AI Art Filter

AI Art Filter — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Artificial Inventor Project

  The Artificial Inventor Project (AIP) is a global legal initiative headed by Professor Ryan Abbott dedicated to pursuing intellectual property (IP) rights for inventions and creative works generated autonomously by artificial intelligence (AI) systems without traditional human inventorship or authorship. The project coordinates a series of pro bono test cases worldwide, aiming to prompt law reform and public debate on how IP law should accommodate non-human creators. == History == In 2019, AIP filed patent applications in multiple jurisdictions, including the United States, United Kingdom, European Patent Office, Australia, Switzerland, and South Africa, naming the AI system DABUS (Device for the Autonomous Bootstrapping of Unified Sentience), created by Stephen Thaler, as the inventor. The aim was to challenge legal norms that require inventors to be natural persons and highlight pressing policy questions about AI-generated innovation and IP regimes. == Legal proceedings by jurisdiction == === Australia === In July 2021, a Federal Court of Australia judge (Beach J) ruled that AI can be considered an inventor under the Patents Act 1990, ordering IP Australia to reinstate the relevant patent. However, the full court then overturned this ruling on appeal and denied further review. === European Patent Office === The EPO Board of Appeal determined in 2022 that only a human inventor may be named, rendering DABUS‑based applications unacceptable. === South Africa === In 2021, a patent was granted listing DABUS as the inventor. As South Africa’s procedural system does not involve substantive inventorship review, the grant proceeded on formal grounds alone. === Switzerland === On 26 June 2025, the Swiss Federal Administrative Court ruled that artificial intelligence systems such as DABUS cannot be listed as inventors on patent applications. The court upheld the existing practice of the Swiss Federal Institute of Intellectual Property (IPI), affirming that only natural persons may be recognized as inventors under Swiss patent law. === United Kingdom === In December 2023, the UK Supreme Court unanimously held that AI systems cannot be legally recognized as inventors, affirming that "an inventor must be a person" under current British law. === United States === In Thaler v. Hirshfeld (2021), a U.S. federal court agreed with the USPTO that inventors must be natural persons, rejecting the DABUS application and setting a precedent consistent with existing statute and administrative policy. == Criticism and impact == The project has fueled substantial discourse. Critics caution that allowing AI inventorship may complicate notions of accountability and ownership. Proponents argue that legal recognition must evolve to avoid disincentivizing innovation produced by AI and to maintain honesty about the true source of invention.

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  AI-assisted reverse engineering

  AI-assisted reverse engineering (AIARE) is a branch of computer science that leverages artificial intelligence (AI), notably machine learning (ML) strategies, to augment and automate the process of reverse engineering. The latter involves breaking down a product, system, or process to comprehend its structure, design, and functionality. AIARE was primarily introduced in the early years of the 21st century, witnessing substantial advancements from the mid-2010s onwards. == Overview == Conventionally, reverse engineering is conducted by specialists who dismantle a system to grasp its working principles, often for the purposes of reproduction, modification, enhancement of compatibility, or forensic examination. This method, while efficient, can be laborious and time-intensive, particularly when dealing with intricate software or hardware systems. AIARE integrates machine learning algorithms to either partially automate or augment this process. It is capable of detecting patterns, relationships, structures, and potential vulnerabilities within the analyzed system, frequently surpassing human experts in speed and accuracy. This has rendered AIARE a critical tool in numerous fields, including cybersecurity, software development, and hardware design and analysis. == Techniques == AIARE encompasses several AI methodologies: === Supervised learning === Supervised learning employs tagged data to train models to recognize system components, their operations, and their interconnections. This method is particularly helpful in software analysis to discover vulnerabilities or enhance compatibility. === Unsupervised learning === Unsupervised learning is utilized to detect concealed patterns and structures in untagged data. It proves beneficial in comprehending complex systems where there's no evident labeling or mapping of components. === Reinforcement learning === Reinforcement learning is employed to build models that progressively refine their system understanding through a process of trial and error. This method is often implemented when deciphering a system's functionality under various circumstances or configurations. === Deep learning === Deep learning is employed for analysis of high-dimensional data. For instance, deep learning techniques can aid in examining the layout and connections of integrated circuits (ICs), substantially reducing the manual effort required for reverse engineering. == Benefits == === Usable Security === AIARE expands usable security as reverse engineering is traditionally slow and highly specialized as it produces dense, low-level information (usually in Assembly or C) when using tools like Ghidra. The use of multiple different methods to interface with models today (such as through chat bots like ChatGPT) greatly reduces the barrier to entry by providing a clear way to interact with the user and even providing meaningful decompiled source code. In addition, either done automatically or through prompt engineering, a model is capable of producing a high-level summary and explanation of its reverse engineering efforts in human-readable form that doesn't require much knowledge on code. === Speedup === AIARE is capable of processing data much faster than humans, providing a boost in speed when analyzing said data. In the context of computer security, this can greatly speed up incident management or response and malware detection as AIARE can be automated to drastically reduce the manual effort usually associated with reverse engineering. == Limitations == In an effort to improve readability for reverse engineering, AI-generated code may introduce erroneous bugs not present in the source. This compromises the correctness of the code if not carefully validated and will throw off reverse engineering efforts. Additionally, AIARE's weakness in zero-shot prompting makes gathering accurate data without reference data in the prompt more inconsistent, thus requiring a user to provide some quality data of their own that hurts its usability.

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  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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  Enterprise bus matrix

  The enterprise bus matrix is a data warehouse planning tool and model created by Ralph Kimball, and is part of the data warehouse bus architecture. The matrix is the logical definition of one of the core concepts of Kimball's approach to dimensional modeling conformed dimension. The bus matrix defines part of the data warehouse bus architecture and is an output of the business requirements phase in the Kimball lifecycle. It is applied in the following phases of dimensional modeling and development of the data warehouse. The matrix can be categorized as a hybrid model, being part technical design tool, part project management tool and part communication tool == Background == The need for an enterprise bus matrix stems from the way one goes about creating the overall data warehouse environment. Historically there have been two approaches: a structured, centralized and planned approach and a more loosely defined, department specific approach, in which solutions are developed in a more independent matter. Autonomous projects can result in a range of isolated stove pipe data marts. Naturally each approach has its issues; the visionary approach often struggles with long delivery cycles and lack of reaction time as needs emerge and scope issues arise. On the other hand, the development of isolated data marts leads to stovepipe systems that lack synergy in development. Over time this approach will lead to a so-called data-mart-in-a-box architecture where interoperability and lack of cohesion is apparent, and can hinder the realization of an overall enterprise data warehouse. As an attempt to handle this issue, Ralph Kimball introduced the enterprise bus. == Description == The bus matrix purpose is one of high abstraction and visionary planning on the data warehouse architectural level. By dictating coherency in the development and implementation of an overall data warehouse the bus architecture approach enables an overall vision of the broader enterprise integration and consistency while at the same time dividing the problem into more manageable parts – all in a technology and software independent manner. The bus matrix and architecture builds upon the concept of conformed dimensions, creating a structure of common dimensions that ideally can be used across the enterprise by all business processes related to the data warehouse and the corresponding fact tables from which they derive their context. According to Kimball and Margy Ross's article “Differences of Opinion” "The Enterprise Data warehouse built on the bus architecture ”identifies and enforces the relationship between business process metrics (facts) and descriptive attributes (dimensions)”. The concept of a bus is well known in the language of information technology, and is what reflects the conformed dimension concept in the data warehouse, creating the skeletal structure where all parts of a system connect, ensuring interoperability and consistency of data, and at the same time considers future expansion. This makes the conformed dimensions act as the integration ‘glue’, creating a robust backbone of the enterprise Data Warehouse.

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  Imaging phantom

  An imaging phantom, or simply phantom (less commonly spelled fantom), is a specially designed object that is scanned or imaged in the field of medical imaging to evaluate, analyze, and tune the performance of various imaging devices. A phantom is more readily available and provides more consistent results than the use of a living subject or cadaver, while also avoiding direct risks to living subjects. Phantoms were originally employed in 2D x-ray–based imaging techniques such as radiography or fluoroscopy, but more recently phantoms with desired imaging characteristics have been developed for 3D techniques such as SPECT, MRI, CT, ultrasound, PET, and other imaging modalities. == Design == A phantom used to evaluate an imaging device should respond in a similar manner to how human tissues and organs would act in that specific imaging modality. For instance, phantoms made for 2D radiography may hold various quantities of x-ray contrast agents with similar x-ray absorbing properties (such as the attenuation coefficient) to normal tissue to tune the contrast of the imaging device or modulate the patient's exposure to radiation. In such a case, the radiography phantom would not necessarily need to have similar textures and mechanical properties since these are not relevant in x-ray imaging modalities. However, in the case of ultrasonography, a phantom with similar rheological and ultrasound scattering properties to real tissue would be essential, but x-ray absorbing properties would not be relevant. The term "phantom" describes an object that is designed to resemble human tissue and can be evaluated, analyzed or manipulated to study the performance of a medical device. Phantoms are created using a digital file that is rendered through magnetic resonance imaging (MRI) or computer-aided design (CAD). The digital files allow for quick modifications that are read by the 3D printer. The 3D printer will create the product in successive layers using polymeric materials. There are several types of phantoms including tissue-mimicking, radiological phantoms, dental phantoms, BOMABs (used to calibrate whole-body counters), and more.

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  ArchiMate

  ArchiMate ( AR-ki-mayt) is an open and independent enterprise architecture modeling language to support the description, analysis and visualization of architecture within and across business domains in an unambiguous way. ArchiMate is a technical standard from The Open Group and is based on concepts from the now superseded IEEE 1471 standard. It is supported by various tool vendors and consulting firms. ArchiMate is also a registered trademark of The Open Group. The Open Group has a certification program for ArchiMate users, software tools and courses. ArchiMate distinguishes itself from other languages such as Unified Modeling Language (UML) and Business Process Modeling and Notation (BPMN) by its enterprise modelling scope. Also, UML and BPMN are meant for a specific use and they are quite heavy – containing about 150 (UML) and 250 (BPMN) modeling concepts whereas ArchiMate works with just about 50 (in version 2.0). The goal of ArchiMate is to be ”as small as possible”, not to cover every edge scenario imaginable. To be easy to learn and apply, ArchiMate was intentionally restricted “to the concepts that suffice for modeling the proverbial 80% of practical cases". == Overview == ArchiMate offers a common language for describing the construction and operation of business processes, organizational structures, information flows, IT systems, and technical infrastructure. This insight helps the different stakeholders to design, assess, and communicate the consequences of decisions and changes within and between these business domains. The main concepts and relationships of the ArchiMate language can be seen as a framework, the so-called Archimate Framework: It divides the enterprise architecture into a business, application and technology layer. In each layer, three aspects are considered: active elements, an internal structure and elements that define use or communicate information. One of the objectives of the ArchiMate language is to define the relationships between concepts in different architecture domains. The concepts of this language therefore hold the middle between the detailed concepts, which are used for modeling individual domains (for example, the Unified Modeling Language (UML) for modeling software products), and Business Process Model and Notation (BPMN), which is used for business process modeling. == History == ArchiMate is partly based on the now superseded IEEE 1471 standard. It was developed in the Netherlands by a project team from the Telematica Instituut in cooperation with several Dutch partners from government, industry and academia. Among the partners were Ordina NV, Radboud Universiteit Nijmegen, the Leiden Institute for Advanced Computer Science (LIACS) and the Centrum Wiskunde & Informatica (CWI). Later, tests were performed in organizations such as ABN AMRO, the Dutch Tax and Customs Administration and the ABP. The development process lasted from July 2002 to December 2004, and took about 35 person years and approximately 4 million euros. The development was funded by the Dutch government (Dutch Tax and Customs Administration), and business partners, including ABN AMRO and the ABP Pension Fund. In 2008 the ownership and stewardship of ArchiMate was transferred to The Open Group. It is now managed by the ArchiMate Forum within The Open Group. In February 2009 The Open Group published the ArchiMate 1.0 standard as a formal technical standard. In January 2012 the ArchiMate 2.0 standard, and in 2013 the ArchiMate 2.1 standard was released. In June 2016, the Open Group released version 3.0 of the ArchiMate Specification. An update to Archimate 3.0.1 came out in August 2017. Archimate 3.1 was published 5 November 2019. The latest version of the ArchiMate Specification is version 3.2 released October 2022. Version 3.0 adds enhanced support for capability-oriented strategic modelling, new entities representing physical resources (for modelling the ingredients, equipment and transport resources used in the physical world) and a generic metamodel showing the entity types and the relationships between them. == ArchiMate framework == === Core framework === The main concepts and elements of the ArchiMate language are being presented as ArchiMate core framework. It consists of three layers and three aspects. This creates a matrix of combinations. Every layer has its passive structure, behavior and active structure aspects. ==== Layers ==== ArchiMate has a layered and service-oriented look on architectural models. The higher layers make use of services that are provided by the lower layers. Although, at an abstract level, the concepts that are used within each layer are similar, we define more concrete concepts that are specific for a certain layer. In this context, we distinguish three main layers: The business layer is about business processes, services, functions and events of business units. This layer "offers products and services to external customers, which are realized in the organization by business processes performed by business actors and roles". The application layer is about software applications that "support the components in the business with application services". The technology layer deals "with the hardware and communication infrastructure to support the application layer. This layer offers infrastructural services needed to run applications, realized by computer and communication hardware and system software". Each of these main layers can be further divided in sub-layers. For example, in the business layer, the primary business processes realising the products of a company may make use of a layer of secondary (supporting) business processes; in the application layer, the end-user applications may make use of generic services offered by supporting applications. On top of the business layer, a separate environment layer may be added, modelling the external customers that make use of the services of the organisation (although these may also be considered part of the business layer). In line with service orientation, the most important relation between layers is formed by use relations, which show how the higher layers make use of the services of lower layers. However, a second type of link is formed by realisation relations: elements in lower layers may realise comparable elements in higher layers; e.g., a ‘data object’ (application layer) may realise a ‘business object’ (business layer); or an ‘artifact’ (technology layer) may realise either a ‘data object’ or an ‘application component’ (application layer). ==== Aspects ==== Passive structure is the set of entities on which actions are conducted. In the business layer the example would be information objects, in the application layer data objects and in the technology layer, they could include physical objects. Behavior refers to the processes and functions performed by the actors. "Structural elements are assigned to behavioral elements, to show who or what displays the behavior". Active structure is the set of entities that display some behavior, e.g. business actors, devices, or application components. === Full framework === The Full ArchiMate framework is enriched by the physical layer, which was added to allow modeling of “physical equipment, materials, and distribution networks” and was not present in the previous version. The implementation and migration layer adds elements that allow architects to model a state of transition, to mark parts of the architecture that are temporary for the purpose, as the name says, of implementation and migration. Strategy layer adds three elements: resource, capability and course of action. These elements help to incorporate strategic dimension to the ArchiMate language by allowing it to depict the usage of resources and capabilities in order to achieve some strategic goals. Finally, there is a motivation aspect that allows different stakeholders to describe the motivation of specific actors or domains, which can be quite important when looking at one thing from several different angles. It adds several elements like stakeholder, value, driver, goal, meaning etc. == ArchiMate language == The ArchiMate language is formed as a top-level and is hierarchical. On the top, there is a model. A model is a collection of concepts. A concept can be either an element or a relationship. An element can be either of behavior type, structure, motivation or a so-called composite element (which means that it does not fit just one aspect of the framework, but two or more). The functionality of all concepts without a dependency on a specific layer is described by the generic metamodel. This layer-independent description of concepts is useful when trying to understand the mechanics of the Archimate language. === Concepts === ==== Elements ==== The generic elements are distributed into the same categories as the layers: Active structure elements Behavior elements Passive structure elements Motivation elements Active structure e

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  Information seeking

  Information seeking is the process or activity of attempting to obtain information in both human and technological contexts. Information seeking is related to, but different from, information retrieval (IR). == Compared to information retrieval == Traditionally, IR tools have been designed for IR professionals to enable them to effectively and efficiently retrieve information from a source. It is assumed that the information exists in the source and that a well-formed query will retrieve it (and nothing else). It has been argued that laypersons' information seeking on the internet is very different from information retrieval as performed within the IR discourse. Yet, internet search engines are built on IR principles. Since the late 1990s a body of research on how casual users interact with internet search engines has been forming, but the topic is far from fully understood. IR can be said to be technology-oriented, focusing on algorithms and issues such as precision and recall. Information seeking may be understood as a more human-oriented and open-ended process than information retrieval. In information seeking, one does not know whether there exists an answer to one's query, so the process of seeking may provide the learning required to satisfy one's information need. == In different contexts == Much library and information science (LIS) research has focused on the information-seeking practices of practitioners within various fields of professional work. Studies have been carried out into the information-seeking behaviors of librarians, academics, medical professionals, engineers, lawyers and mini-publics(among others). Much of this research has drawn on the work done by Leckie, Pettigrew (now Fisher) and Sylvain, who in 1996 conducted an extensive review of the LIS literature (as well as the literature of other academic fields) on professionals' information seeking. The authors proposed an analytic model of professionals' information seeking behaviour, intended to be generalizable across the professions, thus providing a platform for future research in the area. The model was intended to "prompt new insights... and give rise to more refined and applicable theories of information seeking" (1996, p. 188). The model has been adapted by Wilkinson (2001) who proposes a model of the information seeking of lawyers. Recent studies in this topic address the concept of information-gathering that "provides a broader perspective that adheres better to professionals' work-related reality and desired skills." (Solomon & Bronstein, 2021). == Theories of information-seeking behavior == A variety of theories of information behavior – e.g. Zipf's Principle of Least Effort, Brenda Dervin's Sense Making, Elfreda Chatman's Life in the Round – seek to understand the processes that surround information seeking. In addition, many theories from other disciplines have been applied in investigating an aspect or whole process of information seeking behavior. A review of the literature on information seeking behavior shows that information seeking has generally been accepted as dynamic and non-linear (Foster, 2005; Kuhlthau 2006). People experience the information search process as an interplay of thoughts, feelings and actions (Kuhlthau, 2006). Donald O. Case (2007) also wrote a good book that is a review of the literature. Information seeking has been found to be linked to a variety of interpersonal communication behaviors beyond question-asking, to include strategies such as candidate answers. Robinson's (2010) research suggests that when seeking information at work, people rely on both other people and information repositories (e.g., documents and databases), and spend similar amounts of time consulting each (7.8% and 6.4% of work time, respectively; 14.2% in total). However, the distribution of time among the constituent information seeking stages differs depending on the source. When consulting other people, people spend less time locating the information source and information within that source, similar time understanding the information, and more time problem solving and decision making, than when consulting information repositories. Furthermore, the research found that people spend substantially more time receiving information passively (i.e., information that they have not requested) than actively (i.e., information that they have requested), and this pattern is also reflected when they provide others with information. == Wilson's nested model of conceptual areas == The concepts of information seeking, information retrieval, and information behaviour are objects of investigation of information science. Within this scientific discipline a variety of studies has been undertaken analyzing the interaction of an individual with information sources in case of a specific information need, task, and context. The research models developed in these studies vary in their level of scope. Wilson (1999) therefore developed a nested model of conceptual areas, which visualizes the interrelation of the here mentioned central concepts. Wilson defines models of information behavior to be "statements, often in the form of diagrams, that attempt to describe an information-seeking activity, the causes and consequences of that activity, or the relationships among stages in information-seeking behaviour" (1999: 250).

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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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  Diagnostically acceptable irreversible compression

  Diagnostically acceptable irreversible compression (DAIC) is the amount of lossy compression which can be used on a medical image to produce a result that does not prevent the reader from using the image to make a medical diagnosis. The term was first introduced at a workshop on irreversible compression convened by the European Society of Radiology (ESR) in Palma de Mallorca October 13, 2010, the results of which were reported in a subsequent position paper. == Determination == The "amount of compression" in irreversible compression used to be determined by the compression ratio, where the acceptable minimum is determined by the algorithm (typically JPEG or J2K) and the data type (body part and imaging method). Such a definition is easy to follow, and has been used by medical bodies in 2010 around the world. However, its downside is obvious: the compression ratio tells nothing about the real quality of the image, as different compressors can produce vastly different qualities under the same file size. For example, the JPEG format of 1992 can perform as well as many modern formats given newer techniques exploited in mozjpeg and ISO libjpeg, yet they would be lumped together with the legacy encoders in such a scheme. The image compression community has long used objective quality metrics like SSIM to measure the effects of compression. In the absence of good data regarding SSIM, the ESR review of 2010 concluded that it is still difficult to establish a criterion for whether a particular irreversible compression scheme applied with particular parameters to a particular individual image, or category of images, avoids the introduction of some quantifiable risk of a diagnostic error for any particular diagnostic task. A 2017 study showed that a SSIM variant called 4-G-r (4-component, gradient, structural component of SSIM) best reflects changes in images that affect the decision of radiologists out of 16 SSIM variants. A 2020 study shows that visual information fidelity (VIF), feature similarity index (FSIM), and noise quality metric (NQM) best reflect radiologist preferences out of ten metrics. It also mentions that the original version of SSIM works as poorly as a basic root-mean-square distance (RMSD) for this purpose, a result echoed by the 2017 study. The 4-G-r modification is not tested in the study.

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  Recording format

  A recording format is a format for encoding data for storage on a storage medium. The format can be container information such as sectors on a disk, or user/audience information (content) such as analog stereo audio. Multiple levels of encoding may be achieved in one format. For example, a text encoded page may contain HTML and XML encoding, combined in a plain text file format, using either EBCDIC or ASCII character encoding, on a UDF digitally formatted disk. In electronic media, the primary format is the encoding that requires hardware to interpret (decode) data; while secondary encoding is interpreted by secondary signal processing methods, usually computer software. == Recording container formats == A container format is a system for dividing physical storage space or virtual space for data. Data space can be divided evenly by a system of measurement, or divided unevenly with meta data. A grid may divide physical or virtual space with physical or virtual (dividers) borders, evenly or unevenly. Just as a physical container (such as a file cabinet) is divided by physical borders (such as drawers and file folders), data space is divided by virtual borders. Meta data such as a unit of measurement, address, or meta tags act as virtual borders in a container format. A template may be considered an abstract format for containing a solution as well as the content itself. Systems of measurement Metric system Geographic coordinate system Page grid Film formats Audio data format Video tape format Disk format File format Meta data Text formatting Template Data structure == Raw content formats == A raw content format is a system of converting data to displayable information. Raw content formats may either be recorded in secondary signal processing methods such as a software container format (e.g. digital audio, digital video) or recorded in the primary format. A primary raw content format may be directly observable (e.g. image, sound, motion, smell, sensation) or physical data which only requires hardware to display it, such as a phonographic needle and diaphragm or a projector lamp and magnifying glass.

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  Run-time algorithm specialization

  In computer science, run-time algorithm specialization is a methodology for creating efficient algorithms for costly computation tasks of certain kinds. The methodology originates in the field of automated theorem proving and, more specifically, in the Vampire theorem prover project. The idea is inspired by the use of partial evaluation in optimising program translation. Many core operations in theorem provers exhibit the following pattern. Suppose that we need to execute some algorithm a l g ( A , B ) {\displaystyle {\mathit {alg}}(A,B)} in a situation where a value of A {\displaystyle A} is fixed for potentially many different values of B {\displaystyle B} . In order to do this efficiently, we can try to find a specialization of a l g {\displaystyle {\mathit {alg}}} for every fixed A {\displaystyle A} , i.e., such an algorithm a l g A {\displaystyle {\mathit {alg}}_{A}} , that executing a l g A ( B ) {\displaystyle {\mathit {alg}}_{A}(B)} is equivalent to executing a l g ( A , B ) {\displaystyle {\mathit {alg}}(A,B)} . The specialized algorithm may be more efficient than the generic one, since it can exploit some particular properties of the fixed value A {\displaystyle A} . Typically, a l g A ( B ) {\displaystyle {\mathit {alg}}_{A}(B)} can avoid some operations that a l g ( A , B ) {\displaystyle {\mathit {alg}}(A,B)} would have to perform, if they are known to be redundant for this particular parameter A {\displaystyle A} . In particular, we can often identify some tests that are true or false for A {\displaystyle A} , unroll loops and recursion, etc. == Difference from partial evaluation == The key difference between run-time specialization and partial evaluation is that the values of A {\displaystyle A} on which a l g {\displaystyle {\mathit {alg}}} is specialised are not known statically, so the specialization takes place at run-time. There is also an important technical difference. Partial evaluation is applied to algorithms explicitly represented as codes in some programming language. At run-time, we do not need any concrete representation of a l g {\displaystyle {\mathit {alg}}} . We only have to imagine a l g {\displaystyle {\mathit {alg}}} when we program the specialization procedure. All we need is a concrete representation of the specialized version a l g A {\displaystyle {\mathit {alg}}_{A}} . This also means that we cannot use any universal methods for specializing algorithms, which is usually the case with partial evaluation. Instead, we have to program a specialization procedure for every particular algorithm a l g {\displaystyle {\mathit {alg}}} . An important advantage of doing so is that we can use some powerful ad hoc tricks exploiting peculiarities of a l g {\displaystyle {\mathit {alg}}} and the representation of A {\displaystyle A} and B {\displaystyle B} , which are beyond the reach of any universal specialization methods. == Specialization with compilation == The specialized algorithm has to be represented in a form that can be interpreted. In many situations, usually when a l g A ( B ) {\displaystyle {\mathit {alg}}_{A}(B)} is to be computed on many values of B {\displaystyle B} in a row, a l g A {\displaystyle {\mathit {alg}}_{A}} can be written as machine code instructions for a special abstract machine, and it is typically said that A {\displaystyle A} is compiled. The code itself can then be additionally optimized by answer-preserving transformations that rely only on the semantics of instructions of the abstract machine. The instructions of the abstract machine can usually be represented as records. One field of such a record, an instruction identifier (or instruction tag), would identify the instruction type, e.g. an integer field may be used, with particular integer values corresponding to particular instructions. Other fields may be used for storing additional parameters of the instruction, e.g. a pointer field may point to another instruction representing a label, if the semantics of the instruction require a jump. All instructions of the code can be stored in a traversable data structure such as an array, linked list, or tree. Interpretation (or execution) proceeds by fetching instructions in some order, identifying their type, and executing the actions associated with said type. In many programming languages, such as C and C++, a simple switch statement may be used to associate actions with different instruction identifiers. Modern compilers usually compile a switch statement with constant (e.g. integer) labels from a narrow range by storing the address of the statement corresponding to a value i {\displaystyle i} in the i {\displaystyle i} -th cell of a special array, as a means of efficient optimisation. This can be exploited by taking values for instruction identifiers from a small interval of values. == Data-and-algorithm specialization == There are situations when many instances of A {\displaystyle A} are intended for long-term storage and the calls of a l g ( A , B ) {\displaystyle {\mathit {alg}}(A,B)} occur with different B {\displaystyle B} in an unpredictable order. For example, we may have to check a l g ( A 1 , B 1 ) {\displaystyle {\mathit {alg}}(A_{1},B_{1})} first, then a l g ( A 2 , B 2 ) {\displaystyle {\mathit {alg}}(A_{2},B_{2})} , then a l g ( A 1 , B 3 ) {\displaystyle {\mathit {alg}}(A_{1},B_{3})} , and so on. In such circumstances, full-scale specialization with compilation may not be suitable due to excessive memory usage. However, we can sometimes find a compact specialized representation A ′ {\displaystyle A^{\prime }} for every A {\displaystyle A} , that can be stored with, or instead of, A {\displaystyle A} . We also define a variant a l g ′ {\displaystyle {\mathit {alg}}^{\prime }} that works on this representation and any call to a l g ( A , B ) {\displaystyle {\mathit {alg}}(A,B)} is replaced by a l g ′ ( A ′ , B ) {\displaystyle {\mathit {alg}}^{\prime }(A^{\prime },B)} , intended to do the same job faster.

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  Research data archiving

  Research data archiving is the long-term storage of scholarly research data, including the natural sciences, social sciences, and life sciences. The various academic journals have differing policies regarding how much of their data and methods researchers are required to store in a public archive, and what is actually archived varies widely between different disciplines. Similarly, the major grant-giving institutions have varying attitudes towards public archiving of data. In general, the tradition of science has been for publications to contain sufficient information to allow fellow researchers to replicate and therefore test the research. In recent years this approach has become increasingly strained as research in some areas depends on large datasets which cannot easily be replicated independently. Data archiving is more important in some fields than others. In a few fields, all of the data necessary to replicate the work is already available in the journal article. In drug development, a great deal of data is generated and must be archived so researchers can verify that the reports the drug companies publish accurately reflect the data. Often used interchangeably, Data preservation and data archiving are both about protecting data for the long term, but they serve different purposes. Data preservation focuses on preventing data from being lost, damaged, or destroyed by creating backups, storing data in secure locations, and ensuring it remains accessible when needed. Data archiving, on the other hand, involves moving data that is no longer actively used to a separate storage location for long-term keeping. Archived data is often combined and compressed, and while it can still be accessed, it is not intended for regular use or frequent updates. The requirement of data archiving is a recent development in the history of science. It was made possible by advances in information technology allowing large amounts of data to be stored and accessed from central locations. For example, the American Geophysical Union (AGU) adopted their first policy on data archiving in 1993, about three years after the beginning of the WWW. This policy mandates that datasets cited in AGU papers must be archived by a recognised data center; it permits the creation of "data papers"; and it establishes AGU's role in maintaining data archives. But it makes no requirements on paper authors to archive their data. Prior to organized data archiving, researchers wanting to evaluate or replicate a paper would have to request data and methods information from the author. The academic community expects authors to share supplemental data. This process was recognized as wasteful of time and energy and obtained mixed results. Information could become lost or corrupted over the years. In some cases, authors simply refuse to provide the information. The need for data archiving and due diligence is greatly increased when the research deals with health issues or public policy formation. == Selected policies by journals == === Biotropica === Biotropica requires, as a condition for publication, that the data supporting the results in the paper and metadata describing them must be archived in an appropriate public archive such as Dryad, Figshare, GenBank, TreeBASE, or NCBI. Authors may elect to make the data publicly available as soon as the article is published or, if the technology of the archive allows, embargo access to the data up to three years after article publication. A statement describing Data Availability will be included in the manuscript as described in the instructions to authors. Exceptions to the required archiving of data may be granted at the discretion of the Editor-in-Chief for studies that include sensitive information (e.g., the location of endangered species). Our Editorial explaining the motivation for this policy can be found here. A more comprehensive list of data repositories is available here. Promoting a culture of collaboration with researchers who collect and archive data: The data collected by tropical biologists are often long-term, complex, and expensive to collect. The Board of Editors of Biotropica strongly encourages authors who re-use data archives archived data sets to include as fully engaged collaborators the scientists who originally collected them. We feel this will greatly enhance the quality and impact of the resulting research by drawing on the data collector’s profound insights into the natural history of the study system, reducing the risk of errors in novel analyses, and stimulating the cross-disciplinary and cross-cultural collaboration and training for which the ATBC and Biotropica are widely recognized. NB: Biotropica is one of only two journals that pays the fees for authors depositing data at Dryad. === The American Naturalist === The American Naturalist requires authors to deposit the data associated with accepted papers in a public archive. For gene sequence data and phylogenetic trees, deposition in GenBank or TreeBASE, respectively, is required. There are many possible archives that may suit a particular data set, including the Dryad repository for ecological and evolutionary biology data. All accession numbers for GenBank, TreeBASE, and Dryad must be included in accepted manuscripts before they go to Production. If the data is deposited somewhere else, please provide a link. If the data is culled from published literature, please deposit the collated data in Dryad for the convenience of your readers. Any impediments to data sharing should be brought to the attention of the editors at the time of submission so that appropriate arrangements can be worked out. === Journal of Heredity === The primary data underlying the conclusions of an article are critical to the verifiability and transparency of the scientific enterprise, and should be preserved in usable form for decades in the future. For this reason, Journal of Heredity requires that newly reported nucleotide or amino acid sequences, and structural coordinates, be submitted to appropriate public databases (e.g., GenBank; the EMBL Nucleotide Sequence Database; DNA Database of Japan; the Protein Data Bank; and Swiss-Prot). Accession numbers must be included in the final version of the manuscript. For other forms of data (e.g., microsatellite genotypes, linkage maps, images), the Journal endorses the principles of the Joint Data Archiving Policy (JDAP) in encouraging all authors to archive primary datasets in an appropriate public archive, such as Dryad, TreeBASE, or the Knowledge Network for Biocomplexity. Authors are encouraged to make data publicly available at time of publication or, if the technology of the archive allows, opt to embargo access to the data for a period up to a year after publication. The American Genetic Association also recognizes the vast investment of individual researchers in generating and curating large datasets. Consequently, we recommend that this investment be respected in secondary analyses or meta-analyses in a gracious collaborative spirit. === Molecular Ecology === Molecular Ecology expects that data supporting the results in the paper should be archived in an appropriate public archive, such as GenBank, Gene Expression Omnibus, TreeBASE, Dryad, the Knowledge Network for Biocomplexity, your own institutional or funder repository, or as Supporting Information on the Molecular Ecology web site. Data are important products of the scientific enterprise, and they should be preserved and usable for decades in the future. Authors may elect to have the data publicly available at time of publication, or, if the technology of the archive allows, may opt to embargo access to the data for a period up to a year after publication. Exceptions may be granted at the discretion of the editor, especially for sensitive information such as human subject data or the location of endangered species. === Nature === Such material must be hosted on an accredited independent site (URL and accession numbers to be provided by the author), or sent to the Nature journal at submission, either uploaded via the journal's online submission service, or if the files are too large or in an unsuitable format for this purpose, on CD/DVD (five copies). Such material cannot solely be hosted on an author's personal or institutional web site. Nature requires the reviewer to determine if all of the supplementary data and methods have been archived. The policy advises reviewers to consider several questions, including: "Should the authors be asked to provide supplementary methods or data to accompany the paper online? (Such data might include source code for modelling studies, detailed experimental protocols or mathematical derivations.) === Science === Science supports the efforts of databases that aggregate published data for the use of the scientific community. Therefore, before publication, large data sets (including microarray data, protein or DNA sequences, and atomic c

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  Clone tool

  The clone tool, as it is known in Adobe Photoshop, Inkscape, GIMP, and Corel PhotoPaint, is used in digital image editing to replace information for one part of a picture with information from another part. In other image editing software, its equivalent is sometimes called a rubber stamp tool or a clone brush. == Applications == The clone tool can remove objects by copying a nearby background. The user selects a matching location as the source, then paints over the element to be hidden. A typical use for the tool is in object removal – more colloquially, "airbrushing" or "photoshopping" out an unwanted part of the image. If a part of an image is removed simply by cutting it out, then a hole is left in the background. The Clone tool can fill in this hole convincingly with a copy of the existing background from elsewhere in the image. A common use for this tool is to retouch skin, particularly in portraits, to remove blemishes and make skin tones more even. Cloning can also be used to remove other unwanted elements, such as telephone wires, an unwanted bird in the sky, and the like. A more automated method of object removal uses texture synthesis to fill in gaps. Of these, patch-based texture synthesis or "image quilting" is essentially an automated application of the clone tool, choosing the optimal source area so as to patch over with a minimal seam. In some cases, the undesired object is mixed with the remainder of the image, and a simple circular brush, even with feathering, would not work. For these cases, some programs allow an object to be selected by color/outline so other areas are not affected. Other programs allow edge/color sensitive brushes to deal with such objects. == Healing tool == A similar tool is the healing tool, which occurs in variants such as the healing brush or spot healing tool. These incorporate the existing texture, rather than painting it over.

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  Higuchi dimension

  In fractal geometry, the Higuchi dimension (or Higuchi fractal dimension (HFD)) is an approximate value for the box-counting dimension of the graph of a real-valued function or time series. This value is obtained via an algorithmic approximation so one also talks about the Higuchi method. It has many applications in science and engineering and has been applied to subjects like characterizing primary waves in seismograms, clinical neurophysiology and analyzing changes in the electroencephalogram in Alzheimer's disease. == Formulation of the method == The original formulation of the method is due to T. Higuchi. Given a time series X : { 1 , … , N } → R {\displaystyle X:\{1,\dots ,N\}\to \mathbb {R} } consisting of N {\displaystyle N} data points and a parameter k m a x ≥ 2 {\displaystyle k_{\mathrm {max} }\geq 2} the Higuchi Fractal dimension (HFD) of X {\displaystyle X} is calculated in the following way: For each k ∈ { 1 , … , k m a x } {\displaystyle k\in \{1,\dots ,k_{\mathrm {max} }}\} and m ∈ { 1 , … , k } {\displaystyle m\in \{1,\dots ,k}\} define the length L m ( k ) {\displaystyle L_{m}(k)} by L m ( k ) = N − 1 ⌊ N − m k ⌋ k 2 ∑ i = 1 ⌊ N − m k ⌋ | X N ( m + i k ) − X N ( m + ( i − 1 ) k ) | . {\displaystyle L_{m}(k)={\frac {N-1}{\lfloor {\frac {N-m}{k}}\rfloor k^{2}}}\sum _{i=1}^{\lfloor {\frac {N-m}{k}}\rfloor }|X_{N}(m+ik)-X_{N}(m+(i-1)k)|.} The length L ( k ) {\displaystyle L(k)} is defined by the average value of the k {\displaystyle k} lengths L 1 ( k ) , … , L k ( k ) {\displaystyle L_{1}(k),\dots ,L_{k}(k)} , L ( k ) = 1 k ∑ m = 1 k L m ( k ) . {\displaystyle L(k)={\frac {1}{k}}\sum _{m=1}^{k}L_{m}(k).} The slope of the best-fitting linear function through the data points { ( log ⁡ 1 k , log ⁡ L ( k ) ) } {\displaystyle \left\{\left(\log {\frac {1}{k}},\log L(k)\right)\right\}} is defined to be the Higuchi fractal dimension of the time-series X {\displaystyle X} . == Application to functions == For a real-valued function f : [ 0 , 1 ] → R {\displaystyle f:[0,1]\to \mathbb {R} } one can partition the unit interval [ 0 , 1 ] {\displaystyle [0,1]} into N {\displaystyle N} equidistantly intervals [ t j , t j + 1 ) {\displaystyle [t_{j},t_{j+1})} and apply the Higuchi algorithm to the times series X ( j ) = f ( t j ) {\displaystyle X(j)=f(t_{j})} . This results into the Higuchi fractal dimension of the function f {\displaystyle f} . It was shown that in this case the Higuchi method yields an approximation for the box-counting dimension of the graph of f {\displaystyle f} as it follows a geometrical approach (see Liehr & Massopust 2020). == Robustness and stability == Applications to fractional Brownian functions and the Weierstrass function reveal that the Higuchi fractal dimension can be close to the box-dimension. On the other hand, the method can be unstable in the case where the data X ( 1 ) , … , X ( N ) {\displaystyle X(1),\dots ,X(N)} are periodic or if subsets of it lie on a horizontal line (see Liehr & Massopust 2020).

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  NoSQL

  NoSQL (originally meaning "not only SQL" or "non-relational") refers to a type of database design that stores and retrieves data differently from the traditional table-based structure of relational databases. Unlike relational databases, which organize data into rows and columns like a spreadsheet, NoSQL databases use a single data structure—such as key–value pairs, wide columns, graphs, or documents—to hold information. Since this non-relational design does not require a fixed schema, it scales easily to manage large, often unstructured datasets. NoSQL systems are sometimes called "Not only SQL" because they can support SQL-like query languages or work alongside SQL databases in polyglot-persistent setups, where multiple database types are combined. Non-relational databases date back to the late 1960s, but the term "NoSQL" emerged in the early 2000s, spurred by the needs of Web 2.0 companies like social media platforms. NoSQL databases are popular in big data and real-time web applications due to their simple design, ability to scale across clusters of machines (called horizontal scaling), and precise control over data availability. These structures can speed up certain tasks and are often considered more adaptable than fixed database tables. However, many NoSQL systems prioritize speed and availability over strict consistency (per the CAP theorem), using eventual consistency—where updates reach all nodes eventually, typically within milliseconds, but may cause brief delays in accessing the latest data, known as stale reads. While most lack full ACID transaction support, some, like MongoDB, include it as a key feature. == Barriers to adoption == Barriers to wider NoSQL adoption include their use of low-level query languages instead of SQL, inability to perform ad hoc joins across tables, lack of standardized interfaces, and significant investments already made in relational databases. Some NoSQL systems risk losing data through lost writes or other forms, though features like write-ahead logging—a method to record changes before they’re applied—can help prevent this. For distributed transaction processing across multiple databases, keeping data consistent is a challenge for both NoSQL and relational systems, as relational databases cannot enforce rules linking separate databases, and few systems support both ACID transactions and X/Open XA standards for managing distributed updates. Limitations within the interface environment are overcome using semantic virtualization protocols, such that NoSQL services are accessible to most operating systems. == History == The term NoSQL was used by Carlo Strozzi in 1998 to name his lightweight Strozzi NoSQL open-source relational database that did not expose the standard Structured Query Language (SQL) interface, but was still relational. His NoSQL RDBMS is distinct from the around-2009 general concept of NoSQL databases. Strozzi suggests that, because the current NoSQL movement "departs from the relational model altogether, it should therefore have been called more appropriately 'NoREL'", referring to "not relational". Johan Oskarsson, then a developer at Last.fm, reintroduced the term NoSQL in early 2009 when he organized an event to discuss "open-source distributed, non-relational databases". The name attempted to label the emergence of an increasing number of non-relational, distributed data stores, including open source clones of Google's Bigtable/MapReduce and Amazon's DynamoDB. == Types and examples == There are various ways to classify NoSQL databases, with different categories and subcategories, some of which overlap. What follows is a non-exhaustive classification by data model, with examples: === Key–value store === Key–value (KV) stores use the associative array (also called a map or dictionary) as their fundamental data model. In this model, data is represented as a collection of key–value pairs, such that each possible key appears at most once in the collection. The key–value model is one of the simplest non-trivial data models, and richer data models are often implemented as an extension of it. The key–value model can be extended to a discretely ordered model that maintains keys in lexicographic order. This extension is computationally powerful, in that it can efficiently retrieve selective key ranges. Key–value stores can use consistency models ranging from eventual consistency to serializability. Some databases support ordering of keys. There are various hardware implementations, and some users store data in memory (RAM), while others on solid-state drives (SSD) or rotating disks (aka hard disk drive (HDD)). === Document store === The central concept of a document store is that of a "document". While the details of this definition differ among document-oriented databases, they all assume that documents encapsulate and encode data (or information) in some standard formats or encodings. Encodings in use include XML, YAML, and JSON and binary forms like BSON. Documents are addressed in the database via a unique key that represents that document. Another defining characteristic of a document-oriented database is an API or query language to retrieve documents based on their contents. Different implementations offer different ways of organizing and/or grouping documents: Collections Tags Non-visible metadata Directory hierarchies Compared to relational databases, collections could be considered analogous to tables and documents analogous to records. But they are different – every record in a table has the same sequence of fields, while documents in a collection may have fields that are completely different. === Graph === Graph databases are designed for data whose relations are well represented as a graph consisting of elements connected by a finite number of relations. Examples of data include social relations, public transport links, road maps, network topologies, etc. Graph databases and their query language == Performance == The performance of NoSQL databases is usually evaluated using the metric of throughput, which is measured as operations per second. Performance evaluation must pay attention to the right benchmarks such as production configurations, parameters of the databases, anticipated data volume, and concurrent user workloads. Ben Scofield rated different categories of NoSQL databases as follows: Performance and scalability comparisons are most commonly done using the YCSB benchmark. == Handling relational data == Since most NoSQL databases lack ability for joins in queries, the database schema generally needs to be designed differently. There are three main techniques for handling relational data in a NoSQL database. (See table join and ACID support for NoSQL databases that support joins.) === Multiple queries === Instead of retrieving all the data with one query, it is common to do several queries to get the desired data. NoSQL queries are often faster than traditional SQL queries, so the cost of additional queries may be acceptable. If an excessive number of queries would be necessary, one of the other two approaches is more appropriate. === Caching, replication and non-normalized data === Instead of only storing foreign keys, it is common to store actual foreign values along with the model's data. For example, each blog comment might include the username in addition to a user id, thus providing easy access to the username without requiring another lookup. When a username changes, however, this will now need to be changed in many places in the database. Thus this approach works better when reads are much more common than writes. === Nesting data === With document databases like MongoDB it is common to put more data in a smaller number of collections. For example, in a blogging application, one might choose to store comments within the blog post document, so that with a single retrieval one gets all the comments. Thus in this approach a single document contains all the data needed for a specific task. == ACID and join support == A database is marked as supporting ACID properties (atomicity, consistency, isolation, durability) or join operations if the documentation for the database makes that claim. However, this doesn't necessarily mean that the capability is fully supported in a manner similar to most SQL databases. == Query optimization and indexing in NoSQL databases == Different NoSQL databases, such as DynamoDB, MongoDB, Cassandra, Couchbase, HBase, and Redis, exhibit varying behaviors when querying non-indexed fields. Many perform full-table or collection scans for such queries, applying filtering operations after retrieving data. However, modern NoSQL databases often incorporate advanced features to optimize query performance. For example, MongoDB supports compound indexes and query-optimization strategies, Cassandra offers secondary indexes and materialized views, and Redis employs custom indexing mechanisms tailored to specific use cases. Systems like El

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