s\in {\mathcal {C}}}c(s)=\sum _{s\in {\mathcal {S}}}c(s)x_{s}.} In other words, the linear program LP is a relaxation of the given set-cover problem. Since x ∗ {\displaystyle x^{}} has minimum cost among feasible solutions to the LP, the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover. === Randomized rounding step === In step 3, we must convert the minimum-cost fractional set cover x ∗ {\displaystyle x^{}} into a feasible integer solution x ′ {\displaystyle x'} (corresponding to a true set cover). The rounding step should produce an x ′ {\displaystyle x'} that, with positive probability, has cost within a small factor of the cost of x ∗ {\displaystyle x^{}} .Then (since the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover), the cost of x ′ {\displaystyle x'} will be within a small factor of the optimal cost. As a starting point, consider the most natural rounding scheme: For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( 1 , x s ∗ ) {\displaystyle \min(1,x_{s}^{})} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . With this rounding scheme, the expected cost of the chosen sets is at most ∑ s c ( s ) x s ∗ {\displaystyle \sum _{s}c(s)x_{s}^{}} , the cost of the fractional cover. This is good. Unfortunately the coverage is not good. When the variables x s ∗ {\displaystyle x_{s}^{}} are small, the probability that an element e {\displaystyle e} is not covered is about ∏ s ∋ e 1 − x s ∗ ≈ ∏ s ∋ e exp ⁡ ( − x s ∗ ) = exp ⁡ ( − ∑ s ∋ e x s ∗ ) ≈ exp ⁡ ( − 1 ) . {\displaystyle \prod _{s\ni e}1-x_{s}^{}\approx \prod _{s\ni e}\exp(-x_{s}^{})=\exp {\Big (}-\sum _{s\ni e}x_{s}^{}{\Big )}\approx \exp(-1).} So only a constant fraction of the elements will be covered in expectation. To make x ′ {\displaystyle x'} cover every element with high probability, the standard rounding scheme first scales up the rounding probabilities by an appropriate factor λ > 1 {\displaystyle \lambda >1} . Here is the standard rounding scheme: Fix a parameter λ ≥ 1 {\displaystyle \lambda \geq 1} . For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( λ x s ∗ , 1 ) {\displaystyle \min(\lambda x_{s}^{},1)} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . Scaling the probabilities up by λ {\displaystyle \lambda } increases the expected cost by λ {\displaystyle \lambda } , but makes coverage of all elements likely. The idea is to choose λ {\displaystyle \lambda } as small as possible so that all elements are provably covered with non-zero probability. Here is a detailed analysis. ==== Lemma (approximation guarantee for rounding scheme) ==== Fix λ = ln ⁡ ( 2 | U | ) {\displaystyle \lambda =\ln(2|{\mathcal {U}}|)} . With positive probability, the rounding scheme returns a set cover x ′ {\displaystyle x'} of cost at most 2 ln ⁡ ( 2 | U | ) c ⋅ x ∗ {\displaystyle 2\ln(2|{\mathcal {U}}|)c\cdot x^{}} (and thus of cost O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} times the cost of the optimal set cover). (Note: with care the O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} can be reduced to ln ⁡ ( | U | ) + O ( log ⁡ log ⁡ | U | ) {\displaystyle \ln(|{\mathcal {U}}|)+O(\log \log |{\mathcal {U}}|)} .) ==== Proof ==== The output x ′ {\displaystyle x'} of the random rounding scheme has the desired properties as long as none of the following "bad" events occur: the cost c ⋅ x ′ {\displaystyle c\cdot x'} of x ′ {\displaystyle x'} exceeds 2 λ c ⋅ x ∗ {\displaystyle 2\lambda c\cdot x^{}} , or for some element e {\displaystyle e} , x ′ {\displaystyle x'} fails to cover e {\displaystyle e} . The expectation of each x s ′ {\displaystyle x'_{s}} is at most λ x s ∗ {\displaystyle \lambda x_{s

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  Pronunciation assessment

  Automatic pronunciation assessment uses computer speech recognition to determine how accurately speech has been pronounced, instead of relying on a human instructor or proctor. It is also called speech verification, pronunciation evaluation, and pronunciation scoring. This technology is used to grade speech quality, for language testing, for computer-aided pronunciation teaching (CAPT) in computer-assisted language learning (CALL), for speaking skill remediation, and for accent reduction. Pronunciation assessment is different from dictation or automatic transcription, because instead of determining unknown speech, it verifies learners' pronunciation of known word(s), often from prior transcription of the same utterance; ideally scoring the intelligibility of the learners' speech. Sometimes pronunciation assessment evaluates the prosody of the learners' speech, such as intonation, pitch, tempo, rhythm, and syllable and word stress, although those are usually not essential for being understood in most languages. Pronunciation assessment is also used in reading tutoring, for example in products from Google, Microsoft, and Amira Learning. Automatic pronunciation assessment can also be used to help diagnose and treat speech disorders such as apraxia. == Intelligibility == Intelligibility refers to how well a learner's utterance is understood by a listener, rather than how much it sounds like a native speaker. This is separate from measures of fluency, such as so-called "Goodness of Pronunciation" (GoP) scores, which estimate how closely an utterance aligns with those of native speakers. Intelligibility is widely regarded as the most important communicative goal in pronunciation teaching and assessment. For example, in the Common European Framework of Reference for Languages (CEFR) assessment criteria for "overall phonological control", intelligibility outweighs formally correct pronunciation at all levels. Studies in applied linguistics have shown that accent reduction does not always increase intelligibility because listeners can often comprehend heavily accented speech without difficulty. Pronunciation assessment systems often rely on acoustic methods such as GoP which compare learner speech to reference models to produce phoneme-level scores, which are in turn aggregated to produce word and phrase scores. While these methods are effective for identifying deviations from native speakers' utterances, they do not effectively measure how understandable speech is to human listeners. Intelligibility is influenced by broader linguistic and contextual factors such as stress placement, speech rate, and coarticulation, which are not represented in purely segmental scores. The earliest work on pronunciation assessment avoided measuring genuine listener intelligibility, a shortcoming corrected in 2011 at the Toyohashi University of Technology, and included in the Versant high-stakes English fluency assessment from Pearson and mobile apps from 17zuoye Education & Technology, but still missing in 2023 products from Google Search, Microsoft, Educational Testing Service, Speechace, and ELSA. Assessing authentic listener intelligibility is essential for avoiding inaccuracies from accent bias, especially in high-stakes assessments; from words with multiple correct pronunciations; and from phoneme coding errors in machine-readable pronunciation dictionaries. In 2022, researchers found that some newer speech-to-text systems, based on end-to-end reinforcement learning to map audio signals directly into words, produce word and phrase confidence scores (from 10-25ms audio frame logit aggregation) closely correlated with genuine listener intelligibility. Others have been able to assess intelligibility using Levenshtein or dynamic time warping distance measures from Wav2Vec2 representation of good speech. Further work through 2025 has focused specifically on measuring intelligibility. A 2025 study of 42 pronunciation and speech coaching apps (32 mobile and 10 web) found that none offered intelligibility assessment. Instead, most provided only segmental and accent-focused scoring. About two-thirds of the apps provided some form of specific pronunciation feedback, usually with phonetic transcriptions, but accompanied by visual cues (such as animations of the vocal tract or the lips and tongue from the front) in only about 5% of the apps. Less than a third provided feedback on learner perception of exemplar speech. == Evaluation == Although there are as yet no industry-standard benchmarks for evaluating pronunciation assessment accuracy, researchers occasionally release evaluation speech corpuses for others to use for improving assessment quality. Such evaluation databases often emphasize formally unaccented pronunciation to the exclusion of genuine intelligibility evident from blinded listener transcriptions. As of mid-2025, state of the art approaches for automatically transcribing phonemes typically achieve an error rate of about 10% from known good speech. The International Speech Communication Association (ISCA) 2025 Workshop on Speech and Language Technology in Education (SLaTE) administered a Speak & Improve Challenge: Spoken Language Assessment and Feedback, introducing benchmarks for evaluating pronunciation assessment and remediation systems across languages, accents, and learner populations. The challenge emphasized cross-lingual generalization and alignment with human intelligibility judgments, for more robust and interpretable assessment systems. Ethical issues in pronunciation assessment are present in both human and automatic methods. Authentic validity, fairness, and mitigating bias in evaluation are all crucial. Diverse speech data should be included in automatic pronunciation assessment models. Combining human judgments, especially blinded transcriptions from a wide diversity of listeners, with automated feedback can improve accuracy and fairness. Second language learners benefit substantially from their use of widely available speech recognition systems for dictation, virtual assistants, and AI chatbots. In such systems, users naturally try to correct their own errors evident in speech recognition results that they notice. Such use improves their grammar and vocabulary development along with their pronunciation skills. The extent to which explicit pronunciation assessment and remediation approaches improve on such self-directed interactions remains an open question. Similarly, automatic dictation results have been shown to reflect intelligibility about as well as human scorers. == Recent developments == During 2021–22, a smartphone-based CAPT system was used to sense articulation through both audible and inaudible signals, providing feedback at the phoneme level. Some promising areas for improvement which were being developed in 2024 include articulatory feature extraction and transfer learning to suppress unnecessary corrections. Other interesting advances under development include "augmented reality" interfaces for mobile devices using optical character recognition to provide pronunciation training on text found in user environments. In 2024, audio multimodal large language models were first described as assessing pronunciation. That work has been carried forward by other researchers in 2025 who report positive results. Subsequently, researchers demonstrated pronunciation scoring by providing a language model with textual descriptions of speech, including the speech-to-text transcript, phoneme sequences, pauses, and phoneme sequence matching; this approach can achieve performance similar to multimodal LLMs that analyze raw audio while avoiding their higher computational cost. In 2025, the Duolingo English Test authors published a description of their pronunciation assessment method, purportedly built to measure intelligibility rather than accent imitation. While achieving a correlation of 0.82 with expert human ratings, very close to inter-rater agreement and outperforming alternative methods, the method is nonetheless based on experts' scores along the six-point CEFR common reference levels scale, instead of actual blinded listener transcriptions. Further promising work in 2025 includes assessment feedback aligning learner speech to synthetic utterances using interpretable features, identifying continuous spans of words for remediation feedback; synthesizing corrected speech matching learners' self-perceived voices, which they prefer and imitate more accurately as corrections; and streaming such interactions. On January 21, 2026, Educational Testing Service's TOEFL iBT high-stakes English language test, required by US university admissions and employers from English as a foreign language applicants more often than all other internet-based tests combined, changed its speaking assessments. While official rubrics claim that the new scoring will be based primarily on intelligibility, the new test's technical description indicates that it ju

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  PL/Perl

  PL/Perl (Procedural Language/Perl) is a procedural language supported by the PostgreSQL RDBMS. PL/Perl, as an imperative programming language, allows more control than the relational algebra of SQL. Programs created in the PL/Perl language are called functions and can use most of the features that the Perl programming language provides, including common flow control structures and syntax that has incorporated regular expressions directly. These functions can be evaluated as part of a SQL statement, or in response to a trigger or rule. The design goals of PL/Perl were to create a loadable procedural language that: can be used to create functions and trigger procedures, adds control structures to the SQL language, can perform complex computations, can be defined to be either trusted or untrusted by the server, is easy to use. PL/Perl is one of many "PL" languages available for PostgreSQL PL/pgSQL PL/Java, plPHP, PL/Python, PL/R, PL/Ruby, PL/sh, and PL/Tcl.

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  Ontology engineering

  In computer science, information science and systems engineering, ontology engineering is a field which studies the methods and methodologies for building ontologies, which encompasses a representation, formal naming and definition of the categories, properties and relations between the concepts, data and entities of a given domain of interest. In a broader sense, this field also includes a knowledge construction of the domain using formal ontology representations such as OWL/RDF. A large-scale representation of abstract concepts such as actions, time, physical objects and beliefs would be an example of ontological engineering. Ontology engineering is one of the areas of applied ontology, and can be seen as an application of philosophical ontology. Core ideas and objectives of ontology engineering are also central in conceptual modeling. Ontology engineering aims at making explicit the knowledge contained within software applications, and within enterprises and business procedures for a particular domain. Ontology engineering offers a direction towards solving the inter-operability problems brought about by semantic obstacles, i.e. the obstacles related to the definitions of business terms and software classes. Ontology engineering is a set of tasks related to the development of ontologies for a particular domain. Automated processing of information not interpretable by software agents can be improved by adding rich semantics to the corresponding resources, such as video files. One of the approaches for the formal conceptualization of represented knowledge domains is the use of machine-interpretable ontologies, which provide structured data in, or based on, RDF, RDFS, and OWL. Ontology engineering is the design and creation of such ontologies, which can contain more than just the list of terms (controlled vocabulary); they contain terminological, assertional, and relational axioms to define concepts (classes), individuals, and roles (properties) (TBox, ABox, and RBox, respectively). Ontology engineering is a relatively new field of study concerning the ontology development process, the ontology life cycle, the methods and methodologies for building ontologies, and the tool suites and languages that support them. A common way to provide the logical underpinning of ontologies is to formalize the axioms with description logics, which can then be translated to any serialization of RDF, such as RDF/XML or Turtle. Beyond the description logic axioms, ontologies might also contain SWRL rules. The concept definitions can be mapped to any kind of resource or resource segment in RDF, such as images, videos, and regions of interest, to annotate objects, persons, etc., and interlink them with related resources across knowledge bases, ontologies, and LOD datasets. This information, based on human experience and knowledge, is valuable for reasoners for the automated interpretation of sophisticated and ambiguous contents, such as the visual content of multimedia resources. Application areas of ontology-based reasoning include, but are not limited to, information retrieval, automated scene interpretation, and knowledge discovery. == Languages == An ontology language is a formal language used to encode the ontology. There are a number of such languages for ontologies, both proprietary and standards-based: Common logic is ISO standard 24707, a specification for a family of ontology languages that can be accurately translated into each other. The Cyc project has its own ontology language called CycL, based on first-order predicate calculus with some higher-order extensions. The Gellish language includes rules for its own extension and thus integrates an ontology with an ontology language. IDEF5 is a software engineering method to develop and maintain usable, accurate, domain ontologies. KIF is a syntax for first-order logic that is based on S-expressions. Rule Interchange Format (RIF), F-Logic and its successor ObjectLogic combine ontologies and rules. OWL is a language for making ontological statements, developed as a follow-on from RDF and RDFS, as well as earlier ontology language projects including OIL, DAML and DAML+OIL. OWL is intended to be used over the World Wide Web, and all its elements (classes, properties and individuals) are defined as RDF resources, and identified by URIs. OntoUML is a well-founded language for specifying reference ontologies. SHACL (RDF SHapes Constraints Language) is a language for describing structure of RDF data. It can be used together with RDFS and OWL or it can be used independently from them. XBRL (Extensible Business Reporting Language) is a syntax for expressing business semantics. == Methodologies and tools == DOGMA KAON OntoClean HOZO Protégé (software) Large language models == In life sciences == Life sciences is flourishing with ontologies that biologists use to make sense of their experiments. For inferring correct conclusions from experiments, ontologies have to be structured optimally against the knowledge base they represent. The structure of an ontology needs to be changed continuously so that it is an accurate representation of the underlying domain. Recently, an automated method was introduced for engineering ontologies in life sciences such as Gene Ontology (GO), one of the most successful and widely used biomedical ontology. Based on information theory, it restructures ontologies so that the levels represent the desired specificity of the concepts. Similar information theoretic approaches have also been used for optimal partition of Gene Ontology. Given the mathematical nature of such engineering algorithms, these optimizations can be automated to produce a principled and scalable architecture to restructure ontologies such as GO. Open Biomedical Ontologies (OBO), a 2006 initiative of the U.S. National Center for Biomedical Ontology, provides a common 'foundry' for various ontology initiatives, amongst which are: The Generic Model Organism Project (GMOD) Gene Ontology Consortium Sequence Ontology Ontology Lookup Service The Plant Ontology Consortium Standards and Ontologies for Functional Genomics and more

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