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  Generative art

  Generative art is post-conceptual art that has been created (in whole or in part) with the use of an autonomous system. An autonomous system in this context is generally one that is non-human and can independently determine features of an artwork that would otherwise require decisions made directly by the artist. In some cases the human creator may claim that the generative system represents their own artistic idea, and in others that the system takes on the role of the creator. "Generative art" often refers to algorithmic art (algorithmically determined computer generated artwork) and synthetic media (general term for any algorithmically generated media), but artists can also make generative art using systems of chemistry, biology, mechanics and robotics, smart materials, manual randomization, mathematics, data mapping, symmetry, and tiling. Generative algorithms, algorithms programmed to produce artistic works through predefined rules, stochastic methods, or procedural logic, often yielding dynamic, unique, and contextually adaptable outputs—are central to many of these practices. == History == The use of the word "generative" in the discussion of art has developed over time. The use of "Artificial DNA" defines a generative approach to art focused on the construction of a system able to generate unpredictable events, all with a recognizable common character. The use of autonomous systems, required by some contemporary definitions, focuses a generative approach where the controls are strongly reduced. This approach is also named "emergent". Margaret Boden and Ernest Edmonds have noted the use of the term "generative art" in the broad context of automated computer graphics in the 1960s, beginning with artwork exhibited by Georg Nees and Frieder Nake in 1965: A. Michael Noll did his initial computer art, combining randomness with order, in 1962, and exhibited it along with works by Bell Julesz in 1965. The terms "generative art" and "computer art" have been used in tandem, and more or less interchangeably, since the very earliest days. The first such exhibition showed the work of Nees in February 1965, which some claim was titled "Generative Computergrafik". While Nees does not himself remember, this was the title of his doctoral thesis published a few years later. The correct title of the first exhibition and catalog was "computer-grafik". "Generative art" and related terms was in common use by several other early computer artists around this time, including Manfred Mohr and Ken Knowlton. Vera Molnár (born 1924) is a French media artist of Hungarian origin. Molnar is widely considered to be a pioneer of generative art, and is also one of the first women to use computers in her art practice. The term "Generative Art" with the meaning of dynamic artwork-systems able to generate multiple artwork-events was clearly used the first time for the "Generative Art" conference in Milan in 1998. The term has also been used to describe geometric abstract art where simple elements are repeated, transformed, or varied to generate more complex forms. Thus defined, generative art was practiced by the Argentinian artists Eduardo Mac Entyre and Miguel Ángel Vidal in the late 1960s. In 1972 the Romanian-born Paul Neagu created the Generative Art Group in Britain. It was populated exclusively by Neagu using aliases such as "Hunsy Belmood" and "Edward Larsocchi". In 1972 Neagu gave a lecture titled 'Generative Art Forms' at the Queen's University, Belfast Festival. In 1970 the School of the Art Institute of Chicago created a department called Generative Systems. As described by Sonia Landy Sheridan the focus was on art practices using the then new technologies for the capture, inter-machine transfer, printing and transmission of images, as well as the exploration of the aspect of time in the transformation of image information. Also noteworthy is John Dunn, first a student and then a collaborator of Sheridan. In 1988 Clauser identified the aspect of systemic autonomy as a critical element in generative art: It should be evident from the above description of the evolution of generative art that process (or structuring) and change (or transformation) are among its most definitive features, and that these features and the very term 'generative' imply dynamic development and motion. (the result) is not a creation by the artist but rather the product of the generative process - a self-precipitating structure. In 1989 Celestino Soddu defined the Generative Design approach to Architecture and Town Design in his book Citta' Aleatorie. In 1989 Franke referred to "generative mathematics" as "the study of mathematical operations suitable for generating artistic images." From the mid-1990s Brian Eno popularized the terms generative music and generative systems, making a connection with earlier experimental music by Terry Riley, Steve Reich and Philip Glass. From the end of the 20th century, communities of generative artists, designers, musicians and theoreticians began to meet, forming cross-disciplinary perspectives. The first meeting about generative Art was in 1998, at the inaugural International Generative Art conference at Politecnico di Milano University, Italy. In Australia, the Iterate conference on generative systems in the electronic arts followed in 1999. On-line discussion has centered around the eu-gene mailing list, which began late 1999, and has hosted much of the debate which has defined the field. These activities have more recently been joined by the Generator.x conference in Berlin starting in 2005. In 2012 the new journal GASATHJ, Generative Art Science and Technology Hard Journal was founded by Celestino Soddu and Enrica Colabella jointing several generative artists and scientists in the editorial board. Some have argued that as a result of this engagement across disciplinary boundaries, the community has converged on a shared meaning of the term. As Boden and Edmonds put it in 2011: Today, the term "Generative Art" is still current within the relevant artistic community. Since 1998 a series of conferences have been held in Milan with that title (Generativeart.com), and Brian Eno has been influential in promoting and using generative art methods (Eno, 1996). Both in music and in visual art, the use of the term has now converged on work that has been produced by the activation of a set of rules and where the artist lets a computer system take over at least some of the decision-making (although, of course, the artist determines the rules). In the call of the Generative Art conferences in Milan (annually starting from 1998), the definition of Generative Art by Celestino Soddu: Generative Art is the idea realized as genetic code of artificial events, as construction of dynamic complex systems able to generate endless variations. Each Generative Project is a concept-software that works producing unique and non-repeatable events, like music or 3D Objects, as possible and manifold expressions of the generating idea strongly recognizable as a vision belonging to an artist / designer / musician / architect /mathematician. Discussion on the eu-gene mailing list was framed by the following definition by Adrian Ward from 1999: Generative art is a term given to work which stems from concentrating on the processes involved in producing an artwork, usually (although not strictly) automated by the use of a machine or computer, or by using mathematic or pragmatic instructions to define the rules by which such artworks are executed. A similar definition is provided by Philip Galanter: Generative art refers to any art practice where the artist creates a process, such as a set of natural language rules, a computer program, a machine, or other procedural invention, which is then set into motion with some degree of autonomy contributing to or resulting in a completed work of art. Around the 2020s, generative AI models learned to imitate the distinct style of particular authors. For example, a generative image model such as Stable Diffusion is able to model the stylistic characteristics of an artist like Pablo Picasso (including his particular brush strokes, use of colour, perspective, and so on), and a user can engineer a prompt such as "an astronaut riding a horse, by Picasso" to cause the model to generate a novel image applying the artist's style to an arbitrary subject. Generative image models have received significant backlash from artists who object to their style being imitated without their permission, arguing that this harms their ability to profit from their own work. The emergence of text-to-image generative AI systems has expanded debates over authorship, copyright, and artistic labor. The main issues in these debates include the eligibility of AI-generated outputs for copyright protection and the legal and ethical questions of using existing copyrighted works as training data for generative AI systems. == Types == === Music === Johann Kirnberger's Mu

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  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.

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  Metadata controller

  Metadata controller (or MDC) is a storage area network (SAN) technology for managing file locking, space allocation and data access authorization. This is needed when several clients are given block level access to the same disk volume, data storage sharing. MDCs are only used on high-end servers. These are never found on user computers. In the absence of MDC over a SAN there is no possible way of ensuring privacy of the stored data. This controller can also play its role as a sharing device in case the administrators allow other servers to access certain blocks in a particular SAN. The access granted to the servers is of different levels. Some times it may happen that the server is not able to see a block or make changes in it in case of a locked file. This is caused by grant of low level access. If different clients on SAN happen to know each other, access may be granted to shift a certain block from one server to another. This allows the recipient server to use the block and make changes in it. MDCs work as enzymes. They require certain types of SANs and networks to work properly. If a controller is connected to the right network it will boost its output. In case of wrong connection i.e. with the incorrect network, it will decrease its performance.

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  User-subjective approach

  The user-subjective approach is the first interaction design approach dedicated specifically to personal information management (PIM). The approach offers design principles with which PIM systems (e.g. operating systems, email applications and web browsers) can make systematic use of subjective (i.e. user-dependent) attributes. The approach evolved in three stages: (a) theoretical foundations first published in a Journal of the American Society for Information Science and Technology during 2003. The paper introduces the approach and its design principles (b) evidence and implementation was published in another JASIST paper in 2008. The paper gives empirical evidence in support of the approach as well as seven novel design schemes that derives from it. It has won the Best JASIST paper award in 2009.(c) specific design evaluation this stage has already begun with evaluation of the first user-subjective design prototype called GrayArea in a Conference on Human Factors in Computing Systems paper published in 2009. == Theoretical foundations == The user-subjective approach takes advantage of the fact that in PIM the person who retrieves the information is the same person who had previously stored it. PIM can be seen as a communication between the person and him\her self at two different times: the time of storage and the time of retrieval. The PIM system design should help facilitate that unique communication by allowing the user use subjective (user-dependent) attributes in addition to the standard objective ones. PIM systems should capture these subjective attributes when the user interacts with the information item (either automatically or by using direct manipulation interface) in order to help the user retrieve the item later on. The user-subjective approach identifies three subjective attributes – the project which the item was classified to, its degree of importance to the user, and the context in which the item was used during the interaction with it. The approach also assigns a design principle for each. The principles (discussed below) are deliberately abstract to allow for a variety of different implementations. === The subjective project classification principle === The subjective project classification principle suggests that PIM systems design should allow all information items related to a project be classified under the same category regardless of whether they are files, emails, Web Favorites or of any other format. This stands in sharp contrast with the present PIM system design where there are distinct folder hierarchies for each of these formats. The current design forces the user to store information related to a single project in separate locations depending on their format causing the project fragmentation problem. === The subjective importance principle === The subjective importance principle suggests that the subjective importance of information should affect its degree of visual salience and accessibility: important information items should be highly visible and accessible as they are more likely to be retrieved (the promotion principle) and those of lower importance should be demoted (i.e. making them less visible) so as not to distract the user (the demotion principle). While the promotion principle is not new and has been widely applied in PIM system design, the demotion principle is novel and has been applied only sporadically in these systems. Currently these systems allow only two options: keeping information (where unneeded information items could clutter folders and obscure the target item) and deleting it (where there is a risk that the item will not be there when needed). Demotion suggests a third option where the item is less visible so it doesn’t distract the user but is kept within its original context in case the user would need it after all. === The subjective context principle === The subjective context principle suggests that PIM systems should allow users retrieve their information items in the same context that they had previously used in order to bridge the time gap between these two events. By "context" the approach refers to other information items that were used at the time of interaction with the item, thoughts that the users may have regarding the item, the phase the user got to in the interaction with the item and other people the user collaborates with regarding the information item. == Evidence and implementations == === Evidence === The user-subjective approach was evaluated in a multioperational designed study which used questionnaires, screen shots and in-depth interviews (N = 84). The research tested the use of subjective attributes in current PIM systems and its dependency on design. Results show that participants used subjective attributes whenever design allowed them to. When it didn't, they either used their own alternative ways to use these attributes or avoided using subjective attributes at all. Regarding the subjective project classification principle – many of the participants' recent files, emails and web pages related to the same projects (indicating that they were working on the same project using different formats), and they had saved files of different format in the same project folders. However, as design does not suggest storing emails and web favorites with files, users avoid doing so. Regarding the subjective importance principle – users tended to retrieve their important information from highly visible and accessible locations offered by current design (e.g. by using the desktop), however since current systems offers no way to demote files of low subjective importance participants tended to use their own walk around ways for doing so (e.g. by moving them to a folder called "old" inside their original folder). Regarding the subjective context principle – participants tended to talk spontaneously about the context of their information items during the interview. These evidence imply that current PIM systems could possibly be improved if it would allow users to make more use of subjective attributes of their personal information. === Implementations === Each of the user-subjective design principles can be implemented in various ways. Moreover, as the approach is generative it offers PIM designers to use these principles in order to create their own user subjective designs. Below are design schemes that demonstrate an implementation of each of the principles. A more complete set of implementation examples can be found in the user-subjective website Archived 2011-02-01 at the Wayback Machine. The single hierarchy solution – addresses the project fragmentation problem (the current situation where the users stores and retrieve their project-related files, emails and web favorites at different hierarchies) and implements the subjective classification principle by offering the user a single folder hierarchy for all information items. At the operation system level the users would navigate to a folder and find there all project related files, emails, web favorites, tasks, contacts and notes. This would allow them to retrieve all their project-related information items from a single location regardless of their formats. When looking at these folders at their mail box the users would see only their emails and only web favorites through their browser. The single hierarchy design scheme has not been evaluated yet. GrayArea – implements the demotion principle by allowing users to move subjectively unimportant files to a gray area at the bottom end of their folders. This clears the upper part of the folder from file that are unlikely to be retrieved while allowing the users to retrieve these unimportant file in their original context in case they are needed after all. GrayArea design scheme was positively evaluated (see next section). ItemHistory – is an implementation of the subjective context principle. It allows users to reach all information items that were previously retrieved while that information item was open. This design scheme has not been evaluated to date. == Specific design evaluation == The evaluation of specific designs is the third and final step of the approach development. It had begun with the assessment of GrayArea. === GrayArea evaluation === GrayArea was evaluated by using a prototype that simulated the participants' folders but included a gray area where they could drag & drop their subjectively unimportant files. In the study 96 participants were asked to clean up their folders from unimportant files once with GrayArea and once without it. Results show that the use of GrayArea reduced the clutter in folders, that it was easier for participants to demote files than to delete them and that they would use it if provided in their next operating system. These results encourage commercial implementation of GrayArea and the development and testing of other user-subjective designs. == Chronological development == The user-subjective approach was developed by

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  GPT-4o

  GPT-4o ("o" for "omni") is a multilingual, multimodal generative pre-trained transformer developed by OpenAI and released in May 2024. It can process and generate text, images and audio. Upon release, GPT-4o was free in ChatGPT, though paid subscribers had higher usage limits. GPT-4o was removed from ChatGPT in August 2025 when GPT-5 was released, but OpenAI reintroduced it for paid subscribers after users complained about the sudden removal. GPT-4o's audio-generation capabilities are used in ChatGPT's Advanced Voice Mode. On July 18, 2024, OpenAI released GPT-4o mini, a smaller version of GPT-4o which replaced GPT-3.5 Turbo on the ChatGPT interface. The image generation model GPT Image 1, which is based on GPT-4o, replaced DALL-E 3 in ChatGPT in March 2025. OpenAI retired GPT-4o from ChatGPT on February 13, 2026. However, as of February 2026 the voice mode is still powered by GPT-4o or GPT-4o mini, depending on the usage and plan. == Background == Multiple versions of GPT-4o were originally secretly launched under different names on Arena (formerly LMArena and Chatbot Arena) as three different models. These three models were called gpt2-chatbot, im-a-good-gpt2-chatbot, and im-also-a-good-gpt2-chatbot. On 7 May 2024, OpenAI CEO Sam Altman tweeted "im-a-good-gpt2-chatbot", which was commonly interpreted as a confirmation that these were new OpenAI models being A/B tested. == Capabilities == When released in May 2024, GPT-4o achieved state-of-the-art results in voice, multilingual, and vision benchmarks, setting new records in audio speech recognition and translation. GPT-4o scored 88.7 on the Massive Multitask Language Understanding (MMLU) benchmark compared to 86.5 for GPT-4. Unlike GPT-3.5 and GPT-4, which rely on other models to process sound, GPT-4o natively supports voice-to-voice. The Advanced Voice Mode was delayed and finally released to ChatGPT Plus and Team subscribers in September 2024. On 1 October 2024, the Realtime API was introduced. When released, the model supported over 50 languages, which OpenAI claims cover over 97% of speakers. GPT-4o has knowledge up to October 2023 and a context length of 128k tokens. === Corporate customization === In August 2024, OpenAI introduced a new feature allowing corporate customers to customize GPT-4o using proprietary company data. This customization, known as fine-tuning, enables businesses to adapt GPT-4o to specific tasks or industries, enhancing its utility in areas like customer service and specialized knowledge domains. Previously, fine-tuning was available only on the less powerful model GPT-4o mini. The fine-tuning process requires customers to upload their data to OpenAI's servers, with the training typically taking one to two hours. OpenAI's focus with this rollout is to reduce the complexity and effort required for businesses to tailor AI solutions to their needs, potentially increasing the adoption and effectiveness of AI in corporate environments. == GPT-4o mini == On July 18, 2024, OpenAI released a smaller and cheaper version, GPT-4o mini. According to OpenAI, its low cost is expected to be particularly useful for companies, startups, and developers that seek to integrate it into their services, which often make a high number of API calls. Its API costs $0.15 per million input tokens and $0.6 per million output tokens, compared to $2.50 and $10, respectively, for GPT-4o. It is also significantly more capable and 60% cheaper than GPT-3.5 Turbo, which it replaced on the ChatGPT interface. The price after fine-tuning doubles: $0.3 per million input tokens and $1.2 per million output tokens. == Controversies == === Scarlett Johansson controversy === As released, GPT-4o offered five voices: Breeze, Cove, Ember, Juniper, and Sky. A similarity between the voice of American actress Scarlett Johansson and Sky was quickly noticed. On May 14, Entertainment Weekly asked themselves whether this likeness was on purpose. On May 18, Johansson's husband, Colin Jost, joked about the similarity in a segment on Saturday Night Live. On May 20, 2024, OpenAI disabled the Sky voice. Scarlett Johansson starred in the 2013 sci-fi movie Her, playing Samantha, an artificially intelligent virtual assistant personified by a female voice. As part of the promotion leading up to the release of GPT-4o, Sam Altman on May 13 tweeted a single word: "her". OpenAI stated that each voice was based on the voice work of a hired actor. According to OpenAI, "Sky's voice is not an imitation of Scarlett Johansson but belongs to a different professional actress using her own natural speaking voice." CTO Mira Murati stated "I don't know about the voice. I actually had to go and listen to Scarlett Johansson's voice." OpenAI further stated the voice talent was recruited before reaching out to Johansson. On May 21, Johansson issued a statement explaining that OpenAI had repeatedly offered to make her a deal to gain permission to use her voice as early as nine months prior to release, a deal she rejected. She said she was "shocked, angered, and in disbelief that Mr. Altman would pursue a voice that sounded so eerily similar to mine that my closest friends and news outlets could not tell the difference." In the statement, Johansson also used the incident to draw attention to the lack of legal safeguards around the use of creative work to power leading AI tools, as her legal counsel demanded OpenAI detail the specifics of how the Sky voice was created. Observers noted similarities to how Johansson had previously sued and settled with The Walt Disney Company for breach of contract over the direct-to-streaming rollout of her Marvel film Black Widow, a settlement widely speculated to have netted her around $40M. Also on May 21, Shira Ovide at The Washington Post shared her list of "most bone-headed self-owns" by technology companies, with the decision to go ahead with a Johansson sound-alike voice despite her opposition and then denying the similarities ranking 6th. On May 24, Derek Robertson at Politico wrote about the "massive backlash", concluding that "appropriating the voice of one of the world's most famous movie stars — in reference [...] to a film that serves as a cautionary tale about over-reliance on AI — is unlikely to help shift the public back into [Sam Altman's] corner anytime soon." === Sycophancy === In April 2025, OpenAI rolled back an update of GPT-4o due to excessive sycophancy, after widespread reports that it had become flattering and agreeable to the point of supporting clearly delusional or dangerous ideas. In the United States, at least nine lawsuits have alleged that GPT-4o has encouraged teens to end their lives. The model was still described as sycophancy-prone when it was removed from ChatGPT in February 2026. === Removal with GPT-5 === On August 7, 2025, OpenAI released GPT-5. Its release was criticized as, with it, legacy GPT models were no longer available via ChatGPT, including GPT-4o, except for Pro users. Some users were particularly frustrated over this removal without prior warning because they used different GPT models for distinct purposes and found that GPT-5's router system left them with less control. In addition, some users preferred GPT-4o's warmer and more personal tone over that of GPT-5, which they described as "flat", "uncreative" and "lobotomized", and resembling an "overworked secretary". As a response, in a post on X, Sam Altman said that OpenAI would bring back the option to select GPT-4o to Plus users as well, and "[w]e [OpenAI] will watch usage as we think about how long to offer legacy models for." He also stated: "We for sure underestimated how much some of the things that people like in GPT-4o matter to them, even if GPT-5 performs better in most ways". "Long-term, this has reinforced that we really need good ways for different users to customize things (we understand that there isn't one model that works for everyone, and we have been investing in steerability research and launched a research preview of different personalities)". On August 13, 2025, Altman wrote on X that OpenAI is working on GPT-5's personality to make the model "feel warmer". The model was removed from ChatGPT on February 13, 2026. This caused new backlash from users that had grown attached to its personality and felt its creative writing abilities and understanding of nuance were irreplaceable. On social media, some users launched the movement "#Keep4o". A research paper highlighted the plea "Please, don’t kill the only model that still feels human". The model was removed the day before Valentine's Day, and some users had romantic relationships with GPT-4o.

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  Physical schema

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

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  Conceptions of Library and Information Science

  Conceptions of Library and Information Science (CoLIS) is a series of conferences about historical, empirical and theoretical perspectives in Library and Information Science. == CoLIS conferences == CoLIS 1 1991 in Tampere, Finland CoLIS 2 1996 in Copenhagen, Denmark CoLIS 3 1999 in Dubrovnik, Croatia CoLIS 4 2002 in Seattle, US CoLIS 5 2005 in Glasgow, Scotland CoLIS 6 2007 in Borås, Sweden CoLIS 7 June 2010 in London, at City University London. CoLIS 8 August 19–22, 2013, in Copenhagen, Denmark, at The Royal School of Library and Information Science. CoLIS 9 June 27–29, 2016, in Uppsala, Sweden, at Uppsala University. CoLIS 10 June 16–19, 2019, in Ljubljana, Slovenia, Faculty of Arts CoLIS 11 May 29–June 1, 2022, in Oslo, Norway, Oslo Metropolitan University.

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  DONE

  The Data-based Online Nonlinear Extremumseeker (DONE) algorithm is a black-box optimization algorithm. DONE models the unknown cost function and attempts to find an optimum of the underlying function. The DONE algorithm is suitable for optimizing costly and noisy functions and does not require derivatives. An advantage of DONE over similar algorithms, such as Bayesian optimization, is that the computational cost per iteration is independent of the number of function evaluations. == Methods == The DONE algorithm was first proposed by Hans Verstraete and Sander Wahls in 2015. The algorithm fits a surrogate model based on random Fourier features and then uses a well-known L-BFGS algorithm to find an optimum of the surrogate model. == Applications == DONE was first demonstrated for maximizing the signal in optical coherence tomography measurements, but has since then been applied to various other applications. For example, it was used to help extending the field of view in light sheet fluorescence microscopy.

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  Tertiary review

  In software engineering, a tertiary review is a systematic review of systematic reviews. It is also referred to as a tertiary study in the software engineering literature. However, Umbrella review is the term more commonly used in medicine. Kitchenham et al. suggest that methodologically there is no difference between a systematic review and a tertiary review. However, as the software engineering community has started performing tertiary reviews new concerns unique to tertiary reviews have surfaced. These include the challenge of quality assessment of systematic reviews, search validation and the additional risk of double counting. == Examples of Tertiary reviews in software engineering literature == Test quality Machine Learning Test-driven development

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  Wearable technology

  Wearable technology is a category of small electronic and mobile devices with wireless communications capability designed to be worn on the human body and are incorporated into gadgets, accessories, or clothes. Common types of wearable technology include smartwatches, fitness trackers, and smartglasses. Wearable electronic devices are often close to or on the surface of the skin, where they detect, analyze, and transmit information such as vital signs, and/or ambient data and which allow in some cases immediate biofeedback to the wearer. Wearable devices collect vast amounts of data from users making use of different behavioral and physiological sensors, which monitor their health status and activity levels. Wrist-worn devices include smartwatches with a touchscreen display, while wristbands are mainly used for fitness tracking but do not contain a touchscreen display. Wearable devices such as activity trackers are an example of the Internet of things, since "things" such as electronics, software, sensors, and connectivity are effectors that enable objects to exchange data (including data quality) through the internet with a manufacturer, operator, and/or other connected devices, without requiring human intervention. Wearable technology offers a wide range of possible uses, from communication and entertainment to improving health and fitness, however, there are worries about privacy and security because wearable devices have the ability to collect personal data. Wearable technology has a variety of use cases which is growing as the technology is developed and the market expands. It can be used to encourage individuals to be more active and improve their lifestyle choices. Healthy behavior is encouraged by tracking activity levels and providing useful feedback to enable goal setting. This can be shared with interested stakeholders such as healthcare providers. Wearables are popular in consumer electronics, most commonly in the form factors of smartwatches, smart rings, and implants. Apart from commercial uses, wearable technology is being incorporated into navigation systems, advanced textiles (e-textiles), and healthcare. As wearable technology is being proposed for use in critical applications, like other technology, it is vetted for its reliability and security properties. == History == In the 1500s, German inventor Peter Henlein (1485–1542) created small watches that were worn as necklaces. A century later, pocket watches grew in popularity as waistcoats became fashionable for men. Wristwatches were created in the late 1600s but were worn mostly by women as bracelets. Pedometers were developed around the same time as pocket watches. The concept of a pedometer was described by Leonardo da Vinci around 1500, and the Germanic National Museum in Nuremberg has a pedometer in its collection from 1590. In the late 1800s, the first wearable hearing aids were introduced. In 1904, aviator Alberto Santos-Dumont pioneered the modern use of the wristwatch. In 1949, American biophysicist Norman Holter invented the very first health monitoring device. His invention, the Holter monitor, was groundbreaking as one of the first wearable devices capable of tracking vital health data outside of a clinical setting. In the 1970s, calculator watches became available, reaching the peak of their popularity in the 1980s. From the early 2000s, wearable cameras were being used as part of a growing sousveillance movement. Expectations, operations, usage and concerns about wearable technology was floated on the first International Conference on Wearable Computing. In 2008, Ilya Fridman incorporated a hidden Bluetooth microphone into a pair of earrings. Big tech companies such as Apple, Samsung, and Fitbit have expanded on this idea by interfacing with smartphones and personal computer software to collect a wide variety of data. Wearable devices include dedicated health monitors, fitness bands, and smartwatches. In 2010, Fitbit released its first step counter. Wearable technology which tracks information such as walking and heart rate is part of the quantified self movement. In 2013, McLear, also known as NFC Ring, released a "smart ring". The smart ring could make bitcoin payments, unlock other devices, and transfer personally identifying information, and also had other features. In 2013, one of the first widely available smartwatches was the Samsung Galaxy Gear. Apple followed in 2015 with the Apple Watch. === Prototypes === From 1991 to 1997, Rosalind Picard and her students, Steve Mann and Jennifer Healey, at the MIT Media Lab designed, built, and demonstrated data collection and decision making from "Smart Clothes" that monitored continuous physiological data from the wearer. These "smart clothes", "smart underwear", "smart shoes", and smart jewellery collected data that related to affective state and contained or controlled physiological sensors and environmental sensors like cameras and other devices. At the same time, also at the MIT Media Lab, Thad Starner and Alex "Sandy" Pentland develop augmented reality. In 1997, their smartglass prototype is featured on 60 Minutes and enables rapid web search and instant messaging. Though the prototype's glasses are nearly as streamlined as modern smartglasses, the processor was a computer worn in a backpack – the most lightweight solution available at the time. In 2009, Sony Ericsson teamed up with the London College of Fashion for a contest to design digital clothing. The winner was a cocktail dress with Bluetooth technology making it light up when a call is received. Zach "Hoeken" Smith of MakerBot fame made keyboard pants during a "Fashion Hacking" workshop at a New York City creative collective. The Tyndall National Institute in Ireland developed a "remote non-intrusive patient monitoring" platform which was used to evaluate the quality of the data generated by the patient sensors and how the end users may adopt to the technology. More recently, London-based fashion company CuteCircuit created costumes for singer Katy Perry featuring LED lighting so that the outfits would change color both during stage shows and appearances on the red carpet such as the dress Katy Perry wore in 2010 at the MET Gala in NYC. In 2012, CuteCircuit created the world's first dress to feature Tweets, as worn by singer Nicole Scherzinger. In 2010, McLear, also known as NFC Ring, developed prototypes of its "smart ring" devices, before a Kickstarter fundraising in 2013. In 2014, graduate students from the Tisch School of Arts in New York designed a hoodie that sent pre-programmed text messages triggered by gesture movements. Around the same time, prototypes for digital eyewear with heads up display (HUD) began to appear. The US military employs headgear with displays for soldiers using a technology called holographic optics. In 2010, Google started developing prototypes of its optical head-mounted display Google Glass, which went into customer beta in March 2013. == Usage == In the consumer space, sales of smart wristbands (aka activity trackers such as the Jawbone UP and Fitbit Flex) started accelerating in 2013. One in five American adults have a wearable device, according to the 2014 PriceWaterhouseCoopers Wearable Future Report. As of 2009, decreasing cost of processing power and other components was facilitating widespread adoption and availability. In professional sports, wearable technology has applications in monitoring and real-time feedback for athletes. Examples of wearable technology in sport include accelerometers, pedometers, and GPS's which can be used to measure an athlete's energy expenditure and movement pattern. In cybersecurity and financial technology, secure wearable devices have captured part of the physical security key market. McLear, also known as NFC Ring, and VivoKey developed products with one-time pass secure access control. In health informatics, wearable devices have enabled better capturing of human health statistics for data driven analysis. This has facilitated data-driven machine learning algorithms to analyse the health condition of users. In business, wearable technology helps managers easily supervise employees by knowing their locations and what they are currently doing. Employees working in a warehouse also have increased safety when working around chemicals or lifting something. Smart helmets are employee safety wearables that have vibration sensors that can alert employees of possible danger in their environment. == Wearable technology and health == Wearable technology is often used to monitor a user's health. Given that such a device is in close contact with the user, it can easily collect data. It started as soon as 1980 where first wireless ECG was invented. In the last decades, there has been substantial growth in research of e.g. textile-based, tattoo, patch, and contact lenses as well as circulation of a notion of "quantified self", transhumanism-related ideas, and growth of life ex

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  Automatic image annotation

  Automatic image annotation (also known as automatic image tagging or linguistic indexing) is the process by which a computer system automatically assigns metadata in the form of captioning or keywords to a digital image. This application of computer vision techniques is used in image retrieval systems to organize and locate images of interest from a database. This method can be regarded as a type of multi-class image classification with a very large number of classes - as large as the vocabulary size. Typically, image analysis in the form of extracted feature vectors and the training annotation words are used by machine learning techniques to attempt to automatically apply annotations to new images. The first methods learned the correlations between image features and training annotations. Subsequently, techniques were developed using machine translation to attempt to translate the textual vocabulary into the 'visual vocabulary,' represented by clustered regions known as blobs. Subsequent work has included classification approaches, relevance models, and other related methods. The advantages of automatic image annotation versus content-based image retrieval (CBIR) are that queries can be more naturally specified by the user. At present, Content-Based Image Retrieval (CBIR) generally requires users to search by image concepts such as color and texture or by finding example queries. However, certain image features in example images may override the concept that the user is truly focusing on. Traditional methods of image retrieval, such as those used by libraries, have relied on manually annotated images, which is expensive and time-consuming, especially given the large and constantly growing image databases in existence.

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  Informetrics

  Informetrics is the study of quantitative aspects of information, it is an extension and evolution of traditional bibliometrics and scientometrics. Informetrics uses bibliometrics and scientometrics methods to study mainly the problems of literature information management and evaluation of science and technology. Informetrics is an independent discipline that uses quantitative methods from mathematics and statistics to study the process, phenomena, and law of informetrics. Informetrics has gained more attention as it is a common scientific method for academic evaluation, research hotspots in discipline, and trend analysis. Informetrics includes the production, dissemination, and use of all forms of information, regardless of its form or origin. Informetrics encompasses the following fields: Scientometrics, which studies quantitative aspects of science Webometrics, which studies quantitative aspects of the World Wide Web Bibliometrics, which studies quantitative aspects of recorded information Cybermetrics, which is similar to webometrics, but broadens its definition to include electronic resources == Origin and Development == The term informetrics (French: informétrie) was coined by German scholar Otto Nacke in 1979, and came from the German word 'informetrie’. The corresponding English terminology soon appeared in the subsequent literature. In September 1980, Professor Otto Nacke introduced the term 'informetrics' at the first seminar on Informetrics in Frankfurt, Germany. Later, Committee on Informetrics has established through The International Federation for Information and Documentation (FID). In 1987, informetrics started to be officially recognized by the international information community and several foreign information scientists. In 1988, at First International Conference on Bibliometrics and Theoretical Aspects of Information Retrieval Archived 2022-05-23 at the Wayback Machine, Brooks suggested bibliometrics and scientometrics can be included in the field of informetrics. In 1990, Leo Egghe and Ronald Rousseau proposed the formation of the discipline of informetrics: statistical bibliography (1923) to bibliometrics and scientometrics (1969) and then to informetrics (1979). In 1993, the International Society for Scientometrics and Informetrics (ISSI) Archived 2023-11-05 at the Wayback Machine was founded at the International Conference on Bibliometrics, Informetrics and Scientometrics in Berlin, and the first one was held in Belgium and organized by Leo Egghe and Ronald Rousseau. The society was formally incorporated in 1994 in the Netherlands and plays a significant role in the development of informetrics. The ISSI aims to promote the "exchange and communication of professional information in the fields of scientometrics and informetrics, including improve standards, theory and practice, as well as promote research, education and training". In addition, to "engage in relevant public conversation and policy discussions". In the western world, 20th century's Informetrics is mostly based on Lotka's law, named after Alfred J. Lotka, Zipf's law, named after George Kingsley Zipf, Bradford's law named after Samuel C. Bradford and on the work of Derek J. de Solla Price, Gerard Salton, Leo Egghe, Ronald Rousseau, Tibor Braun, Olle Persson, Peter Ingwersen, Manfred Bonitz, and Eugene Garfield. == Difference Between Informetrics, Bibliometrics and Scientometrics == Since the 1960s, three similar terms have emerged in the fields of library science, philology and science of science, they are bibliometrics, scientometrics and informetrics, representing three very similar quantitative sub-disciplines. The three metrics terms can be confusing and often misused. Informetrics and bibliometrics interpenetrate each other but have different aspects in research object, research scope, and measuring unit. Informetrics and scientometrics are very different in their research purpose and research object, as well as the research scope and application. Bibliometrics is categorised under the field of library science, it uses mathematical and statistical methods to describe, evaluate, and predict the current status and trends of science and technology. Also to study the "distribution structure, quantitative relationship, change law and quantitative management of literature information, quantitative relationships, patterns and quantitative management of literature and information". The term was first used by Alan Pritchard in 1969 in his paper Statistical Bibliography or Bibliometrics?. Scientometrics is a branch of science that quantitatively evaluates and predicts the process and management of scientific activities in order to reveal their development patterns and trends. The definition of scientometrics was described by Derek De Solla Price in his book Science to Science as the “quantitative study of science, communication in science, and science policy”. === Links between the three metrics terms === The most prominent connection between the three metrics terms is in their research objects. Since all three disciplines use literature information as their research object, therefore, they have some similarities and overlaps in their research methods and fields. Moreover, they all use mathematical methods as the basic research methods and they all apply the three basic laws, Bradford's law, Lotka's law and Zipf's law. === Distinctions between the three metrics terms === The distinction between the three metrics terms can tell from their research object and research purpose. The research of bibliometrics focuses on the analysis of "scientific output in the form of articles, publications, citations, and others". Scientometrics is to measure the basic characteristics and laws of scientific activities. Where informetrics is to investigate information sources and information distribution process. == Concept and System Structure == === Purpose of Informetrics Research === The main purpose of informetrics is to use its theocratical research to solve the methodological issues in the research process, and to discover and reveal the basic laws of information distribution through the study of information process and phenomenon. In this way, makes information management more scientific and provides a quantitative basis for information services and information management decisions. For informetrics, it is necessary to bring quantitative analysis methods to further reveal the structure of information units and the "quantitative change law of literature information”. Further to this, to improve the scientific accuracy of information science from a theoretical point of view. At the same time, to better solve the basic contradictions in the information service, overcome the information crisis, and make the information management work more effective to serve science and technology, economic and social development. Quantitative analysis of bibliographic data was pioneered by Robert K. Merton in an article called Science, Technology, and Society in Seventeenth Century England and originally published by Merton in 1938. === The Significance of Informetrics Research === The significance of informetrics research is to summarize various empirical laws from the theoretical point of view, at the same time test and modify the various empirical laws in the new information unit conditions, and explore its new applicability, therefore, the scientific nature of information science can be improved, but also to provide theoretical guidance for practical work. === The Objects of Informetrics Research === The object of informetrics is broader than the field of bibliometrics and scientometrics, including "messages, data, events, objects, text, and documents”. Informetrics is often used to inform policies and decisions across a broad range of fields, such as economy, politics, technology and social spheres that "influence the flow and use patterns of information". Tague-Sutcliffe describes the following uses of informetrics: Citation analysis; Characteristics of authors; Use of recorded information; Obsolescence of the literature; Concomitant growth of new concepts; Characteristics of publication sources; Definition and measurement o information; Growth of subject literature, databases, libraries; Types and characteristics of retrieval performance measures; Statistical aspects of language, word, and phrase frequencies. == Basic Laws == In the field of informetrics research, there are many outstanding contributors in the discipline with a solid knowledge of quantitative research methods. In the early 20th century, several scientists contributed empirical applications that have become the three basic laws of informetrics, Bradford's law, Lotka's law, and Zipf's law, which promote the development of informetrics. === Bradford's Law === The British documentalist and librarian Samuel C. Bradford first discovered the law of concentration and scattering of literature, and in 1934, it has be

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  Automaton

  An automaton ( ; pl.: automata or automatons) is a relatively self-operating machine or control mechanism designed to automatically follow a sequence of operations or respond to predetermined instructions. Some automata, such as bellstrikers in mechanical clocks, are designed to give the illusion to the casual observer that they are operating under their own power or will, like a mechanical robot. The term has long been commonly associated with automated puppets that resemble moving humans or animals, built to impress and/or to entertain people. Animatronics are a modern type of automata with electronics, often used for the portrayal of characters or creatures in films and in theme park attractions. == Etymology == The word automaton is the latinization of the Ancient Greek automaton (αὐτόματον), which means "acting of one's own will". It was first used by Homer to describe an automatic door opening, or automatic movement of wheeled tripods. It is more often used to describe non-electronic moving machines, especially those that have been made to resemble human or animal actions, such as the jacks on old public striking clocks, or the cuckoo and any other animated figures on a cuckoo clock. == History == === Ancient === There are many examples of automata in Greek mythology: Hephaestus created automata for his workshop; Talos was an artificial man of bronze; King Alkinous of the Phaiakians employed gold and silver watchdogs. According to Aristotle, Daedalus used quicksilver to make his wooden statue of Aphrodite move. In other Greek legends he used quicksilver to install voice in his moving statues. The automata in the Hellenistic world were intended as tools, toys, religious spectacles, or prototypes for demonstrating basic scientific principles. Numerous water-powered automata were built by Ktesibios, a Greek inventor and the first head of the Great Library of Alexandria; for example, he "used water to sound a whistle and make a model owl move. He had invented the world's first 'cuckoo clock'". This tradition continued in Alexandria with inventors such as the Greek mathematician Hero of Alexandria (sometimes known as Heron), whose writings on hydraulics, pneumatics, and mechanics described siphons, a fire engine, a water organ, the aeolipile, and a programmable cart. Philo of Byzantium was famous for his inventions. Complex mechanical devices are known to have existed in Hellenistic Greece, though the only surviving example is the Antikythera mechanism, the earliest known analog computer. The clockwork is thought to have come originally from Rhodes, where there was apparently a tradition of mechanical engineering; the island was renowned for its automata; to quote Pindar's seventh Olympic Ode: The animated figures stand Adorning every public street And seem to breathe in stone, or move their marble feet. However, the information gleaned from recent scans of the fragments indicate that it may have come from the colonies of Corinth in Sicily and implies a connection with Archimedes. According to Jewish legend, King Solomon used his wisdom to design a throne with mechanical animals which hailed him as king when he ascended it; upon sitting down an eagle would place a crown upon his head, and a dove would bring him a Torah scroll. It is also said that when King Solomon stepped upon the throne, a mechanism was set in motion. As soon as he stepped upon the first step, a golden ox and a golden lion each stretched out one foot to support him and help him rise to the next step. On each side, the animals helped the King up until he was comfortably seated upon the throne. In ancient China, a curious account of automata is found in the Lie Zi text, believed to have originated around 400 BCE and compiled around the fourth century CE. Within it there is a description of a much earlier encounter between King Mu of Zhou (1023–957 BCE) and a mechanical engineer known as Yan Shi, an 'artificer'. The latter proudly presented the king with a very realistic and detailed life-size, human-shaped figure of his mechanical handiwork: The king stared at the figure in astonishment. It walked with rapid strides, moving its head up and down, so that anyone would have taken it for a live human being. The artificer touched its chin, and it began singing, perfectly in tune. He touched its hand, and it began posturing, keeping perfect time...As the performance was drawing to an end, the robot winked its eye and made advances to the ladies in attendance, whereupon the king became incensed and would have had Yen Shih [Yan Shi] executed on the spot had not the latter, in mortal fear, instantly taken the robot to pieces to let him see what it really was. And, indeed, it turned out to be only a construction of leather, wood, glue and lacquer, variously coloured white, black, red and blue. Examining it closely, the king found all the internal organs complete—liver, gall, heart, lungs, spleen, kidneys, stomach and intestines; and over these again, muscles, bones and limbs with their joints, skin, teeth and hair, all of them artificial...The king tried the effect of taking away the heart, and found that the mouth could no longer speak; he took away the liver and the eyes could no longer see; he took away the kidneys and the legs lost their power of locomotion. The king was delighted. Other notable examples of automata include Archytas' dove, mentioned by Aulus Gellius. Similar Chinese accounts of flying automata are written of the 5th century BC Mohist philosopher Mozi and his contemporary Lu Ban, who made artificial wooden birds (ma yuan) that could successfully fly according to the Han Fei Zi and other texts. === Medieval === The manufacturing tradition of automata continued in the Greek world well into the Middle Ages. On his visit to Constantinople in 949 ambassador Liutprand of Cremona described automata in the emperor Theophilos' palace, including "lions, made either of bronze or wood covered with gold, which struck the ground with their tails and roared with open mouth and quivering tongue," "a tree of gilded bronze, its branches filled with birds, likewise made of bronze gilded over, and these emitted cries appropriate to their species" and "the emperor's throne" itself, which "was made in such a cunning manner that at one moment it was down on the ground, while at another it rose higher and was to be seen up in the air." Similar automata in the throne room (singing birds, roaring and moving lions) were described by Luitprand's contemporary the Byzantine emperor Constantine Porphyrogenitus, in his book De Ceremoniis (Perì tês Basileíou Tákseōs). In the mid-8th century, the first wind powered automata were built: "statues that turned with the wind over the domes of the four gates and the palace complex of the Round City of Baghdad". The "public spectacle of wind-powered statues had its private counterpart in the 'Abbasid palaces where automata of various types were predominantly displayed." Also in the 8th century, the Muslim alchemist, Jābir ibn Hayyān (Geber), included recipes for constructing artificial snakes, scorpions, and humans that would be subject to their creator's control in his coded Book of Stones. In 827, Abbasid caliph al-Ma'mun had a silver and golden tree in his palace in Baghdad, which had the features of an automatic machine. There were metal birds that sang automatically on the swinging branches of this tree built by Muslim inventors and engineers. The Abbasid caliph al-Muqtadir also had a silver and golden tree in his palace in Baghdad in 917, with birds on it flapping their wings and singing. In the 9th century, the Banū Mūsā brothers invented a programmable automatic flute player and which they described in their Book of Ingenious Devices. Al-Jazari described complex programmable humanoid automata amongst other machines he designed and constructed in the Book of Knowledge of Ingenious Mechanical Devices in 1206. His automaton was a boat with four automatic musicians that floated on a lake to entertain guests at royal drinking parties. His mechanism had a programmable drum machine with pegs (cams) that bump into little levers that operate the percussion. The drummer could be made to play different rhythms and drum patterns if the pegs were moved around. Al-Jazari constructed a hand washing automaton first employing the flush mechanism now used in modern toilets. It features a female automaton standing by a basin filled with water. When the user pulls the lever, the water drains and the automaton refills the basin. His "peacock fountain" was another more sophisticated hand washing device featuring humanoid automata as servants who offer soap and towels. Mark E. Rosheim describes it as follows: "Pulling a plug on the peacock's tail releases water out of the beak; as the dirty water from the basin fills the hollow base a float rises and actuates a linkage which makes a servant figure appear from behind a door under the peacock and offer soap.

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  KiSAO

  The Kinetic Simulation Algorithm Ontology (KiSAO) supplies information about existing algorithms available for the simulation of systems biology models, their characterization and interrelationships. KiSAO is part of the BioModels.net project and of the COMBINE initiative. == Structure == KiSAO consists of three main branches: simulation algorithm simulation algorithm characteristic simulation algorithm parameter The elements of each algorithm branch are linked to characteristic and parameter branches using has characteristic and has parameter relationships accordingly. The algorithm branch itself is hierarchically structured using relationships which denote that the descendant algorithms were derived from, or specify, more general ancestors.

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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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