AI Coding Quality

AI Coding Quality — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Process map

  Process map is a global-system process model that is used to outline the processes that make up the business system and how they interact with each other. Process map shows the processes as objects, which means it is a static and non-algorithmic view of the processes. It should be differentiated from a detailed process model, which shows a dynamic and algorithmic view of the processes, usually known as a process flow diagram. There are different notation standards that can be used for modelling process maps, but the most notable ones are TOGAF Event Diagram, Eriksson-Penker notation, and ARIS Value Added Chain. == Global process models == Global characteristics of the business system are captured by global or system models. Global process models are presented using different methodologies and sometimes under different names. Most notably, they are named process map in Visual Paradigm and MMABP, value-added chain in ARIS, and process diagram in Eriksson-Penker notation – which can easily lead to the confusion with process flow (detailed process model). Global models are mainly object-oriented and present a static view of the business system; they do not describe dynamic aspects of processes. A process map shows the presence of processes and their mutual relationships. The requirement for the global perspective of the system as a supplementary to the internal process logic description results from the necessity of taking into consideration not only the internal process logic but also its significant surroundings. The algorithmic process model cannot take the place of this perspective since it represents the system model of the process. The detailed process model and the global process model represent different perspectives on the same business system, so these models must be mutually consistent. A macro process map represents the major processes required to deliver a product or service to the customer. These macro process maps can be further detailed in sub-diagrams. It is often the case that process maps cross different functional areas of the organization. Process maps are used by many companies to have a holistic view of all processes and the connections between them. Maps help in navigating the sub-processes and make understanding of the organization's operations easier. The process map shows relationships and dependencies between processes and its focus should be on core business processes of the organization. A process map can be seen as the most abstract level of the process architecture, and it acts as the introduction to the more detailed levels. A process map that is correctly designed is able to provide a general understanding of a company's operations. Designing the process map is an important and strategic step for the organization, and it is followed by further business process modelling implementation. == Context == Methodology for Modelling and Analysis of Business Process (MMABP) is a business process modelling methodology developed at the Department of Information Technology, Faculty of Informatics and Statistics of the Prague University of Economics and Business. The methodology is defined as a “general methodology for modelling business systems using informatics methods and approaches”. Methodology is used to analyse business processes and to develop a comprehensive model of the system. The goal of developing a model is to be used for process optimization. The model should be created following the characteristics and specifics of the organization in question and following external influences that can affect the organization. The model should be optimal from an economic perspective, but it should also be optimal from a factual perspective, meaning that it should be as simple as possible while maintaining complete functionality. Business system modelling is based on a two-dimensional approach: Real World structure (substance) – set of objects and their relationships Real World behaviour – set of mutually connected business processes Additionally, there are also two views of the systems: Global view of the system Detailed view of the system's parts This results in the need to model the system from four different perspectives in order to achieve the complete and comprehensive view of the business system. MMABP also proposes which notation languages can be used for modelling each perspective, and it also suggests some improvements to the notation languages in order to fit the purpose. Global view of the objects – Conceptual model (Class diagram) Detailed view of the objects – Object life cycle (State Chart) Global view of the processes – Process map (Eriksson-Penker Diagram/TOGAF Event Diagram/ARIS VAC) Detailed view of the processes – Model of the process flow (BPMN Diagram) Data Flow Diagram (DFD) is additional diagram used for describing the required functionalities of the information system. == Notation standards == === Eriksson-Penker Diagram === Eriksson-Penker diagram is a tool used in business model analysis and design. It is named after Hans-Erik Eriksson and Magnus Penker, who developed the concept in their book "Business modelling with UML: Business Patterns at Work”. Eriksson-Penker diagrams are used to map out the key components of a business model and how they interact with one another. The diagrams typically consist of a series of boxes and lines that represent the different elements of the business model, such as the value proposition, customer segments, channels, revenue streams, and key resources. The lines between the boxes represent the relationships and dependencies between the different elements of the business model. These diagrams are useful for visualizing and understanding the various components of a business model, and can help organizations identify potential areas for improvement or areas of risk. They can also be used as a communication tool to help stakeholders understand the business model and its underlying assumptions. These diagrams are useful for visualizing and understanding the various components of a business model, and can help organizations identify potential areas for improvement or areas of risk. They can also be used as a communication tool to help stakeholders understand the business model and its underlying assumptions. It is possible to use Eriksson-Penker diagrams to create a global process view of a business. In this case, a diagram would be used to map out the key processes and activities that are involved in the business, as well as the relationships and dependencies between these processes. For example, an Eriksson-Penker diagram could be used to depict the various steps involved in the product development process, from concept development to market launch. It could also be used to show how different functions within the organization, such as marketing, sales, and production, interact and depend on one another to support the overall business. Eriksson-Penker diagram is one of the most popular de facto standards that can be used for an object-oriented global view of business processes. It is developed as an extension of the UML, and it is often used together with the BPMN to compensate for the lack of possibility to model the global view with this widely accepted standard. === TOGAF Event Diagram === TOGAF (The Open Group Architecture Framework) is a framework for enterprise architecture that provides a common language and set of standards for designing, planning, implementing, and governing an enterprise's IT architecture. TOGAF event diagrams are diagrams used in the TOGAF framework to represent the flow of events within a system or process. The TOGAF Event Diagram is a visual representation of the events within an organization or system. It can be used to show the sequence of events that occur in a particular process, as well as the relationships between the events and the stakeholders involved. TOGAF Event Diagrams can be useful in creating a global process view because they provide a visual representation of the events, which can be helpful in understanding how the process fits into the larger context of the organization. TOGAF Event Diagram is the most perspective standard for the system view of processes today. It is used to represent the system of processes as well as their connections to the functional organizational structure. === ARIS Value Added Chain === ARIS (Architecture of Integrated Information Systems) is a methodology and a set of tools for designing and managing business processes. It is based on the idea that business processes are the core of an organization and that they can be modelled and optimized to improve efficiency and effectiveness. The ARIS methodology provides a framework for understanding and analysing business processes, as well as for designing and implementing improvements to those processes. It includes a set of graphical modelling languages and tools for creating process models, as well as a database for storing and managing pr

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  Group concept mapping

  Group concept mapping is a structured methodology for organizing the ideas of a group on any topic of interest and representing those ideas visually in a series of interrelated maps. It is a type of integrative mixed method, combining qualitative and quantitative approaches to data collection and analysis. Group concept mapping allows for a collaborative group process with groups of any size, including a broad and diverse array of participants. Since its development in the late 1980s by William M.K. Trochim at Cornell University, it has been applied to various fields and contexts, including community and public health, social work, health care, human services,, instructional interventions, and biomedical research and evaluation. == Overview == Group concept mapping integrates qualitative group processes with multivariate analysis to help a group organize and visually represent its ideas on any topic of interest through a series of related maps. It combines the ideas of diverse participants to show what the group thinks and values in relation to the specific topic of interest. It is a type of structured conceptualization used by groups to develop a conceptual framework, often to help guide evaluation and planning efforts. Group concept mapping is participatory in nature, allowing participants to have an equal voice and to contribute through various methods. A group concept map visually represents all the ideas of a group and how they relate to each other, and depending on the scale, which ideas are more relevant, important, or feasible. == Process == Group concept mapping involves a structured multi-step process, including brainstorming, sorting and rating, multidimensional scaling and cluster analysis, and the generation and interpretation of multiple maps. The first step requires participants to brainstorm a large set of statements relevant to the topic of interest, usually in response to a focus prompt. Participants are then asked to individually sort those statements into categories based on their perceived similarity and rate each statement on one or more scales, such as importance or feasibility. The data is then analyzed using The Concept System software, which creates a series of interrelated maps using multidimensional scaling (MDS) of the sort data, hierarchical clustering of the MDS coordinates applying Ward's method, and the computation of average ratings for each statement and cluster of statements. The resulting maps display the individual statements in two-dimensional space with more similar statements located closer to each other, and grouped into clusters that partition the space on the map. The Concept System software also creates other maps that show the statements in each cluster rated on one or more scales, and absolute or relative cluster ratings between two cluster sets. As a last step in the process, participants are led through a structured interpretation session to better understand and label all the maps. == History == Group concept mapping was developed as a methodology in the late 1980s by William M.K. Trochim at Cornell University. Trochim is considered to be a leading evaluation expert, and he has taught evaluation and research methods at Cornell since 1980. Originally called "concept mapping", the methodology has evolved since its inception with the maturation of the field and the continued advancement of the software, which is now a Web application. == Uses == Group concept mapping can be used with any group for any topic of interest. It is often used by government agencies, academic institutions, national associations, not-for-profit and community-based organizations, and private businesses to help turn the ideas of the group into measurable actions. This includes in the areas of organizational development, strategic planning, needs assessment, curriculum development, research, and evaluation. Group concept mapping is well-documented, well-established methodology, and it has been used in hundreds of published papers. == Versus concept mapping and mind mapping == More generally, concept mapping is any process used for visually representing relationships between ideas in pictures or diagrams. A concept map is typically a diagram of multiple ideas, often represented as boxes or circles, linked in a graph (network) structure through arrows and words where each idea is connected to another. The technique was originally developed in the 1970s by Joseph D. Novak at Cornell University. Concept mapping may be done by an individual or a group. A mind map is a diagram used to visually represent information, centering on one word or idea with categories and sub-categories radiating off of it in a tree structure. Popularized by Tony Buzan in the 1970s, mind mapping is often a spontaneous exercise done by an individual or group to gather information about what they think around a single topic. Unlike Novak's concept maps and Buzan's mind maps, group concept mapping has a structured mathematical process (sorting and rating, multidimensional scaling and cluster analysis) for organizing and visually representing multiple ideas of a group through a series of specific steps. In other words, in group concept mapping, the resulting visual representations are mathematically generated from mixed (qualitative and quantitative) data collected from a group of research subjects, whereas in Novak's concept maps and Buzan's mind maps the visual representations are drawn directly by the subjects resulting in diagrams that are qualitative data and final product at the same time.

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  Liveness test

  A liveness test, liveness check or liveness detection is an automated method for determining whether a subject is a real person or part of a spoofing attack. The technique is used as part of know your customer checks in financial services and during facial age estimation. Liveness detection is a cornerstone of digital safety. == Test process == The threat in face spoofing attacks is that "the attacker only needs to find a good face swap library on Github and understand how to inject the model into the camera feed during the KYC process". Fraudsters usually buy stolen IDs on the dark web to start a deepfake attack. An AI-powered generative adversarial network (GAN) can then generate the face swapping model that many online verification services fail to detect. Low level hackers may use face swapping apps such as SwapFace, DeepFaceLive, and Swapstream (increasing interest for those apps in 2023 according to Google Trends). In a video liveness test, users are typically asked to look into a camera and to move, smile or blink, and features of their moving face may then be compared to that of a still image. Artificial intelligence is used to counter presentation attacks such as deepfakes or users wearing hyperrealistic masks, or video injection attacks. Other forms of liveness test include checking for a pulse when using a fingerprint scanner or checking that a person's voice is not a recording or artificially generated during speaker recognition. == Adoption and certification == In a 2022 report published by the security firm Sensity, it was demonstrated that the liveness test of most US banks was easily cheated with new and publicly-available AI-powered techniques. Many of these banks disregarded the results of the report. In the first half of 2023, the security firm iProov detected a 704% increase in face-swap attacks. In 2023, in the UK, many customers of Ryanair were upset to have to go through many ID verification checks, including liveness tests, before boarding, as the airline was using it as a mean to deter customers to buy tickets through third-party websites. In the first half of 2024 iBeta Quality Assurance issued 18 new ISO/IEC 30107-3 Presentation Attack Detection certificates, raising the cumulative total to 85 since 2018. In January 2024, the Department of Homeland Security (DHS) opened applications from vendors to test their Liveness test. Identity frauds peaked during the COVID-19 lockdown, leading government agencies to take reinforced measures to secure their digital applications.

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  Effective accelerationism

  Effective accelerationism (e/acc) is a 21st-century ideological movement that advocates for an explicitly pro-technology stance. Its proponents believe that unrestricted technological progress, especially driven by artificial intelligence, is a solution to universal human problems, such as poverty, war, and climate change. They perceive themselves as a counterweight to more cautious views on technological innovation and often label their opponents derogatorily as "doomers" or "decels" (short for decelerationists). The movement carries utopian undertones and advocates for faster AI progress to ensure human survival and propagate consciousness throughout the universe. Although effective accelerationism has been described as a fringe movement and as cult-like, it has gained mainstream visibility in 2023. A number of high-profile Silicon Valley figures, including investors Marc Andreessen and Garry Tan, explicitly endorsed it by adding "e/acc" to their public social media profiles. == Etymology and central beliefs == Effective accelerationism, a portmanteau of "effective altruism" and "accelerationism", is a fundamentally techno-optimist movement. According to Guillaume Verdon, one of the movement's founders, its aim is for human civilization to "clim[b] the Kardashev gradient", meaning its purpose is for human civilization to rise to next levels on the Kardashev scale by maximizing energy usage. To achieve this goal, effective accelerationism wants to accelerate technological progress. It is strongly focused on artificial general intelligence (AGI), because it sees AGI as fundamental for climbing the Kardashev scale. The movement therefore advocates for unrestricted development and deployment of artificial intelligence. Regulation of artificial intelligence and government intervention in markets more generally is met with opposition. Many of its proponents have libertarian views and think that AGI will be most aligned if many AGIs compete against each other on the marketplace. The founders of the movement see it as rooted in Jeremy England's theory on the origin of life, which is focused on entropy and thermodynamics. According to them, the universe aims to increase entropy, and life is a way of increasing it. By spreading life throughout the universe and making life use up ever increasing amounts of energy, the universe's purpose would thus be fulfilled. == History == === Intellectual origins === While Nick Land is seen as the intellectual originator of contemporary accelerationism in general, the precise origins of effective accelerationism remain unclear. The earliest known reference to the movement can be traced back to a May 2022 newsletter published by four pseudonymous authors known by their X (formerly Twitter) usernames @BasedBeffJezos, @bayeslord, @zestular and @creatine_cycle. Effective accelerationism is an extension of the TESCREAL movement, being etymologically derived from Effective Altruism and heavily rooted in the older Silicon Valley subcultures of transhumanism and extropianism (which similarly emphasized the value of progress and resisted efforts to restrain the development of technology), alongside elements of singularitarianism, cosmism, and longtermism. It is also often considered to have emerged at least in part from the work of the Cybernetic Culture Research Unit (of which Nick Land was a leading member, alongside writers such as Mark Fisher and Sadie Plant). It is sometimes compared and contrasted with the work of philosopher Benjamin Bratton on planetary computation. === Disclosure of the identity of BasedBeffJezos === Forbes disclosed in December 2023 that the @BasedBeffJezos persona is maintained by Guillaume Verdon, a Canadian former Google quantum computing engineer and theoretical physicist. The revelation was supported by a voice analysis conducted by the National Center for Media Forensics of the University of Colorado Denver, which further confirmed the match between Jezos and Verdon. The magazine justified its decision to disclose Verdon's identity on the grounds of it being "in the public interest". On 29 December 2023 Guillaume Verdon was interviewed by Lex Fridman on the Lex Fridman Podcast and introduced as the "creator of the effective accelerationism movement". === Second Trump presidency === Following Donald Trump's victory in the 2024 U.S. presidential election, several prominent tech industry figures expressed support for positions aligned with effective accelerationism, particularly regarding deregulation and technological advancement. The potential appointment of Elon Musk to government roles focused on auditing federal programs drew support from venture capitalists who anticipated reduced regulatory oversight of the technology sector. Notable tech figures publicly connected these developments to the movement's principles. Aaron Levie, CEO of Box, expressed support for "removing unnecessary red tape and over-regulation", while Mark Pincus, early Facebook investor and Zynga founder, explicitly referenced "effective accelerationism" in his post-election commentary. Venture capitalists viewed the incoming administration as an opportunity to ease regulations that had affected technology mergers and acquisitions during the previous years. == Relation to other movements == === Traditional accelerationism === Traditional accelerationism, as developed by the British philosopher Nick Land, sees the acceleration of technological change as a way to bring about a fundamental transformation of current culture, society, and the political economy. This is done through capitalism, which Land views as "an autonomous force that’s reconfiguring society" that can overcome its limits if intensified. Land's work has also been characterized as concerning "the supposedly inevitable 'disintegration of the human species' when artificial intelligence improves sufficiently." While both concern ideas like a technocapital singularity and AGI progress, effective accelerationism focuses on using AGI for the greatest ethical good for conscious life and civilization (whether human or machine), as well as expanding civilization and maximizing energy usage in order to align with the "will of the universe". Land focuses on capitalist self-optimization as the driver of modernity, progress, and the eroding of existing social orders. Land has expressed support for effective accelerationism, while Thomas Murphy referred to the movement as "Nick Land diluted for LinkedIn". === Effective altruism === Effective accelerationism diverges from the principles of effective altruism, which prioritizes using evidence and reasoning to identify the most effective ways to altruistically improve the world. This divergence comes primarily from one of the causes effective altruists focus on – AI existential risk. Effective altruists (particularly longtermists) argue that AI companies should be cautious and strive to develop safe AI systems, as they fear that any misaligned AGI could eventually lead to human extinction. Proponents of effective accelerationism generally consider existential risks from AGI to be negligible, and claim that even if they were not, decentralized free markets would much better mitigate this risk than centralized governmental regulation. === Degrowth === Effective accelerationism stands in stark contrast with the degrowth movement, sometimes described by it as "decelerationism" or "decels". The degrowth movement advocates for reducing economic activity and consumption to address ecological and social issues. Effective accelerationism on the contrary embraces technological progress, energy consumption and the dynamics of capitalism, rather than advocating for a reduction in economic activity. == Reception == The "Techno-Optimist Manifesto", a 2023 essay by Marc Andreessen, has been described by the Financial Times and the German Süddeutsche Zeitung as espousing the views of effective accelerationism. Mother Jones also characterized it as expressing effective accelerationism and reported that Andressen cited Land's work. David Swan of The Sydney Morning Herald has criticized effective accelerationism due to its opposition to government and industry self-regulation. He argues that "innovations like AI needs thoughtful regulations and guardrails ... to avoid the myriad mistakes Silicon Valley has already made." During the 2023 Reagan National Defense Forum, U.S. Secretary of Commerce Gina Raimondo cautioned against embracing the "move fast and break things" mentality associated with "effective acceleration [sic]". She emphasized the need to exercise caution in dealing with AI, stating "that's too dangerous. You can't break things when you are talking about AI." In a similar vein, Ellen Huet argued on Bloomberg News that some of the ideas of the movement were "deeply unsettling", focusing especially on Guillaume Verdon's "post-humanism" and the view that "natural selection could lead AI to replace us as the dominant spe

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  Gollum browser

  Gollum browser is a discontinued web browser for accessing Wikipedia. Since 2017, Gollum is no longer accessible online. Gollum is designed to browse Wikipedia in an easier way than directly using the web browser. Links external to Wikipedia are opened in the user's regular browser. Gollum is opened from a regular browser and makes a window that puts the Wikipedia search bar on the toolbar. Gollum was created by Harald Hanek in 2005 using PHP and Ajax. According to one blogger, Gollum provides a way to bypass censorship of Wikipedia in China. == Languages == Though the website is available only in English and German, Gollum's GUI is available in more than 32 languages and can browse nearly 50 Wikipedia editions. === Gollum's GUI === === Browsable Wikipedia editions ===

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  Semantic analysis (knowledge representation)

  Semantic analysis is a method for eliciting and representing knowledge about organisations. Initially the problem must be defined by domain experts and passed to the project analyst(s). The next step is the generation of candidate affordances. This step will generate a list of semantic units that may be included in the schema. The candidate grouping follows where some of the semantic units that will appear in the schema are placed in simple groups. Finally the groups will be integrated together into an ontology chart. Semantic analysis always starts from the problem definition which if not clear, require the analyst to employ relevant literature, interviews with the stakeholders and other techniques towards collecting supplementary information. All assumptions made must be genuine and not limiting the system.

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  The Synthetic Party

  Det Syntetiske Parti (English: The Synthetic Party) is a political party driven by artificial intelligence (AI), founded in May 2022 in Denmark. The party aims to represent non-voters and fringe political parties while raising awareness of AI's societal role and exploring how it can be integrated into democratic processes. == Founder == The founder and continuous party secretary is Asker Bryld Staunæs, a philosopher from Aarhus University and a conceptual artist. == Main goal == The political goals have been machine learned from texts by Danish fringe parties since 1970 and represent the 20 percent of Danes who do not vote in the election. The party is synthetic; as such, many of the policies, such as universal basic income, can be contradictory to one another. == International collaborations == The Synthetic Party has signed bilateral collaboration agreements with the Finnish AI Party and AI Party (Japan) concerning the development of a global project created around artificial intelligence and politics These collaborations were expanded during the exhibition-event Synthetic Summit (28 February – 13 April 2025) at Kunsthal Aarhus, curated by Computer Lars (Asker Bryld Staunæs) on behalf of The Synthetic Party. The summit staged parliamentary scenography, performances, and computer sculptures, and invited both the public and policymakers to encounter an international line-up of AI parties and virtual politicians. Aarhus University described the event as part of Staunæs's PhD research, positioning it as an international top-meeting of virtual politicians. Participants included the Japanese AI Party, the Swedish AI Party, the Finnish AI Party, Parker Politics (New Zealand), Lex AI (Brazil), the Simiyya collective (Egypt/Sweden), the Synthetic Party (Denmark), and Wiktoria Cukt 2.0 (Poland). As part of the summit, the one-day AI World Congress was held on 1 March 2025, structured as a performative assembly where each group participated through both machinic agents and human delegates. Sessions were chaired by participating parties, with Computer Lars delivering the opening presentation. Throughout the day, contributions were synthesized into a common record using a shared AI system. The congress concluded with the adoption of the Synthetic Summit Resolution, a collectively authored treaty of algorithmic governance. Signatories included Floor Kist and Nick Gerritsen (Parker Politics), Michihito Matsuda (Japanese AI Party), Emma Bexell (Swedish AI Party), Samee Haapa (Finnish AI Party), Pedro Markun (Lex AI), Kristian T. Madsen and Michael Birkebæk Jensen (NextGen Democracy / DemAI), Asker Bryld Staunæs, Benjamin Asger Krog Møller, Caroline Sofie Axelsson, Life with Artificials (The Synthetic Party), and Piotr Wyrzykowski (Wiktoria Cukt 2.0).

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  VoID

  The Vocabulary of Interlinked Datasets (VoID) is a vocabulary for providing concise summaries (metadata) of Resource Description Framework (RDF) datasets—meaningful collections of semantic triples—using the syntax of RDF Schema. It can be used for general metadata (such as information about the license of the dataset), access metadata (information about how to access the dataset), structural metadata (information about how the dataset is structured), and linking metadata (information about links between datasets). A linked dataset is a collection of data, published and maintained by a single provider, available as RDF on the Web, where at least some of the resources in the dataset are identified by dereferencable Uniform Resource Identifiers (URIs). VoID is used to provide metadata on RDF datasets to facilitate query processing on a graph of interlinked datasets in the Semantic Web.

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  Curvelet

  Curvelets are a non-adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and scientific computing. Wavelets generalize the Fourier transform by using a basis that represents both location and spatial frequency. For 2D or 3D signals, directional wavelet transforms go further, by using basis functions that are also localized in orientation. A curvelet transform differs from other directional wavelet transforms in that the degree of localisation in orientation varies with scale. In particular, fine-scale basis functions are long ridges; the shape of the basis functions at scale j is 2 − j {\displaystyle 2^{-j}} by 2 − j / 2 {\displaystyle 2^{-j/2}} so the fine-scale bases are skinny ridges with a precisely determined orientation. Curvelets are an appropriate basis for representing images (or other functions) which are smooth apart from singularities along smooth curves, where the curves have bounded curvature, i.e. where objects in the image have a minimum length scale. This property holds for cartoons, geometrical diagrams, and text. As one zooms in on such images, the edges they contain appear increasingly straight. Curvelets take advantage of this property, by defining the higher resolution curvelets to be more elongated than the lower resolution curvelets. However, natural images (photographs) do not have this property; they have detail at every scale. Therefore, for natural images, it is preferable to use some sort of directional wavelet transform whose wavelets have the same aspect ratio at every scale. When the image is of the right type, curvelets provide a representation that is considerably sparser than other wavelet transforms. This can be quantified by considering the best approximation of a geometrical test image that can be represented using only n {\displaystyle n} wavelets, and analysing the approximation error as a function of n {\displaystyle n} . For a Fourier transform, the squared error decreases only as O ( 1 / n ) {\displaystyle O(1/{\sqrt {n}})} . For a wide variety of wavelet transforms, including both directional and non-directional variants, the squared error decreases as O ( 1 / n ) {\displaystyle O(1/n)} . The extra assumption underlying the curvelet transform allows it to achieve O ( ( log ⁡ n ) 3 / n 2 ) {\displaystyle O({(\log n)}^{3}/{n^{2}})} . Efficient numerical algorithms exist for computing the curvelet transform of discrete data. The computational cost of the discrete curvelet transforms proposed by Candès et al. (Discrete curvelet transform based on unequally-spaced fast Fourier transforms and based on the wrapping of specially selected Fourier samples) is approximately 6–10 times that of an FFT, and has the same dependence of O ( n 2 log ⁡ n ) {\displaystyle O(n^{2}\log n)} for an image of size n × n {\displaystyle n\times n} . == Curvelet construction == To construct a basic curvelet ϕ {\displaystyle \phi } and provide a tiling of the 2-D frequency space, two main ideas should be followed: Consider polar coordinates in frequency domain Construct curvelet elements being locally supported near wedges The number of wedges is N j = 4 ⋅ 2 ⌈ j 2 ⌉ {\displaystyle N_{j}=4\cdot 2^{\left\lceil {\frac {j}{2}}\right\rceil }} at the scale 2 − j {\displaystyle 2^{-j}} , i.e., it doubles in each second circular ring. Let ξ = ( ξ 1 , ξ 2 ) T {\displaystyle {\boldsymbol {\xi }}=\left(\xi _{1},\xi _{2}\right)^{T}} be the variable in frequency domain, and r = ξ 1 2 + ξ 2 2 , ω = arctan ⁡ ξ 1 ξ 2 {\displaystyle r={\sqrt {\xi _{1}^{2}+\xi _{2}^{2}}},\omega =\arctan {\frac {\xi _{1}}{\xi _{2}}}} be the polar coordinates in the frequency domain. We use the ansatz for the dilated basic curvelets in polar coordinates: ϕ ^ j , 0 , 0 := 2 − 3 j 4 W ( 2 − j r ) V ~ N j ( ω ) , r ≥ 0 , ω ∈ [ 0 , 2 π ) , j ∈ N 0 {\displaystyle {\hat {\phi }}_{j,0,0}:=2^{\frac {-3j}{4}}W(2^{-j}r){\tilde {V}}_{N_{j}}(\omega ),r\geq 0,\omega \in [0,2\pi ),j\in N_{0}} To construct a basic curvelet with compact support near a ″basic wedge″, the two windows W {\displaystyle W} and V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} need to have compact support. Here, we can simply take W ( r ) {\displaystyle W(r)} to cover ( 0 , ∞ ) {\displaystyle (0,\infty )} with dilated curvelets and V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} such that each circular ring is covered by the translations of V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} . Then the admissibility yields ∑ j = − ∞ ∞ | W ( 2 − j r ) | 2 = 1 , r ∈ ( 0 , ∞ ) . {\displaystyle \sum _{j=-\infty }^{\infty }\left|W(2^{-j}r)\right|^{2}=1,r\in (0,\infty ).} see Window Functions for more information For tiling a circular ring into N {\displaystyle N} wedges, where N {\displaystyle N} is an arbitrary positive integer, we need a 2 π {\displaystyle 2\pi } -periodic nonnegative window V ~ N {\displaystyle {\tilde {V}}_{N}} with support inside [ − 2 π N , 2 π N ] {\displaystyle \left[{\frac {-2\pi }{N}},{\frac {2\pi }{N}}\right]} such that ∑ l = 0 N − 1 V ~ N 2 ( ω − 2 π l N ) = 1 {\displaystyle \sum _{l=0}^{N-1}{\tilde {V}}_{N}^{2}\left(\omega -{\frac {2\pi l}{N}}\right)=1} , for all ω ∈ [ 0 , 2 π ) {\displaystyle \omega \in \left[0,2\pi \right)} , V ~ N {\displaystyle {\tilde {V}}_{N}} can be simply constructed as 2 π {\displaystyle 2\pi } -periodizations of a scaled window V ( N ω 2 π ) {\displaystyle V\left({\frac {N\omega }{2\pi }}\right)} . Then, it follows that ∑ l = 0 N j − 1 | 2 3 j 4 ϕ ^ j , 0 , 0 ( r , ω − 2 π l N j ) | 2 = | W ( 2 − j r ) | 2 ∑ l = 0 N j − 1 V ~ N j 2 ( ω − 2 π l N ) = | W ( 2 − j r ) | 2 {\displaystyle \sum _{l=0}^{N_{j}-1}\left|2^{\frac {3j}{4}}{\hat {\phi }}_{j,0,0}\left(r,\omega -{\frac {2\pi l}{N_{j}}}\right)\right|^{2}=\left|W(2^{-j}r)\right|^{2}\sum _{l=0}^{N_{j}-1}{\tilde {V}}_{N_{j}}^{2}\left(\omega -{\frac {2\pi l}{N}}\right)=\left|W(2^{-j}r)\right|^{2}} For a complete covering of the frequency plane including the region around zero, we need to define a low pass element ϕ ^ − 1 := W 0 ( | ξ | ) {\displaystyle {\hat {\phi }}_{-1}:=W_{0}(\left|\xi \right|)} with W 0 2 ( r ) 2 := 1 − ∑ j = 0 ∞ W ( 2 − j r ) 2 {\displaystyle W_{0}^{2}(r)^{2}:=1-\sum _{j=0}^{\infty }W(2^{-j}r)^{2}} that is supported on the unit circle, and where we do not consider any rotation. == Applications == Image processing Seismic exploration Fluid mechanics PDEs solving Compressed sensing

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  Mathematical model

  A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences, social sciences and engineering. In particular, the field of operations research studies the use of mathematical modelling and related tools to solve problems in business or military operations. A model may help to characterize a system by studying the effects of different components, which may be used to make predictions about behavior or solve specific problems. == Elements of a mathematical model == Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed. In the physical sciences, a traditional mathematical model contains most of the following elements: Governing equations Supplementary sub-models Defining equations Constitutive equations Assumptions and constraints Initial and boundary conditions Classical constraints and kinematic equations == Classifications == Mathematical models are of different types: === Linear vs. nonlinear === If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. All other models are considered nonlinear. The definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them. For example, in a statistical linear model, it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables. Similarly, a differential equation is said to be linear if it can be written with linear differential operators, but it can still have nonlinear expressions in it. In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model. Linear structure implies that a problem can be decomposed into simpler parts that can be treated independently or analyzed at a different scale, and therefore that the results will remain valid if the initial is recomposed or rescaled. Nonlinearity, even in fairly simple systems, is often associated with phenomena such as chaos and irreversibility. Although there are exceptions, nonlinear systems and models tend to be more difficult to study than linear ones. A common approach to nonlinear problems is linearization, but this can be problematic if one is trying to study aspects such as irreversibility, which are strongly tied to nonlinearity. === Static vs. dynamic === A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models are typically represented by differential equations or difference equations. === Explicit vs. implicit === If all of the input parameters of the overall model are known, and the output parameters can be calculated by a finite series of computations, the model is said to be explicit. But sometimes it is the output parameters which are known, and the corresponding inputs must be solved for by an iterative procedure, such as Newton's method or Broyden's method. In such a case the model is said to be implicit. For example, a jet engine's physical properties such as turbine and nozzle throat areas can be explicitly calculated given a design thermodynamic cycle (air and fuel flow rates, pressures, and temperatures) at a specific flight condition and power setting, but the engine's operating cycles at other flight conditions and power settings cannot be explicitly calculated from the constant physical properties. === Discrete vs. continuous === A discrete model treats objects as discrete, such as the particles in a molecular model or the states in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe flows, temperatures and stresses in a solid, and electric field that applies continuously over the entire model due to a point charge. === Deterministic vs. probabilistic (stochastic) === A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions. Conversely, in a stochastic model—usually called a "statistical model"—randomness is present, and variable states are not described by unique values, but rather by probability distributions. === Deductive, inductive, or floating === A deductive model is a logical structure based on a theory. An inductive model arises from empirical findings and generalization from them. If a model rests on neither theory nor observation, it may be described as a 'floating' model. Application of mathematics in social sciences outside of economics has been criticized for unfounded models. Application of catastrophe theory in science has been characterized as a floating model. === Strategic vs. non-strategic === Models used in game theory are distinct in the sense that they model agents with incompatible incentives, such as competing species or bidders in an auction. Strategic models assume that players are autonomous decision makers who rationally choose actions that maximize their objective function. A key challenge of using strategic models is defining and computing solution concepts such as the Nash equilibrium. An interesting property of strategic models is that they separate reasoning about rules of the game from reasoning about behavior of the players. == Construction == In business and engineering, mathematical models may be used to maximize a certain output. The system under consideration will require certain inputs. The system relating inputs to outputs depends on other variables too: decision variables, state variables, exogenous variables, and random variables. Decision variables are sometimes known as independent variables. Exogenous variables are sometimes known as parameters or constants. The variables are not independent of each other as the state variables are dependent on the decision, input, random, and exogenous variables. Furthermore, the output variables are dependent on the state of the system (represented by the state variables). Objectives and constraints of the system and its users can be represented as functions of the output variables or state variables. The objective functions will depend on the perspective of the model's user. Depending on the context, an objective function is also known as an index of performance, as it is some measure of interest to the user. Although there is no limit to the number of objective functions and constraints a model can have, using or optimizing the model becomes more involved (computationally) as the number increases. For example, economists often apply linear algebra when using input–output models. Complicated mathematical models that have many variables may be consolidated by use of vectors where one symbol represents several variables. === A priori information === Mathematical modeling problems are often classified into black box or white box models, according to how much a priori information on the system is available. A black-box model is a system of which there is no a priori information available. A white-box model (also called glass box or clear box) is a system where all necessary information is available. Practically all systems are somewhere between the black-box and white-box models, so this concept is useful only as an intuitive guide for deciding which approach to take. Usually, it is preferable to use as much a priori information as possible to make the model more accurate. Therefore, the white-box models are usually considered easier, because if you have used the information correctly, then the model will behave correctly. Often the a priori information comes in forms of knowing the type of functions relating different variables. For example, if we make a model of how a medicine works in a human system, we know that usually the amount of medicine in the blood is an exponentially decaying function, but we are still left with several unknown parameters; how

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  Reason maintenance

  Reason maintenance is a knowledge representation approach to efficient handling of inferred information that is explicitly stored. Reason maintenance distinguishes between base facts, which can be defeated, and derived facts. As such it differs from belief revision which, in its basic form, assumes that all facts are equally important. Reason maintenance was originally developed as a technique for implementing problem solvers. It encompasses a variety of techniques that share a common architecture: two components—a reasoner and a reason maintenance system—communicate with each other via an interface. The reasoner uses the reason maintenance system to record its inferences and justifications of ("reasons" for) the inferences. The reasoner also informs the reason maintenance system which are the currently valid base facts (assumptions). The reason maintenance system uses the information to compute the truth value of the stored derived facts and to restore consistency if an inconsistency is derived. == Truth maintenance system == A truth maintenance system, or TMS, is a knowledge representation method for representing both beliefs and their dependencies and an algorithm called the "truth maintenance algorithm" that manipulates and maintains the dependencies. The name truth maintenance is due to the ability of these systems to restore consistency. A truth maintenance system maintains consistency between old believed knowledge and current believed knowledge in the knowledge base (KB) through revision. If the current believed statements contradict the knowledge in the KB, then the KB is updated with the new knowledge. It may happen that the same data will again be believed, and the previous knowledge will be required in the KB. If the previous data are not present, but may be required for new inference. But if the previous knowledge was in the KB, then no retracing of the same knowledge is needed. The use of TMS avoids such retracing; it keeps track of the contradictory data with the help of a dependency record. This record reflects the retractions and additions which makes the inference engine (IE) aware of its current belief set. == Algorithm == Each statement having at least one valid justification is made a part of the current belief set. When a contradiction is found, the statement(s) responsible for the contradiction are identified and the records are appropriately updated. This process is called dependency-directed backtracking. The TMS algorithm maintains the records in the form of a dependency network. Each node in the network is an entry in the KB (a premise, antecedent, or inference rule etc.) Each arc of the network represent the inference steps through which the node was derived. A premise is a fundamental belief which is assumed to be true. They do not need justifications. The set of premises are the basis from which justifications for all other nodes will be derived. == Justification == There are two types of justification for a node. They are: Support list [SL] Conditional proof (CP) == Examples == Many kinds of truth maintenance systems exist. Two major types are single-context and multi-context truth maintenance. In single context systems, consistency is maintained among all facts in memory (KB) and relates to the notion of consistency found in classical logic. Multi-context systems support paraconsistency by allowing consistency to be relevant to a subset of facts in memory, a context, according to the history of logical inference. This is achieved by tagging each fact or deduction with its logical history. Multi-agent truth maintenance systems perform truth maintenance across multiple memories, often located on different machines. de Kleer's assumption-based truth maintenance system (ATMS, 1986) was utilized in systems based upon KEE on the Lisp Machine. The first multi-agent TMS was created by Mason and Johnson. It was a multi-context system. Bridgeland and Huhns created the first single-context multi-agent system.

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  Hyperion Data Center

  The Richland Parish Data Center, nicknamed "Hyperion", is a planned artificial intelligence data center by Meta Platforms under-construction along Highway La. 183 in Richland Parish, Louisiana, just outside of Holly Ridge. It is one of a number of "titan clusters" being built in preparation for the emergence of AI superintelligence. Modern technological researchers disagree as to whether or not superintelligence will ever exist, though Meta CEO Mark Zuckerberg has expressed belief that its creation is inevitable. Current plans allot for the investment of $27 billion, as the structure is built from 2025 to 2030. == History == Meta was considering potential locations for their flagship data center in early 2024. Before being announced later in December, the plan was completely secret; meetings held between involved organisations and even government officials could only refer to it by the codename "Project Sucre" to protect it from potential corporate espionage. The data center was first announced on 04 December 2024, though its full scale was yet to be revealed. At first, Meta would not even claim responsibility for it, channelling all of its investments through the secret shell subsidiary Laidley LLC. We set out looking for a place where we could expand into gigawatts pretty quickly, and really get moving within that community on a large plot of land very quickly. We looked at finding very, very large contiguous plots of land that had access to the infrastructure that we need, the energy that we needed, and could move very, very quickly for us. The Louisiana-based Entergy Corporation, aiming for the facility to be built in its own backyard, negotiated a deal with the government of Louisiana to provide Meta with enormous tax breaks if they agreed to build Hyperion there. The Louisiana legislature responded by passing Act 730, which provides significant tax rebates on the purchase or lease of equipment for building and operating data centers. Meta found the arrangement acceptable, and bought a plot of land from the government. The government also had to further amend its laws to allow Meta to do this, as pre-existing policy forbade purchasing land directly from the government instead of hosting a public auction. The plot of land, originally called Franklin Farms, was purchased from the Franklin family in 2006 by the government, intending for it to be developed into an automotive manufacturing plant. Greater attention was brought to Hyperion it when Zuckerberg posted about the project on 14 July 2025 on Threads. The project subsequently caught media attention for its large size, as Zuckerberg's post portrayed the structure superimposed over Manhattan (pictured). The construction site spans 2,250 acres (9.1 km2) with a planned floor area of 4,000,000 square feet (371612 m2), making it the third largest building in the world by floor area upon completion. Meta initially reported the construction cost to be over $10 billion, but in October 2025, it announced a partnership with Blue Owl Capital providing for at least $27 billion. == Operation == The facility is expected to consume up to 5 gigawatts (GW) of computational power, more electricity than is currently used by the entire State of Louisiana. As part of their deal made with Meta, Entergy plans to be able to produce at least 3.8 GW of electricity for the operation. == Response to the project == Louisiana Governor Jeff Landry thanked Meta for their decision to build Hyperion in Louisiana, stating that it would "create opportunities for Louisiana workers to fill high-paying jobs of the future." and calling it "A New Chapter" for the state. The Louisiana Economic Development (LED) state agency further praised the project, citing Meta's estimate that it would create 1,500 jobs. Additionally, Richland Parish Supervisor Joey Evans stated that he was excited about the project. As part of their agreement with Meta, Energy announced their plan to increase electricity production state-wide. They say that this will result in the cost of energy reducing, though Entergy filings revealed in June 2025 that the cost of electricity would rise and be passed onto consumers. Meta also pledged to match all of Hyperion's power consumption with 100% environmentally friendly electricity production. So far, Entergy has begun building three gas-powered combined-cycle power plants and a substation in response to the project. Delta Community College announced in response to Hyperion's construction that it would expand its construction and trade programs. In January 2025, Business Facilities Magazine selected Hyperion for its annual Deal of the Year Platinum Award for 2024. Much of the initial backlash following Hyperion's announcement centered around the fast-tracked approval of the project by the state government, and scepticism around Meta's various claims (environmental friendliness, 100% renewable energy, local economic stimulation, price reductions). The Sierra Club criticised Meta for gentrifying the surrounding area, and was highly sceptical of their promise to keep it environmentally friendly. Environmental activist group Earthjustice attempted to have a subpoena of Meta approved to determine if they were compliant with environmental protection laws, though they were unsuccessful. Many residents of Holy Ridge have been critical of the construction, complaining about the increased construction vehicle traffic and intense gentrification. Another point of contention is Meta's continued reliance on out-of-state contractors in the facility's construction in spite of their previous commitment to "hire as many local folk as [we] possibly can." In spite of Entergy's continual denial that the facility's construction will not adversely affect the power grid, numerous electrical outages have been reported since construction began.

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  Local-first software

  Local-first software is a software engineering approach in which an application stores its data primarily on the user's own device rather than on remote servers. Users can read and write data without an Internet connection, and changes are synchronized across devices in the background when connectivity is available. The approach differs from conventional cloud-based applications, where the server holds the authoritative copy of user data and the client acts as a thin client. The term was coined in a 2019 paper published by researchers at Ink & Switch, an independent research lab, and presented at the Onward! conference at ACM SIGPLAN. The paper, sometimes referred to as a manifesto, was authored by Martin Kleppmann, Adam Wiggins, Peter van Hardenberg, and Mark McGranaghan. == Background == Before the widespread adoption of Internet-connected software in the 2000s, most desktop applications stored data as files on the user's local disk. Users had direct access to their files and could copy, back up, or delete them at will. The rise of software as a service (SaaS) and cloud-based applications like Google Docs shifted data storage to centralized servers. While cloud applications made real-time collaboration across devices straightforward, they introduced a dependency on the service provider: if the provider discontinued the service or experienced an outage, users could lose access to their data. A related concept, "offline-first," emerged in the early 2010s and focused on making web applications resilient to network interruptions. The local-first approach built on these earlier efforts while placing greater emphasis on long-term data ownership and end-to-end encryption. == Origins == === Ink & Switch manifesto === Ink & Switch is an industrial research lab co-founded by Adam Wiggins, who had earlier co-founded Heroku. Martin Kleppmann, an associate professor in the Department of Computer Science and Technology at the University of Cambridge, was a co-author of the 2019 paper. The manifesto proposed seven "ideals" for local-first software: Fast — Operations respond without network round-trips. Multi-device — Data synchronizes across a user's devices. Offline — Users can read and write data without a network connection. Collaboration — Multiple users can work on the same data concurrently. Longevity — Data remains accessible even if the software vendor ceases operation. Privacy — End-to-end encryption protects user data. User control — The vendor cannot restrict how users access or use their data. The paper surveyed existing approaches to data storage and collaboration — ranging from email attachments and Dropbox-style file synchronization to web applications and mobile backends — and argued that none of them satisfied all seven ideals simultaneously. === Role of CRDTs === The manifesto identified conflict-free replicated data types (CRDTs) as a promising technical foundation for local-first applications. CRDTs are data structures that allow multiple replicas to be edited independently and then merged without conflicts, a property first formalized in research by Marc Shapiro and colleagues around 2011. Kleppmann and collaborators at Ink & Switch developed Automerge, an open-source CRDT library for JSON documents, to make these algorithms available to application developers. == Adoption and community == Developer interest in the local-first approach grew after the 2019 paper spread on Hacker News and at developer conferences In August 2023, Wired published a feature article on the movement, describing it as an effort to reduce reliance on large cloud providers. The first Local-First Conf took place on 30 May 2024 in Berlin, with talks by Kleppmann and developers from companies including Linear and Anytype. The community has continued to expand, with regular "LoFi" meetups, a podcast (localfirst.fm), and a third edition of the conference planned for Berlin in July 2026. == Criticisms and limitations == Developers and commentators have pointed out practical difficulties with the local-first approach. Synchronizing data between multiple devices that may be offline for extended periods introduces complexity that cloud-based architectures avoid. Conflict resolution, even with CRDTs, can produce results that are technically consistent but semantically unexpected to users. Schema migrations across thousands of client devices running different application versions pose another difficulty that does not arise with server-side databases. Web browsers impose storage limits and may evict locally stored data. Safari, for instance, has been reported to clear IndexedDB data after seven days of inactivity on a given site, which undermines the assumption that local data is persistent. There is also disagreement within the local-first community about whether a fully decentralized architecture is required. The original manifesto described decentralization as the "logical end goal," but a number of products that identify as local-first still depend on centralized servers for authentication, backup, or synchronization. In a talk at Local-First Conf 2024, Kleppmann said the seven ideals are better understood as a "gradient" rather than a strict checklist.

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  Otterly.ai

  Otterly.ai is an Austrian software company, founded in 2024, that provides tools for generative engine optimization, the practice of monitoring and optimizing results in large language models. == History == Otterly.ai was co-founded in 2024 by Thomas Peham, Klaus-M. Schremser and Josef Trauner. The concept for OtterlyAI was developed in response to the increasing use of generative AI tools in digital search and content discovery. The company announced a technology partnership with SEO platform Semrush in January 2025.

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  Unique name assumption

  The unique name assumption is a simplifying assumption made in some ontology languages and description logics. In logics with the unique name assumption, different names always refer to different entities in the world. It was included in Ray Reiter's discussion of the closed-world assumption often tacitly included in Database Management Systems (e.g. SQL) in his 1984 article "Towards a logical reconstruction of relational database theory" (in M. L. Brodie, J. Mylopoulos, J. W. Schmidt (editors), Data Modelling in Artificial Intelligence, Database and Programming Languages, Springer, 1984, pages 191–233). The standard ontology language OWL does not make this assumption, but provides explicit constructs to express whether two names denote the same or distinct entities. owl:sameAs is the OWL property that asserts that two given names or identifiers (e.g., URIs) refer to the same individual or entity. owl:differentFrom is the OWL property that asserts that two given names or identifiers (e.g., URIs) refer to different individuals or entities.

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