AI Assistant Esri

AI Assistant Esri — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Screen space directional occlusion

    Screen space directional occlusion

    Screen space directional occlusion (SSDO) is a computer graphics technique enhancing screen space ambient occlusion (SSAO) by taking direction into account to sample the ambient light (both the light coming directly at an object, as well as the light reflected off of the object directly behind it), to better approximate global illumination. SSDO was introduced by Tobias Ritschel, Thorsten Grosch, and Hans-Peter Seidel in their 2009 ACM Symposium on Interactive 3D Graphics and Games paper Approximating dynamic global illumination in image space, which describes it as extending SSAO to directional occlusion with one diffuse indirect bounce of light; later literature notes that SSDO still suffers from common screen-space artifacts such as noise and banding. == Method == The original SSDO paper describes a two-pass screen-space approach, with one pass for direct lighting and a second pass for indirect bounces. Later literature describes SSDO as assuming a general shadowing direction that allows color bleeding and a single light bounce.

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  • Manhattan address algorithm

    Manhattan address algorithm

    The Manhattan address algorithm is a series of formulas used to estimate the closest east–west cross street for building numbers on north–south avenues in the New York City borough of Manhattan. == Algorithm == To find the approximate number of the closest cross street, divide the building number by a divisor (generally 20) and add (or subtract) the "tricky number" from the table below: For the north–south avenues, there are typically 20 address numbers between consecutive east–west streets (10 on either side of the avenue). A standard land lot on each avenue was originally 20 feet (6.1 m) wide, and there is about 200 feet (61 m) between each pair of east–west streets, for ten land lots between each pair of streets. The exceptions are Riverside Drive, as well as Fifth Avenue and Central Park West between 59th and 110th streets, which use a divisor of 10. These avenues all have buildings only on one side of the street, with a park on the other side. The "tricky number" often corresponds to a street near the southern end of the avenue. There are some notable exceptions: York Avenue address numbers are continuations of Avenue A address numbers, since the avenue was originally called Avenue A. East End Avenue address numbers are continuations of Avenue B address numbers, since the avenue was originally called Avenue B. Sixth Avenue and Broadway start south of Houston Street, the southern boundary of the Manhattan street numbering system. Although Park Avenue's southern terminus is at 32nd Street, a homeowner at 34th Street wanted the address "1 Park Avenue" (this was later changed). === Examples === For example, if you are at 62 Avenue B, 62 ÷ 20 ≈ 3 {\displaystyle 62\div 20\approx 3} , then add the "tricky number" 3 {\displaystyle 3} to give 6 {\displaystyle 6} . The nearest cross street to 62 Avenue B is East 6th Street. If you are at 78 Riverside Drive, 78 ÷ 10 ≈ 8 {\displaystyle 78\div 10\approx 8} , then add the "tricky number" 72 {\displaystyle 72} to give 80 {\displaystyle 80} . The nearest cross street to 78 Riverside Drive is West 80th Street. If you are at 501 5th Avenue, 501 ÷ 20 ≈ 25 {\displaystyle 501\div 20\approx 25} , then add the "tricky number" 18 {\displaystyle 18} to give 43 {\displaystyle 43} . The nearest cross street to 501 5th Avenue is actually 42nd Street, not 43rd Street, as the Manhattan address algorithm only gives approximate answers.

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  • Operational historian

    Operational historian

    In manufacturing, an operational historian is a time-series database application that is developed for operational process data. Historian software is often embedded or used in conjunction with standard DCS and PLC control systems to provide enhanced data capture, validation, compression, and aggregation capabilities. Historians have been deployed in almost every industry and contribute to functions such as supervisory control, performance monitoring, quality assurance, and, more recently, machine learning applications which can learn from vast quantities of historical data. These systems were originally developed to capture instrumentation and control data, which led many to use the term "tag" for a stream of process data, referring to the physical "tags" which had been placed on instrumentation for manually capturing data. Raw data may be accessed via OPC HDA, SQL, or REST API interfaces. == Operational Support == Operational historians are typically used within the manufacturing facility by engineers and operators for supervisory functions and analysis. An operational historian will typically capture all instrumentation and control data, whereas an enterprise historian that is deployed to support business functions will capture only a subset of the plant data. Typically, these applications offer data access through dedicated APIs (Application Programming Interfaces) and SDKs (Software Development Kits) which offer high-performance read and write operations. These operate through vendor-specific or custom applications. Front-end tools for trending process data over time are the most common interfaces to these databases. Because these applications are typically deployed next to or near the source of their process data, they are often marketed and sold as 'real-time database systems.' This distinction varies among vendors, who often have to make tradeoffs in performance between data capture and presentation, and application and analysis functionality. The following is a list of typical challenges for operational historians: data collection from instrumentation and controls storage and archiving of very large volumes of data organization of data in the form of "tags" or "points" limiting of monitoring (alarms) and validation aggregation and interpolation manual data entry (MDE) == Data access == As opposed to enterprise historians, the data access layer in the operational historian is designed to offer sophisticated data fetching modes without complex information analysis facilities. The following settings are typically available for data access operations: Data scope (single point or tag, history based on time range, history based on sample count) Request modes (raw data, last-known value, aggregation, interpolation) Sampling (single point, all points without sampling, all points with interval sampling) Data omission (based on the sample quality, based on the sample value, based on the count) Even though the operational historians are rarely relational database management systems, they often offer SQL-based interfaces to query the database. In most of such implementations, the dialect does not follow the SQL standard in order to provide syntax for specifying data access operations parameters.

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  • Uncertain database

    Uncertain database

    An uncertain database is a kind of database studied in database theory. The goal of uncertain databases is to manage information on which there is some uncertainty. Uncertain databases make it possible to explicitly represent and manage uncertainty on the data, usually in a succinct way. == Formal definition == At the basis of uncertain databases is the notion of possible world. Specifically, a possible world of an uncertain database is a (certain) database which is one of the possible realizations of the uncertain database. A given uncertain database typically has more than one, and potentially infinitely many, possible worlds. A formalism to represent uncertain databases then explains how to succinctly represent a set of possible worlds into one uncertain database. == Types of uncertain databases == Uncertain database models differ in how they represent and quantify these possible worlds: Incomplete databases are a compact representation of the set of possible worlds – the use of NULL in SQL, arguably the most commonplace instantiation of uncertain databases, is an example of incomplete database model. Probabilistic databases are a compact representation of a probability distribution over the set of possible worlds. Fuzzy databases are a compact representation of a fuzzy set of the possible worlds. Though mostly studied in the relational setting, uncertain database models can also be defined in other relational models such as graph databases or XML databases. === Incomplete database === The most common database model is the relational model. Multiple incomplete database models have been defined over the relational model, that form extensions to the relational algebra. These have been called Imieliński–Lipski algebras: Relations with NULL values, also called Codd tables c-tables v-tables === Example === The following table is a relation of an incomplete database, described in the formalism of NULL values: There are infinitely many possible worlds for this incomplete database, obtained by replacing the "NULL" values with concrete values. For instance, the following relation is a possible world:

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  • Contract management software

    Contract management software

    Contract management software constitutes software and associated data management used to support contract management, contract lifecycle management, and contractor management on projects in the procurement of goods and services. It may be used together with project management software. == History == Historically, contract management was seen as a "paper-intensive" process. Early steps from the early 2000's reported by the Aberdeen Group required extensive data conversion work to enable documents to be handled electronically. With the adoption of the European Union's General Data Protection Regulation (GDPR) in 2016, companies needed to take additional steps in regards to contract management. Each data responsible entity was obliged to sign data processing agreements (DPAs) with the various vendors, who treat personal data on behalf of the data responsible. DPAs need to be regularly controlled, adjusted and renewed, which adds an extra agreement to such vendors or at least an extra DPA addendum to each agreement. By 2018, Ardent Partner's research had found that software used for automating contract management activities was being more extensively used among major companies or businesses with "Best-in-Class" procurement teams. Contract management process automation was found to be closely linked with more effective internal business collaboration, standardization and risk management. == Advantages and key functions == Using contract management software can have multiple benefits compared to manually managing paper contracts. This software can help keep track of multiple activities and can have features for automating administration, ensuring compliance, monitoring risk, running reports and triggering alerts. In addition to these types of features, contract management software systems provide a centralized repository for employees to quickly access all contracts worldwide in one place. Contract management software is produced by many companies, working on a range of scales and offering varying degrees of customizability. Basic functions should include the ability to store contract documents, track changes to contract documents, search documents for a particular criterion, send key date alerts and to report required aspects of the contract. Other functions include managing a new contract request, capturing related data, following a document through a review and approval process, and collecting digital signatures. Contract management software may also be an aid to project portfolio management and spend analysis, and may also monitor KPIs. Leading contract management software provides contract visibility, monitoring, and compliance to automate and streamline the contract lifecycle process. Contract management software which uses artificial intelligence (AI) can identify contract types based on pattern recognition. AI contracting software trains its algorithms on a set of contract data to recognize patterns and extract variables such as clauses, dates, and parties. It also offers simple prediction capabilities, by sorting through a large volume of contracts and flagging individual contracts based on specified criteria. AI software can also read contracts in multiple formats and languages, extract contract data, and provide analytics. It can reduce the risk of human error in contract drafting and review. A centralized repository provides a critical advantage allowing for all contract documents to be stored within one location. Having contracts stored in multiple locations can delay and interrupt the contracting process. == Contract risk management software (CRMS) for capital projects == Very large enterprises, such as capital expenditure (capex) projects, involve multiple parties and high risk and uncertainty. They are unlike traditional operating contracts in that they are subject to shared deadlines in unique situations. As the complexity of these unique projects increases, the relationships between parties become more important. This requires contract management software, or contract risk management software (CRMS), to become more dynamic and responsive. The terms of these capex contracts necessarily involve assumptions at the start of the process and are likely to change over the lifetime of the project lifecycle. For this reason, CRMS must be capable of recording one single instance of agreed changes to contract terms and incorporating these changes in an auditable and legally robust way. With multiple decision makers involved, CRMS should also make accountability more transparent and enable faster decisions about variation proposals.

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  • Algorithmic transparency

    Algorithmic transparency

    Algorithmic transparency is the principle that the factors that influence the decisions made by algorithms should be visible, or transparent, to the people who use, regulate, and are affected by systems that employ those algorithms. Although the phrase was coined in 2016 by Nicholas Diakopoulos and Michael Koliska about the role of algorithms in deciding the content of digital journalism services, the underlying principle dates back to the 1970s and the rise of automated systems for scoring consumer credit. The phrases "algorithmic transparency" and "algorithmic accountability" are sometimes used interchangeably – especially since they were coined by the same people – but they have subtly different meanings. Specifically, "algorithmic transparency" states that the inputs to the algorithm and the algorithm's use itself must be known, but they need not be fair. "Algorithmic accountability" implies that the organizations that use algorithms must be accountable for the decisions made by those algorithms, even though the decisions are being made by a machine, and not by a human being. Current research around algorithmic transparency interested in both societal effects of accessing remote services running algorithms, as well as mathematical and computer science approaches that can be used to achieve algorithmic transparency. In the United States, the Federal Trade Commission's Bureau of Consumer Protection studies how algorithms are used by consumers by conducting its own research on algorithmic transparency and by funding external research. In the European Union, the data protection laws that came into effect in May 2018 include a "right to explanation" of decisions made by algorithms, though it is unclear what this means. Furthermore, the European Union founded The European Center for Algorithmic Transparency (ECAT).

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  • Vinberg's algorithm

    Vinberg's algorithm

    In mathematics, Vinberg's algorithm is an algorithm, introduced by Ernest Borisovich Vinberg, for finding a fundamental domain of a hyperbolic reflection group. Conway (1983) used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1 in terms of the Leech lattice. == Description of the algorithm == Let Γ < I s o m ( H n ) {\displaystyle \Gamma <\mathrm {Isom} (\mathbb {H} ^{n})} be a hyperbolic reflection group. Choose any point v 0 ∈ H n {\displaystyle v_{0}\in \mathbb {H} ^{n}} ; we shall call it the basic (or initial) point. The fundamental domain P 0 {\displaystyle P_{0}} of its stabilizer Γ v 0 {\displaystyle \Gamma _{v_{0}}} is a polyhedral cone in H n {\displaystyle \mathbb {H} ^{n}} . Let H 1 , . . . , H m {\displaystyle H_{1},...,H_{m}} be the faces of this cone, and let a 1 , . . . , a m {\displaystyle a_{1},...,a_{m}} be outer normal vectors to it. Consider the half-spaces H k − = { x ∈ R n , 1 | ( x , a k ) ≤ 0 } . {\displaystyle H_{k}^{-}=\{x\in \mathbb {R} ^{n,1}|(x,a_{k})\leq 0\}.} There exists a unique fundamental polyhedron P {\displaystyle P} of Γ {\displaystyle \Gamma } contained in P 0 {\displaystyle P_{0}} and containing the point v 0 {\displaystyle v_{0}} . Its faces containing v 0 {\displaystyle v_{0}} are formed by faces H 1 , . . . , H m {\displaystyle H_{1},...,H_{m}} of the cone P 0 {\displaystyle P_{0}} . The other faces H m + 1 , . . . {\displaystyle H_{m+1},...} and the corresponding outward normals a m + 1 , . . . {\displaystyle a_{m+1},...} are constructed by induction. Namely, for H j {\displaystyle H_{j}} we take a mirror such that the root a j {\displaystyle a_{j}} orthogonal to it satisfies the conditions (1) ( v 0 , a j ) < 0 {\displaystyle (v_{0},a_{j})<0} ; (2) ( a i , a j ) ≤ 0 {\displaystyle (a_{i},a_{j})\leq 0} for all i < j {\displaystyle i Read more →

  • Hall circles

    Hall circles

    Hall circles (also known as M-circles and N-circles) are a graphical tool in control theory used to obtain values of a closed-loop transfer function from the Nyquist plot (or the Nichols plot) of the associated open-loop transfer function. Hall circles have been introduced in control theory by Albert C. Hall in his thesis. == Construction == Consider a closed-loop linear control system with open-loop transfer function given by transfer function G ( s ) {\displaystyle G(s)} and with a unit gain in the feedback loop. The closed-loop transfer function is given by T ( s ) = G ( s ) 1 + G ( s ) {\textstyle T(s)={\frac {G(s)}{1+G(s)}}} . To check the stability of T(s), it is possible to use the Nyquist stability criterion with the Nyquist plot of the open-loop transfer function G(s). Note, however, that the Nyquist plot of G(s) does not give the actual values of T(s). To get this information from the G(s)-plane, Hall proposed to construct the locus of points in the G(s)-plane such that T(s) has constant magnitude and also the locus of points in the G(s)-plane such that T(s) has constant phase angle. Given a positive real value M representing a fixed magnitude, and denoting G(s) by z, the points satisfying M = | T ( s ) | = | G ( s ) | | 1 + G ( s ) | = | z | | 1 + z | {\displaystyle M=|T(s)|={\frac {|G(s)|}{|1+G(s)|}}={\frac {|z|}{|1+z|}}} are given by the points z in the G(s)-plane such that the ratio of the distance between z and 0 and the distance between z and -1 is equal to M. The points z satisfying this locus condition are circles of Apollonius, and this locus is known in the context of control systems as M-circles. Given a positive real value N representing a phase angle, the points satisfying N = arg ⁡ [ G ( s ) 1 + G ( s ) ] = arg ⁡ [ G ( s ) ] − arg ⁡ [ 1 + G ( s ) ] = arg ⁡ [ z ] − arg ⁡ [ 1 + z ] {\displaystyle N=\arg \left[{\frac {G(s)}{1+G(s)}}\right]=\arg[G(s)]-\arg[1+G(s)]=\arg[z]-\arg[1+z]} are given by the points z in the G(s)-plane such that the angle between -1 and z and the angle between 0 and z is constant. In other words, the angle opposed to the line segment between -1 and 0 must be constant. This implies that the points z satisfying this locus condition are arcs of circles, and this locus is known in the context of control systems as N-circles. == Usage == To use the Hall circles, a plot of M and N circles is done over the Nyquist plot of the open-loop transfer function. The points of the intersection between these graphics give the corresponding value of the closed-loop transfer function. Hall circles are also used with the Nichols plot and in this setting, are also known as Nichols chart. Rather than overlaying directly the Hall circles over the Nichols plot, the points of the circles are transferred to a new coordinate system where the ordinate is given by 20 log 10 ⁡ ( | G ( s ) | ) {\displaystyle 20\log _{10}(|G(s)|)} and the abscissa is given by arg ⁡ ( G ( s ) ) {\displaystyle \arg(G(s))} . The advantage of using Nichols chart is that adjusting the gain of the open loop transfer function directly reflects in up and down translation of the Nichols plot in the chart.

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  • WomanStats Project

    WomanStats Project

    The WomanStats Project is a donor-funded research and database project housed at Brigham Young University that "seeks to collect detailed statistical data on the status of women around the world, and to connect that data with data on the security of states." The WomanStats Database aims to provide a comprehensive compilation of information on the status of women in the world. Coders comb the extant literature and conduct expert interviews to find qualitative and quantitative information on over 300 indicators of women's status in 174 countries with populations of at least 200,000. Access to the online database is free. == History and structure == WomanStats began as an outgrowth of a paper Dr. Valerie M. Hudson (of the Brigham Young University Political Science department) and one of her graduate students, Andrea den Boer, published in International Security on the association between national security and the abnormal sex ratio in Asia. After the success and influence of their first article, (later added as one of their top twenty national security articles of that journal of all time), Hudson and den Boer did further research on the connection between the status of women and national security, but found that there was no single database that covered the range of topics that they needed for their research. Consequently, they began compiling information on variables regarding the status of women around the world. The database was officially formed in 2001 and grew exponentially as it later added more variables. The Project went live on the Internet in July 2007. The principal investigators are: Valerie M. Hudson (International Relations), Bonnie Ballif-Spanvill (Psychology, emeritus), and Chad F. Emmett (Geography) all from Brigham Young University, Mary Caprioli from the University of Minnesota, Duluth (International Relations), Rose McDermott from Brown University (International Relations), Andrea Den Boer from the University of Kent at Canterbury in the United Kingdom (International Relations) and S. Matthew Stearmer from the Ohio State University (Sociology; doctoral student). Approximately a dozen undergraduate and graduate students at Brigham Young University and Texas A&M University work at any one time as coders for the project. The coders take the raw quantitative and qualitative data collected in government reports, news articles, research papers, etc. and sort the applicable information on women into categories. They may also implement scales developed by the principal investigators, or that they (the students) themselves have developed. == Database == As of February 2011, the database has 307 variables, covers 174 nations with populations over 200,000, uses 18,015 sources and contains over 111,000 individual data points. All data is referenced to original sources. Not every variable has information for each country; similarly, not all countries have information for each variable: overall, about 70% of country-variable combinations have information. These database coding gaps exist where information is not available or is incomplete, or variables are not collected and reported by governments or international organizations. At times, information from different sources may be contradictory, and the WomanStats Database records this discrepant information for triangulation purposes. == Users and role of the database == The database is meant to help fill a hole in the extant data on the situation of women around the world. WomanStats data and research has been vetted and/or used by the United Nations, the United States Department of Defense, the Central Intelligence Agency, and the World Bank. Their data and research were also used by the United States Senate Committee on Foreign Relations in crafting the International Violence Against Women’s Act. The Inter-Agency Network on Women and Gender Equality (IANWGE) of the United Nations has stated that the WomanStats project "filled a major gap in the availability of data on women" (2007). Victor Asal and Mitchell Brown, researchers not affiliated with WomanStats, stated in an article published in Politics and Policy that "one of the most significant challenges of cross-national empirical studies of the prevalence of interpersonal violence is the paucity of available data, particularly reliable data," and that "WomanStats has allowed for an important first glimpse at analyzing the factors related to interpersonal violence." They conclude by stating that "Our findings suggest that, in the same way that larger disciplinary resources have invested in interstate and intrastate war, disciplinary resources need to be expended in creating a data set exploring interpersonal violence. Until the rights and the lives of women and children are taken as seriously as the survival of states by more proactively collaborating on projects like WomanStats, we will continue to only have a small lens through which to understand problems like this." Princeton University professor Evan S. Liberman wrote, "Although data on political regimes and group conflict have been in far greater demand by political scientists than data on gender politics and policies, two gender-related databases provide...examples of innovative HIRDs. Both the Womanstats database project (Hudson et al. 2009) and the Research Network on Gender Politics and the State (RNGS) project (McBride et al. 2008) are well-integrated presentations of quantitative and qualitative data characterizing the quality of gender relations around the world and, in particular, analytic descriptions of the treatment of women."." == Research == The research component of WomanStats focuses on exploring the relationship between the situation of women and the behavior and security of states. Current research initiatives include: Exploring the relationship between violent instability and inequity and family law. Examining the effect of polygyny and marriage market dislocations on the rise of suicide terrorism. Documenting discrepancies between laws on the books and cultural practices on the ground concerning gender issues. Investigating how well the situation of women predicts the peacefulness of nations-states, compared to their variables such as democracy, wealth, and civilization. The Project has published articles in International Security, International Studies Quarterly, Peace and Conflict, Journal of Peace Research, Political Psychology, Cumberland Law Review, and World Political Review, and has a forthcoming book from Columbia University Press.

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  • Subject (documents)

    Subject (documents)

    In library and information science documents (such as books, articles and pictures) are classified and searched by subject – as well as by other attributes such as author, genre and document type. This makes "subject" a fundamental term in this field. Library and information specialists assign subject labels to documents to make them findable. There are many ways to do this and in general there is not always consensus about which subject should be assigned to a given document. To optimize subject indexing and searching, we need to have a deeper understanding of what a subject is. The question: "what is to be understood by the statement 'document A belongs to subject category X'?" has been debated in the field for more than 100 years (see below) == Theoretical view == === Charles Ammi Cutter (1837–1903) === For Cutter the stability of subjects depends on a social process in which their meaning is stabilized in a name or a designation. A subject "referred [...] to those intellections [...] that had received a name that itself represented a distinct consensus in usage" (Miksa, 1983a, p. 60) and: the "systematic structure of established subjects" is "resident in the public realm" (Miksa, 1983a, p. 69); "[s]ubjects are by their very nature locations in a classificatory structure of publicly accumulated knowledge (Miksa, 1983a, p. 61). Bernd Frohmann adds: "The stability of the public realm in turn relies upon natural and objective mental structures which, with proper education, govern a natural progression from particular to general concepts. Since for Cutter, mind, society, and SKO [Systems of Knowledge Organization] stand one behind the other, each supporting each, all manifesting the same structure, his discursive construction of subjects invites connections with discourses of mind, education, and society. The Dewey Decimal Classification (DDC), by contrast, severs those connections. Melvil Dewey emphasized more than once that his system maps no structure beyond its own; there is neither a "transcendental deduction" of its categories nor any reference to Cutter's objective structure of social consensus. It is content-free: Dewey disdained any philosophical excogitation of the meaning of his class symbols, leaving the job of finding verbal equivalents to others. His innovation and the essence of the system lay in the notation. The DDC is a poorly semiotic system of expanding nests of ten digits, lacking any referent beyond itself. In it, a subject is wholly constituted in terms of its position in the system. The essential characteristic of a subject is a class symbol which refers only to other symbols. Its verbal equivalent is accidental, a merely pragmatic characteristic... .... The conflict of interpretations over "subjects" became explicit in the battles between "bibliography" (an approach to subjects having much in common with Cutter's) and Dewey's "close classification". William Fletcher spoke for the scholarly bibliographer.... Fletcher's "subjects", like Cutter's, referred to the categories of a fantasized, stable social order, whereas Dewey's subjects were elements of a semiological system of standardized, techno-bureaucratic administrative software for the library in its corporate, rather than high culture, incarnation". (Frohmann, 1994, 112–113). Cutter's early view on what a subject is, is probably wiser than most understandings that dominated the 20th century – and also the understanding reflected in the ISO-standard quoted below. The early statements quoted by Frohmann indicate that subjects are somehow shaped in social processes. When that is said, it should be added that they are not particularly detailed or clear. We only get a vague idea of the social nature of subjects. === S. R. Ranganathan (1892–1972) === A classification system with an explicit theoretical foundation is Ranganathan's Colon Classification. Ranganathan provided an explicit definition of the concept of "subject": Subject – an organized body of ideas, whose extension and intension are likely to fall coherently within the field of interests and comfortably within the intellectual competence and the field of inevitable specialization of a normal person. A related definition is given by one of Ranganathan's students: A subject is an organized and systematized body of ideas. It may consist of one idea or a combination of several... Ranganathan's definition of "subject" is strongly influenced by his Colon Classification system. The colon system is based on the combination of single elements from facets to subject designation. This is the reason why the combined nature of subjects are emphasized so strongly. It leads, however, to absurdities such as the claim that gold cannot be a subject (but is alternatively termed "an isolate"). This aspect of the theory has been criticized by Metcalfe (1973, p. 318). Metcalfe's skepticism regarding Ranganathan's theory is formulated in hard words (op. cit., p. 317): "This pseudo-science imposed itself on British disciples from about 1950 on...". It seems unacceptable that Ranganathan defines the word subject in a way that favors his own system. A scientific concept like "subject" should make it possible to compare different ways of establishing access to information. Whether or not subjects are combined or not should be examined once their definition has been given, it should not determined a priori, in the definition. Besides the emphasis on the combined, organizing and systematizing nature of subjects contains Ranganathan's definition of subject the pragmatic demand, that a subject should be determined in a way that suits a normal person's competency or specialization. Again we see a strange kind of wishful thinking mixing a general understanding of a concept with demands put by his own specific system. One thing is what the word subject means, quite another issue is how to provide subject descriptions that fulfill demands such as the specificity of a given information retrieval language which fulfill demands put on the system, such as precision and recall. If researchers too often define terms in ways that favor specific kinds of systems, that are such definitions not useful to provide more general theories about subjects, subject analysis and IR. Among other things are comparative studies of different kinds of systems made difficult. Based on these arguments, as well as additional arguments which have been used in the literature, we may conclude that Ranganathan's definition of the concept "subject" is not suited for scientific use. Like the definition of "subject" given by the ISO-standard for topic maps, may Ranganathan's definition be useful within his own closed system. The purpose of a scientific and scholarly field is, however, to examine the relative fruitfulness of systems such as topic maps and Colon Classification. For such purpose is another understanding of "subject" necessary. === Patrick Wilson (1927–2003) === In his book Wilson (1968) examined – in particular by thought experiments – the suitability of different methods of examining the subject of a document. The methods were: identifying the author's purpose for writing the document, weighing the relative dominance and subordination of different elements in the picture, which the reading imposes on the reader, grouping or count the document's use of concepts and references, construing a set of rules for selecting elements deemed necessary (as opposed to unnecessary) for the work as a whole. Patrick Wilson shows convincingly that each of these methods are insufficient to determine the subject of a document and is led to conclude ( p. 89): "The notion of the subject of a writing is indeterminate..." or, on p. 92 (about what users may expect to find using a particular position in a library classification system): "For nothing definite can be expected of the things found at any given position". In connection to the last quote has Wilson an interesting footnote in which he writes that authors of documents often use terms in ambiguous ways ("hostility" is used as an example). Even if the librarian could personally develop a very precise understanding of a concept, he would be unable to use it in his classification, because none of the documents use the term in the same precise way. Based on this argumentation is Wilson led to conclude: "If people write on what are for them ill-defined phenomena, a correct description of their subjects must reflect the ill-definedness". Wilson's concept of subject was discussed by Hjørland (1992) who found that it is problematic to give up the precise understanding of such a basic term in LIS. Wilson's arguments led him to an agnostic position which Hjørland found unacceptable and unnecessary. Concerning the authors' use of ambiguous terms, the role of the subject analysis is to determine which documents would be fruitful for users to identify whether or not the documents use one or another term or whether a given term i

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  • Collective operation

    Collective operation

    Collective operations are building blocks for interaction patterns, that are often used in SPMD algorithms in the parallel programming context. Hence, there is an interest in efficient realizations of these operations. A realization of the collective operations is provided by the Message Passing Interface (MPI). == Definitions == In all asymptotic runtime functions, we denote the latency α {\displaystyle \alpha } (or startup time per message, independent of message size), the communication cost per word β {\displaystyle \beta } , the number of processing units p {\displaystyle p} and the input size per node n {\displaystyle n} . In cases where we have initial messages on more than one node we assume that all local messages are of the same size. To address individual processing units we use p i ∈ { p 0 , p 1 , … , p p − 1 } {\displaystyle p_{i}\in \{p_{0},p_{1},\dots ,p_{p-1}\}} . If we do not have an equal distribution, i.e. node p i {\displaystyle p_{i}} has a message of size n i {\displaystyle n_{i}} , we get an upper bound for the runtime by setting n = max ( n 0 , n 1 , … , n p − 1 ) {\displaystyle n=\max(n_{0},n_{1},\dots ,n_{p-1})} . A distributed memory model is assumed. The concepts are similar for the shared memory model. However, shared memory systems can provide hardware support for some operations like broadcast (§ Broadcast) for example, which allows convenient concurrent read. Thus, new algorithmic possibilities can become available. == Broadcast == The broadcast pattern is used to distribute data from one processing unit to all processing units, which is often needed in SPMD parallel programs to dispense input or global values. Broadcast can be interpreted as an inverse version of the reduce pattern (§ Reduce). Initially only root r {\displaystyle r} with i d {\displaystyle id} 0 {\displaystyle 0} stores message m {\displaystyle m} . During broadcast m {\displaystyle m} is sent to the remaining processing units, so that eventually m {\displaystyle m} is available to all processing units. Since an implementation by means of a sequential for-loop with p − 1 {\displaystyle p-1} iterations becomes a bottleneck, divide-and-conquer approaches are common. One possibility is to utilize a binomial tree structure with the requirement that p {\displaystyle p} has to be a power of two. When a processing unit is responsible for sending m {\displaystyle m} to processing units i . . j {\displaystyle i..j} , it sends m {\displaystyle m} to processing unit ⌈ ( i + j ) / 2 ⌉ {\displaystyle \left\lceil (i+j)/2\right\rceil } and delegates responsibility for the processing units ⌈ ( i + j ) / 2 ⌉ . . j {\displaystyle \left\lceil (i+j)/2\right\rceil ..j} to it, while its own responsibility is cut down to i . . ⌈ ( i + j ) / 2 ⌉ − 1 {\displaystyle i..\left\lceil (i+j)/2\right\rceil -1} . Binomial trees have a problem with long messages m {\displaystyle m} . The receiving unit of m {\displaystyle m} can only propagate the message to other units, after it received the whole message. In the meantime, the communication network is not utilized. Therefore pipelining on binary trees is used, where m {\displaystyle m} is split into an array of k {\displaystyle k} packets of size ⌈ n / k ⌉ {\displaystyle \left\lceil n/k\right\rceil } . The packets are then broadcast one after another, so that data is distributed fast in the communication network. Pipelined broadcast on balanced binary tree is possible in O ( α log ⁡ p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} , whereas for the non-pipelined case it takes O ( ( α + β n ) log ⁡ p ) {\displaystyle {\mathcal {O}}((\alpha +\beta n)\log p)} cost. == Reduce == The reduce pattern is used to collect data or partial results from different processing units and to combine them into a global result by a chosen operator. Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} initially. All m i {\displaystyle m_{i}} are aggregated by ⊗ {\displaystyle \otimes } and the result is eventually stored on p 0 {\displaystyle p_{0}} . The reduction operator ⊗ {\displaystyle \otimes } must be associative at least. Some algorithms require a commutative operator with a neutral element. Operators like s u m {\displaystyle sum} , m i n {\displaystyle min} , m a x {\displaystyle max} are common. Implementation considerations are similar to broadcast (§ Broadcast). For pipelining on binary trees the message must be representable as a vector of smaller object for component-wise reduction. Pipelined reduce on a balanced binary tree is possible in O ( α log ⁡ p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} . == All-Reduce == The all-reduce pattern (also called allreduce) is used if the result of a reduce operation (§ Reduce) must be distributed to all processing units. Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} initially. All m i {\displaystyle m_{i}} are aggregated by an operator ⊗ {\displaystyle \otimes } and the result is eventually stored on all p i {\displaystyle p_{i}} . Analog to the reduce operation, the operator ⊗ {\displaystyle \otimes } must be at least associative. All-reduce can be interpreted as a reduce operation with a subsequent broadcast (§ Broadcast). For long messages a corresponding implementation is suitable, whereas for short messages, the latency can be reduced by using a hypercube (Hypercube (communication pattern) § All-Gather/ All-Reduce) topology, if p {\displaystyle p} is a power of two. All-reduce can also be implemented with a butterfly algorithm and achieve optimal latency and bandwidth. All-reduce is possible in O ( α log ⁡ p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} , since reduce and broadcast are possible in O ( α log ⁡ p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} with pipelining on balanced binary trees. All-reduce implemented with a butterfly algorithm achieves the same asymptotic runtime. == Prefix-Sum/Scan == The prefix-sum or scan operation is used to collect data or partial results from different processing units and to compute intermediate results by an operator, which are stored on those processing units. It can be seen as a generalization of the reduce operation (§ Reduce). Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} . The operator ⊗ {\displaystyle \otimes } must be at least associative, whereas some algorithms require also a commutative operator and a neutral element. Common operators are s u m {\displaystyle sum} , m i n {\displaystyle min} and m a x {\displaystyle max} . Eventually processing unit p i {\displaystyle p_{i}} stores the prefix sum ⊗ i ′ <= i {\displaystyle \otimes _{i'<=i}} m i ′ {\displaystyle m_{i'}} . In the case of the so-called exclusive prefix sum, processing unit p i {\displaystyle p_{i}} stores the prefix sum ⊗ i ′ < i {\displaystyle \otimes _{i' Read more →

  • Read–write conflict

    Read–write conflict

    In computer science, in the field of databases, read–write conflict, also known as unrepeatable reads, is a computational anomaly associated with interleaved execution of transactions. Specifically, a read–write conflict occurs when a "transaction requests to read an entity for which an unclosed transaction has already made a write request." Given a schedule S S = [ T 1 T 2 R ( A ) R ( A ) W ( A ) C o m . R ( A ) W ( A ) C o m . ] {\displaystyle S={\begin{bmatrix}T1&T2\\R(A)&\\&R(A)\\&W(A)\\&Com.\\R(A)&\\W(A)&\\Com.&\end{bmatrix}}} In this example, T1 has read the original value of A, and is waiting for T2 to finish. T2 also reads the original value of A, overwrites A, and commits. However, when T1 reads from A, it discovers two different versions of A, and T1 would be forced to abort, because T1 would not know what to do. This is an unrepeatable read. This could never occur in a serial schedule, in which each transaction executes in its entirety before another begins. Strict two-phase locking (Strict 2PL) or Serializable Snapshot Isolation (SSI) prevent this conflict. == Real-world example == Alice and Bob are using a website to book tickets for a specific show. Only one ticket is left for the specific show. Alice signs on first to see that only one ticket is left, and finds it expensive. Alice takes time to decide. Bob signs on and also finds one ticket left, and orders it instantly. Bob purchases and logs off. Alice decides to buy a ticket, to find there are no tickets. This is a typical read–write conflict situation.

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  • Edge inference

    Edge inference

    Edge inference is the process of running machine learning or deep learning models on local devices (edge devices) such as smartphones, IoT devices, embedded systems, and edge servers instead of centralized cloud computing infrastructure. A key feature of edge computing is edge inference, which allows for real-time data processing, low latency, and improved privacy by reducing the amount of data sent to remote servers.

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  • List of library and information science journals

    List of library and information science journals

    This list covers the journals, magazines, periodicals already published and continuing in the discipline of library and information science (LIS). It doesn't include ceased titles or predatory journals. Titles listed were taken from various scholarly sources, UGC Care and Wikipedia articles. == LIS journal prestige as assessed by LIS faculty == In a 2013 article by Laura Manzari, 232 LIS faculty members from ALA-accredited information science programs ranked the most prestigious journals in library and information science. The following journals were ranked in the top ten most prestigious: Journal of the Association for Information Science and Technology The Library Quarterly Annual Review of Information Science and Technology Journal of Documentation Library Trends Library and Information Science Research Information Processing and Management Journal of Education for Library and Information Science Education College & Research Libraries First Monday (journal) A subsequent study by Safón and Docampo in 2023 identified impactful LIS journals based on their influence on papers published in other LIS publications. Journals listed in the top ten in this study that did not appear in Manzari's list include: Scientometrics International Journal of Information Management Quantitative Science Studies MIS Quarterly Information and Management Journal of the Association for Information Systems Journal of Informetrics The Journal of Academic Librarianship == India == Annals of Library and Information Studies. (Pub: CSIR-NIScPR ), Formerly: Annals of Library Science. ISSN 0003-4835. (1954-) OPEN ACCESS Collnet Journal of Scientrometrics and Information Management (Pub: Taru Publications, Online through Taylor and Francis) ISSN: 0973-7766 Online 2168-930X. College Libraries (Pub: West Bengal College Librarians’ Association (WBCLA) ISSN 0972-1975, Quarterly DESIDOC Journal of Library and Information Technology (DJLIT) (Formerly: DESIDOC Bulletin 0970-8154, DESIDOC Bulletin of Information Technology. 0971-4383/0974-0643) (Pub: Defence Scientific Information & Documentation Centre) ISSN: 0974-0643, ISSN: 0976-4658 (O), Bi-monthly, OPEN ACCESS. Grandhalaya Sarvaswam (Bilingual: Telugu & English) [Pub: Andhra Pradesh Library Association, Vijayawada, Andhra Pradesh, India] (1915–) Gyankosh: Journal of Library and Information Management. (Pub: Integrated Academy Of Management And Technology. Through: Indian Journals.Com). ISSN: 2229-4023 (P), 2249-3182. Half yearly. IASLIC Bulletin (Pub: Indian Association of Special Libraries and Information Centres) ISSN: 0018-8411. Quarterly (1956-) IASLIC Newsletter (Pub: Indian Association of Special Libraries and Information Centres. (Pub: Indian Association of Special Libraries and Information Centres) ISSN 0018-845X. Monthly. (1966-) INFLIBNET Newsletter. (Pub: INFLIBNET). Monthly. Informatics Studies. (Pub: Centre For Informatics Research And Development). Quarterly. Through: Indian journals.com. ISSN: 2583-8994 (Online), 2320-530X (Print) ISST Journal of Advances in Librarianship (Pub:Intellectuals Society for Socio-Techno Welfare) ISSN: 0976-9021. Semiannual. Journal of Advanced Research in Library and Information Science. (JALIS Publishers). 4/year. ISSN 2277-2219. Journal of Indian Library Association (Pub: Indian Library Association). ISSN (P) 2277-5145 O) 2456-513X. Quarterly. (1965-). Journal of Scientometric Research. (Pub: Phcog.Net). ISSN (P) 2321-6654, (O) 2320-0057]; Frequency : Triannual. KELPRO Bulletin (Pub: Kerala Library Professionals' Organisation - KELPRO). ISSN 0975-4911( Print),2582-497X (O).(1993-) KIIT Journal of Library and Information Management (Pub: KIIT University, online through Indian Journals.com) Half yearly. ISSN: 2348-0858. Library Herald. (Pub: Delhi Library Association - DLA). Quarterly. ISSN: 0024-2292. Library Progress (International). (Pub: Bpas Publications, Through: ). Half yearly. ISSN: 0970-1052. (O) ISSN: 2320-317X. (1981-) Pearl: A Journal of Library and Information Science. (Pub: University Library Teacher's Association of Andhra Pradesh, Hyderabad), ISSN: 0973-7081 (print), 0975-6922 (online). Quarterly. RBU Journal of Library and Information Science. (Pub: Rabindra Bharati University).ISSN: 0972-2750. Annual. SALIS Journal of Information Management and Technology - SJIMT. (Pub: Society for the Advancement of Library and Information Science). Half-yearly. ISSN 0975-4105. SALIS Journal of Library and Information Science - SJLIS: an International Journal. (Pub: Society for the Advancement of Library and Information Science). Half-yearly. ISSN: 0973-3108. SRELS journal of Information and Knowledge (Formerly: Library Science with a Slant to Documentation, ISSN: 0024-2543; Library Science with a Slant to Documentation and Information Studies ISSN: 0970-6089; SRELS Journal of Information Management ISSN: ). Quarterly. ISSN: 2583-9314 (O) World Digital Libraries. Half yearly. ISSN: 0974-567X (P), 0975-7597 (O). == Other countries == African Journal of Library, Archives and Information Science Art Libraries Journal (Cambridge University Press) Bibliothèque de l'École des Chartes Canadian Journal of Information and Library Science Cataloging & Classification Quarterly Communications in Information Literacy Cataloging & Classification Quarterly Catholic Library Association Children and Libraries Code4Lib Journal College & Research Libraries Communications in Information Literacy Disability in Library and Information Studies Electronic Journal of Academic and Special Librarianship El Profesional de la Información (es) (EPI) (Formerly Information World en Español) Evidence Based Library and Information Practice (journal) Faslname-ye Ketab Florida Libraries. Florida Library Association. Georgia Library Quarterly. Quarterly. (Pub: Georgia Library Association). Hipertext.net IFLA Journal In the Library with the Lead Pipe Information & Culture International Journal of Information Retrieval Research (IJIRR) Information Processing and Management Information Research Information Sciences (journal) Information Visualization (journal) Information, Communication & Society International Journal of Geographical Information Science Information Research: An International Electronic Journal (IR) Internet Research (journal) Issues in Science and Technology Librarianship Italian Journal of Library and Information Studies (JLIS.it) JLIS.it Journal of Documentation (JDoc) Journal of Information Ethics Journal of Information Science (JIS) Journal of Information Technology Journal of Informetrics Journal of Librarianship and Information Science Journal of Library & Information Studies - JLIS. (Pub: National Taiwan University) Journal of Library Administration Journal of Religious & Theological Information Journal of the Association for Information Science and Technology (Formerly Journal of the American Society for Information Science and Technology) (JASIST) Journal of the Medical Library Association Journal of the Canadian Health Libraries Association (Pub: Canadian Health Libraries Association). Knowledge Organization (journal) Knowledge Quest. (Pub: American Association of School Librarians) Library and Information Science Abstracts Library Literature and Information Science Library, Information Science & Technology Abstracts Library Literature and Information Science Retrospective Library Review (journal) Library Trends Libri (journal) Malaysian Journal of Library and Information Science MLA Forum New Century Library New Review of Children's Literature and Librarianship Notes (journal) Portal – Libraries and the Academy Progressive Librarian, Progressive Librarians Guild Reference and User Services Quarterly Reference Services Review Research Evaluation (journal) Scientometrics (journal) Serials Review South African Journal of Libraries and Information Science The Charleston Advisor The Christian Librarian, from the Association of Christian Librarians The Journal of Academic Librarianship The Library Quarterly (LQ) The Public-Access Computer Systems Review TripleC Webolog

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  • Flajolet–Martin algorithm

    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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