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
Ogle app
Ogle is a free smartphone based social media application. It is available for iOS and Android. Ogle acts like a school wide forum that lets users and users' classmates share and interact. Users can share photos, videos, questions, even thoughts and watch submissions grow in popularity as other users vote and comment on them. == App Features == Campus Feed: Interact by watching and posting videos or pictures to your campus story. Photos and Videos: share what you want with many different timing options. Interact: Chat with friends and groups, or share a moment for all to see. Real-name system: choose to register an account with username and profile picture. Custom Stickers: Create stickers to add creativity and zest to your pictures. Flash Interaction: All private chat and group chat history will be deleted after 24 hours on Ogle Chat. == Controversies == Users can post anything on Ogle using text, photos, and videos. As a result, some Ogle user's sense of anonymity, posts have targeted specific schools and students with abusive and hurtful content. The Ogle app's user anonymity makes it difficult for school officials to quickly investigate issues that occur within the Ogle app. On March 28, 2016, three people were arrested after violent threats were made against an Anaheim high school. 18-year-old Miguel Meza was arrested Sunday afternoon during a traffic stop, along with his passenger, 23-year-old Johnny Aguilar. Police said both men had loaded handguns. Aguilar was also accused of violating his probation. "It is concerning the fact that they did have firearms, but we don't have a crystal ball. We can't determine if they possessed those firearms to engage in some kind of school violence or if they had it for another reason," Sgt. Daron Wyatt with the Anaheim Police Department said. Officials said Meza and Aguilar have known gang ties and detectives began investigating Meza after threats were made against the school on Ogle. On February 29, 2016, Santa Cruz County sheriff's deputies arrested a 16-year-old Aptos High School student Friday, accused of making an online threat of gun violence at Aptos High and Monte Vista Christian."He basically told detectives that it was all a joke. It's not a joke. You have multiple resources being spent to investigate these cases," said Santa Cruz County Sheriff's Sgt. Roy Morales. The schools remained open throughout the week, with a huge police presence on campus. In an anonymous emailed statement to the Daily Pilot on Thursday, the "Ogle team" said: "We are aware of the concern, and cyberbullying is absolutely NOT our intention for the app. Our goal for this app is to create a free and safe community space for students, for a better communication. We are currently working around the clock to improve the app. As a matter of fact, we are also in contact with local police departments, anti-bullying organizations and local high schools to try to help the students." In response to these incidents, Ogle expressed that they takes the safety of its users seriously and does not condone any type of behavior that is illegal or in violation of its content policies. The company also said it has instituted a content moderation team to increase review and identify and remove inappropriate content, and take action against “those who violate our community guidelines.”
Xulvi-Brunet–Sokolov algorithm
Xulvi-Brunet and Sokolov's algorithm generates networks with chosen degree correlations. This method is based on link rewiring, in which the desired degree is governed by parameter ρ. By varying this single parameter it is possible to generate networks from random (when ρ = 0) to perfectly assortative or disassortative (when ρ = 1). This algorithm allows to keep network's degree distribution unchanged when changing the value of ρ. == Assortative model == In assortative networks, well-connected nodes are likely to be connected to other highly connected nodes. Social networks are examples of assortative networks. This means that an assortative network has the property that almost all nodes with the same degree are linked only between themselves. The Xulvi-Brunet–Sokolov algorithm for this type of networks is the following. In a given network, two links connecting four different nodes are chosen randomly. These nodes are ordered by their degrees. Then, with probability ρ, the links are randomly rewired in such a way that one link connects the two nodes with the smaller degrees and the other connects the two nodes with the larger degrees. If one or both of these links already existed in the network, the step is discarded and is repeated again. Thus, there will be no self-connected nodes or multiple links connecting the same two nodes. Different degrees of assortativity of a network can be achieved by changing the parameter ρ. Assortative networks are characterized by highly connected groups of nodes with similar degree. As assortativity grows, the average path length and clustering coefficient increase. == Disassortative model == In disassortative networks, highly connected nodes tend to connect to less-well-connected nodes with larger probability than in uncorrelated networks. Examples of such networks include biological networks. The Xulvi-Brunet and Sokolov's algorithm for this type of networks is similar to the one for assortative networks with one minor change. As before, two links of four nodes are randomly chosen and the nodes are ordered with respect to their degrees. However, in this case, the links are rewired (with probability p) such that one link connects the highest connected node with the node with the lowest degree and the other link connects the two remaining nodes randomly with probability 1 − ρ. Similarly, if the new links already existed, the previous step is repeated. This algorithm does not change the degree of nodes and thus the degree distribution of the network.
Information audit
The information audit (IA) extends the concept of auditing from a traditional scope of accounting and finance to the organisational information management system. Information is representative of a resource which requires effective management and this led to the development of interest in the use of an IA. Prior the 1990s and the methodologies of Orna, Henczel, Wood, Buchanan and Gibb, IA approaches and methodologies focused mainly upon an identification of formal information resources (IR). Later approaches included an organisational analysis and the mapping of the information flow. This gave context to analysis within an organisation's information systems and a holistic view of their IR and as such could contribute to the development of the information systems architecture (ISA). In recent years the IA has been overlooked in favour of the systems development process which can be less expensive than the IA, yet more heavily technically focused, project specific (not holistic) and does not favour the top-down analysis of the IA. == Definition == A definition for the Information Audit cannot be universally agreed-upon amongst scholars, however the definition offered by ASLIB received positive support from a few notable scholars including Henczel, Orna and Wood; “(the IA is a) systematic examination of information use, resources and flows, with a verification by reference to both people and existing documents, in order to establish the extent to which they are contributing to an organisation’s objectives” In summary, the term audit itself implies a counting, the IA being much the same yet it counts IR and analyses how they are used and how critical they are to the success of a given task. == Role and scope of an IA == In much the same way as the IA is difficult to define, it can be utilised in a range of contexts by the information professional, from complying with freedom of information legislation to identifying any existing gaps, duplications, bottlenecks or other inefficiencies in information flows and to understand how existing channels can be used for knowledge transfer In 2007 Buchanan and Gibb developed upon their 1998 examination of the IA process by outlining a summary of its main objectives: To identify an organisation’s information resource To identify an organisation’s information needs Furthermore, Buchanan and Gibb went on to state that the IA also had to meet the following additional objectives: To identify the cost/benefits of information resources To identify the opportunities to use the information resources for strategic competitive advantage To integrate IT investment with strategic business initiatives To identify information flow and processes To develop an integrated information strategy and/or policy To create an awareness of the importance of Information Resource Management (IRM) To monitor/evaluate conformance to information related standards, legislations, policy and guidelines. == Methodology evolution == === Overview === In 1976 Riley first published a definition of IA as a way of analysing IR based on a cost-benefit model. Since Riley, scholars have outlined further developed methodologies. Henderson took a cost-benefit approach hoping to draw focus from manpower-costing to information storage and acquisition which he felt was being overlooked. In 1985 Gillman focused upon identifying the relationships which existed between various components in order to map them to one another. Neither Henderson nor Gillman’s methods offered alternative approaches beyond the existing organisational frameworks. Quinn took a hybrid-approach combining Gillman and Henderson’s methods to identify the purpose of existing IR and to position them within the organisation, as did Worlock. The differentiator between Quinn and Worlock lay in Worlock’s consideration of solutions outside of the current organisational structure. These approaches had thus far had paid little attention to the needs of the user or in making structured recommendations for the development of a corporate information strategy. Therefore, here follows a brief outline and overall comparison of four published strategic approaches in order that one might understand the development of the IA methodology. === Burk and Horton === In 1988 Burk and Horton developed InfoMap, the first IA methodology developed for widespread use. It aimed to discover, map and evaluate the IR within an organisation using a 4-stage process: Survey staff using questionnaires/interviews Measure the IR against cost/value Analyse resources Synthesise the findings and map the strengths and weaknesses of the IR against the objectives of the organisation. Although the method inventoried all IR (and therefore met standard ISO 1779) this bottom-up approach revealed limited analysis of the organisation holistically and the steps were not explicit enough. === Orna === Orna produced a top-down methodology in contrast to Burk and Horton, placing emphasis upon the importance of organisational analysis and aimed to assist in the production of a corporate information policy. Initially the method had just 4-stages, this later revised to a 10-stage process which included pre and post-audit stages as below: Conduct a preliminary review to confirm operational/strategic direction Gain support/resource from management Gain commitment from the other stakeholders (staff) Planning including the project, team, tools and techniques Identify the IR, information flow and produce a cost/value assessment Interpret findings based upon current versus desired state Produce a report to present findings Implement recommendations Monitor effects of change Repeat the IA Orna’s method introduced the need for a cyclical IA to be put in place in order for the IR to be continually tracked and improvements made regularly. Again this method was criticised for lacking some practical application and in 2004 Orna revised the methodology once more to try to rectify this problem === Buchanan and Gibb === In 1998, similarly to Orna's earlier publication, Buchanan and Gibb took a top-down approach, drawing techniques from established management disciplines to provide a framework and a level of familiarity for information professionals. This set of techniques was a notable contribution to IA methodologies and understood the need to be flexible for each organisation. Theirs was a 5-stage process: Promote benefits of the IA through seminars/surveys/CEO letter for cooperation Identify the mission objectives of the organisation, define environment (PEST), map information flow and examine organisation culture. Analyse and formulate action plan for problem areas, flow diagrams and a report of findings and recommendations Account for cost of IR and related services using Activity Based Costing (ABC) and Output Based Specification (OBS). Synthesise the whole process in final audit report and provide an information strategy (strategic direction) in relation to the organisation’s mission statement. This was the introduction of a new approach to costing the IR and had an integrated strategic direction, yet the scholars admitted that this method may be impractical for smaller organisations. === Henczel === Henczel’s methodology drew upon the strengths of Orna and Buchanan and Gibb to produce a 7-stage process: Planning and submission of business case for approval to proceed Data collection and development of an IR database and population through survey techniques Structured data analysis Data evaluation, interpretation and formulation of recommendations Communication of recommendations through a report Implementing recommendations through a devised programme The IA as a continuum-establishment of a cyclical process Focus was made once more on the strategic direction of the organisation conducting the IA. Furthermore, Henczel made examination into the use of the IA as a first-step in the development of a knowledge audit or knowledge management strategy as discussed in the later section. == Case studies == Scholars and information professionals have since tested the above methodologies with varied results. An early case study produced by Soy and Bustelo in a Spanish financial institution in 1999 aimed to identify the use of information resources for qualitative and quantitative data analysis due to the rapid expansion of the organisation within a six-year period. Although the methodology was not explicitly credited to any of the above-mentioned scholars, it did follow a strategic (post 1990's) IA process including gaining support from management, the use of questionnaires for data collection, analysis and evaluation of the data, identification and mapping of the IR, cost-analysis and outlining recommendations to assist with the establishment of an Information policy. In addition the IA report suggested that the process would need to be continual (cyclical as Orna, Henczel and Buchanan and Gibb suggest). Conclusions of this case-study stated that th
Data (word)
The word data is most often used as a singular collective mass noun in educated everyday usage. However, due to the history and etymology of the word, considerable controversy has existed on whether it should be considered a mass noun used with verbs conjugated in the singular, or should be treated as the plural of the now-rarely-used datum. == Usage in English == In one sense, data is the plural form of datum. Datum actually can also be a count noun with the plural datums (see usage in datum article) that can be used with cardinal numbers (e.g., "80 datums"); data (originally a Latin plural) is not used like a normal count noun with cardinal numbers and can be plural with plural determiners such as these and many, or it can be used as a mass noun with a verb in the singular form. Even when a very small quantity of data is referenced (one number, for example), the phrase piece of data is often used, as opposed to datum. The debate over appropriate usage continues, but "data" as a singular form is far more common. In English, the word datum is still used in the general sense of "an item given". In cartography, geography, nuclear magnetic resonance and technical drawing, it is often used to refer to a single specific reference datum from which distances to all other data are measured. Any measurement or result is a datum, though data point is now far more common. Data is indeed most often used as a singular mass noun in educated everyday usage. Some major newspapers, such as The New York Times, use it either in the singular or plural. In The New York Times, the phrases "the survey data are still being analyzed" and "the first year for which data is available" have appeared within one day. The Wall Street Journal explicitly allows this usage in its style guide. The Associated Press style guide classifies data as a collective noun that takes the singular when treated as a unit but the plural when referring to individual items (e.g., "The data is sound" and "The data have been carefully collected"). In scientific writing, data is often treated as a plural, as in These data do not support the conclusions, but the word is also used as a singular mass entity like information (e.g., in computing and related disciplines). British usage now widely accepts treating data as singular in standard English, including everyday newspaper usage at least in non-scientific use. UK scientific publishing still prefers treating it as a plural. Some UK university style guides recommend using data for both singular and plural use, and others recommend treating it only as a singular in connection with computers. The IEEE Computer Society allows usage of data as either a mass noun or plural based on author preference, while IEEE in the editorial style manual indicates to always use the plural form. Some professional organizations and style guides require that authors treat data as a plural noun. For example, the Air Force Flight Test Center once stated that the word data is always plural, never singular.
Chirplet transform
In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets. Similar to the wavelet transform, chirplets are usually generated from (or can be expressed as being from) a single mother chirplet (analogous to the so-called mother wavelet of wavelet theory). == Definitions == The term chirplet transform was coined by Steve Mann, as the title of the first published paper on chirplets. The term chirplet itself (apart from chirplet transform) was also used by Steve Mann, Domingo Mihovilovic, and Ronald Bracewell to describe a windowed portion of a chirp function. In Mann's words: A wavelet is a piece of a wave, and a chirplet, similarly, is a piece of a chirp. More precisely, a chirplet is a windowed portion of a chirp function, where the window provides some time localization property. In terms of time–frequency space, chirplets exist as rotated, sheared, or other structures that move from the traditional parallelism with the time and frequency axes that are typical for waves (Fourier and short-time Fourier transforms) or wavelets. The chirplet transform thus represents a rotated, sheared, or otherwise transformed tiling of the time–frequency plane. Although chirp signals have been known for many years in radar, pulse compression, and the like, the first published reference to the chirplet transform described specific signal representations based on families of functions related to one another by time–varying frequency modulation or frequency varying time modulation, in addition to time and frequency shifting, and scale changes. In that paper, the Gaussian chirplet transform was presented as one such example, together with a successful application to ice fragment detection in radar (improving target detection results over previous approaches). The term chirplet (but not the term chirplet transform) was also proposed for a similar transform, apparently independently, by Mihovilovic and Bracewell later that same year. == Applications == The first practical application of the chirplet transform was in water-human-computer interaction (WaterHCI) for marine safety, to assist vessels in navigating through ice-infested waters, using marine radar to detect growlers (small iceberg fragments too small to be visible on conventional radar, yet large enough to damage a vessel). Other applications of the chirplet transform in WaterHCI include the SWIM (Sequential Wave Imprinting Machine). More recently other practical applications have been developed, including image processing (e.g. where there is periodic structure imaged through projective geometry), as well as to excise chirp-like interference in spread spectrum communications, in EEG processing, and Chirplet Time Domain Reflectometry. == Extensions == The warblet transform is a particular example of the chirplet transform introduced by Mann and Haykin in 1992 and now widely used. It provides a signal representation based on cyclically varying frequency modulated signals (warbling signals).
Collaborative diffusion
Collaborative Diffusion is a type of pathfinding algorithm which uses the concept of antiobjects, objects within a computer program that function opposite to what would be conventionally expected. Collaborative Diffusion is typically used in video games, when multiple agents must path towards a single target agent. For example, the ghosts in Pac-Man. In this case, the background tiles serve as antiobjects, carrying out the necessary calculations for creating a path and having the foreground objects react accordingly, whereas having foreground objects be responsible for their own pathing would be conventionally expected. Collaborative Diffusion is favored for its efficiency over other pathfinding algorithms, such as A, when handling multiple agents. Also, this method allows elements of competition and teamwork to easily be incorporated between tracking agents. Notably, the time taken to calculate paths remains constant as the number of agents increases.