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IT baseline protection

The IT baseline protection (German: IT-Grundschutz) approach from the German Federal Office for Information Security (BSI) is a methodology to identify and implement computer security measures in an organization. The aim is the achievement of an adequate and appropriate level of security for IT systems. To reach this goal the BSI recommends "well-proven technical, organizational, personnel, and infrastructural safeguards". Organizations and federal agencies show their systematic approach to secure their IT systems (e.g. Information Security Management System) by obtaining an ISO/IEC 27001 Certificate on the basis of IT-Grundschutz. == Overview baseline security == The term baseline security signifies standard security measures for typical IT systems. It is used in various contexts with somewhat different meanings. For example: Microsoft Baseline Security Analyzer: Software tool focused on Microsoft operating system and services security Cisco security baseline: Vendor recommendation focused on network and network device security controls Nortel baseline security: Set of requirements and best practices with a focus on network operators ISO/IEC 13335-3 defines a baseline approach to risk management. This standard has been replaced by ISO/IEC 27005, but the baseline approach was not taken over yet into the 2700x series. There are numerous internal baseline security policies for organizations, The German BSI has a comprehensive baseline security standard, that is compliant with the ISO/IEC 27000-series == BSI IT baseline protection == The foundation of an IT baseline protection concept is initially not a detailed risk analysis. It proceeds from overall hazards. Consequently, sophisticated classification according to damage extent and probability of occurrence is ignored. Three protection needs categories are established. With their help, the protection needs of the object under investigation can be determined. Based on these, appropriate personnel, technical, organizational and infrastructural security measures are selected from the IT Baseline Protection Catalogs. The Federal Office for Security in Information Technology's IT Baseline Protection Catalogs offer a "cookbook recipe" for a normal level of protection. Besides probability of occurrence and potential damage extents, implementation costs are also considered. By using the Baseline Protection Catalogs, costly security analyses requiring expert knowledge are dispensed with, since overall hazards are worked with in the beginning. It is possible for the relative layman to identify measures to be taken and to implement them in cooperation with professionals. The BSI grants a baseline protection certificate as confirmation for the successful implementation of baseline protection. In stages 1 and 2, this is based on self declaration. In stage 3, an independent, BSI-licensed auditor completes an audit. Certification process internationalization has been possible since 2006. ISO/IEC 27001 certification can occur simultaneously with IT baseline protection certification. (The ISO/IEC 27001 standard is the successor of BS 7799-2). This process is based on the new BSI security standards. This process carries a development price which has prevailed for some time. Corporations having themselves certified under the BS 7799-2 standard are obliged to carry out a risk assessment. To make it more comfortable, most deviate from the protection needs analysis pursuant to the IT Baseline Protection Catalogs. The advantage is not only conformity with the strict BSI, but also attainment of BS 7799-2 certification. Beyond this, the BSI offers a few help aids like the policy template and the GSTOOL. One data protection component is available, which was produced in cooperation with the German Federal Commissioner for Data Protection and Freedom of Information and the state data protection authorities and integrated into the IT Baseline Protection Catalog. This component is not considered, however, in the certification process. == Baseline protection process == The following steps are taken pursuant to the baseline protection process during structure analysis and protection needs analysis: The IT network is defined. IT structure analysis is carried out. Protection needs determination is carried out. A baseline security check is carried out. IT baseline protection measures are implemented. Creation occurs in the following steps: IT structure analysis (survey) Assessment of protection needs Selection of actions Running comparison of nominal and actual. === IT structure analysis === An IT network includes the totality of infrastructural, organizational, personnel, and technical components serving the fulfillment of a task in a particular information processing application area. An IT network can thereby encompass the entire IT character of an institution or individual division, which is partitioned by organizational structures as, for example, a departmental network, or as shared IT applications, for example, a personnel information system. It is necessary to analyze and document the information technological structure in question to generate an IT security concept and especially to apply the IT Baseline Protection Catalogs. Due to today's usually heavily networked IT systems, a network topology plan offers a starting point for the analysis. The following aspects must be taken into consideration: The available infrastructure, The organizational and personnel framework for the IT network, Networked and non-networked IT systems employed in the IT network. The communications connections between IT systems and externally, IT applications run within the IT network. === Protection needs determination === The purpose of the protection needs determination is to investigate what protection is sufficient and appropriate for the information and information technology in use. In this connection, the damage to each application and the processed information, which could result from a breach of confidentiality, integrity or availability, is considered. Important in this context is a realistic assessment of the possible follow-on damages. A division into the three protection needs categories "low to medium", "high" and "very high" has proved itself of value. "Public", "internal" and "secret" are often used for confidentiality. === Modelling === Heavily networked IT systems typically characterize information technology in government and business these days. As a rule, therefore, it is advantageous to consider the entire IT system and not just individual systems within the scope of an IT security analysis and concept. To be able to manage this task, it makes sense to logically partition the entire IT system into parts and to separately consider each part or even an IT network. Detailed documentation about its structure is prerequisite for the use of the IT Baseline Protection Catalogs on an IT network. This can be achieved, for example, via the IT structure analysis described above. The IT Baseline Protection Catalogs' components must ultimately be mapped onto the components of the IT network in question in a modelling step. === Baseline security check === The baseline security check is an organisational instrument offering a quick overview of the prevailing IT security level. With the help of interviews, the status quo of an existing IT network (as modelled by IT baseline protection) relative to the number of security measures implemented from the IT Baseline Protection Catalogs are investigated. The result is a catalog in which the implementation status "dispensable", "yes", "partly", or "no" is entered for each relevant measure. By identifying not yet, or only partially, implemented measures, improvement options for the security of the information technology in question are highlighted. The baseline security check gives information about measures, which are still missing (nominal vs. actual comparison). From this follows what remains to be done to achieve baseline protection through security. Not all measures suggested by this baseline check need to be implemented. Peculiarities are to be taken into account! It could be that several more or less unimportant applications are running on a server, which have lesser protection needs. In their totality, however, these applications are to be provided with a higher level of protection. This is called the (cumulation effect). The applications running on a server determine its need for protection. Several IT applications can run on an IT system. When this occurs, the application with the greatest need for protection determines the IT systems protection category. Conversely, it is conceivable that an IT application with great protection needs does not automatically transfer this to the IT system. This may happen because the IT system is configured redundantly, or because only an inconsequential part is running on it. This is called the (distribution effect). This is the case, fo
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AdTruth

AdTruth is a software product and the digital media division of 41st Parameter, a company headquartered in Scottsdale, Arizona, with regional offices in San Jose, California; London, England; and Munich, Germany. AdTruth allows marketers to recognize and reach target audiences across online devices. AdTruth software identifies users for targeting, tracking, performance tracking across digital media, including mobile and desktop, by analysing patterns in large numbers of advertisements served over the internet, rather than through the use of cookies. == History == AdTruth was founded in 2011 by Ori Eisen of 41st Parameter, to repurpose the company's fraud detection and prevention technology, for use within the advertising industry to accurately target intended audiences, particularly in mobile. Eisen was joined by James Lamberti in the role of vice president and general manager. In 2012 41st Parameter raised $13 million in Series D financing from Norwest Venture Partners, Kleiner Perkins Caufield & Byers, Jafco Ventures and Georgian Partners, bringing total funding to about $35 million. In May 2012, AdTruth hosted a meeting of digital media executives to discuss Apple’s UDID deprecation, with the intent of developing a device-neutral replacement standard. AdTruth joined the World Wide Web Consortium's Tracking Protection Working Group, which provides guidance for implementing and adhering to Do Not Track policies. AdTruth also worked with privacy firm Truste to create a privacy compliant Do Not Track-style mechanism for mobile. In 2013, the company Experian purchased 41st Parameter, acquiring AdTruth as part of the deal. == Product == AdTruth software helps marketers track, target and retarget consumers using more than 100 parameters, including milliseconds in differences in the internal clock setting, to recognize a particular device anonymously. AdTruth's technology uses non-UDID information to identify a wide range of devices for cookieless ad targeting. Its technology currently has about a 90 percent accuracy rate on iOS, higher on Android and desktop. AdTruth also has mobile web to app bridging capabilities as well as DeviceInsight technology, enabling marketers to identify users across mobile web and app content. 41st Parameter's patented AdTruth technology is being used by MdotM, in response to the deprecation of the UDID that included tracking and targeting capabilities. == Competitors == AdTruth's main competitor is BlueCava, which deploys a similar device-fingerprinting technology.
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Contract management software

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

The International Conference on Language Resources and Evaluation is an international conference organised by the ELRA Language Resources Association every other year (on even years) with the support of institutions and organisations involved in Natural language processing. The series of LREC conferences was launched in Granada in 1998. == History of conferences == The survey of the LREC conferences over the period 1998-2013 was presented during the 2014 conference in Reykjavik as a closing session. It appears that the number of papers and signatures is increasing over time. The average number of authors per paper is higher as well. The percentage of new authors is between 68% and 78%. The distribution between male (65%) and female (35%) authors is stable over time. The most frequent technical term is "annotation", then comes "part-of-speech". == The LRE Map == The LRE Map was introduced at LREC 2010 and is now a regular feature of the LREC submission process for both the conference papers and the workshop papers. At the submission stage, the authors are asked to provide some basic information about all the resources (in a broad sense, i.e. including tools, standards and evaluation packages), either used or created, described in their papers. All these descriptors are then gathered in a global matrix called the LRE Map. This feature has been extended to several other conferences.
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ChatGPT

ChatGPT is a generative artificial intelligence chatbot developed by OpenAI. Originally released in November 2022, the product uses large language models—specifically generative pre-trained transformers (GPTs)—to generate text, speech, and images in response to user prompts. ChatGPT accelerated the AI boom, an ongoing period marked by rapid investment and public attention toward the field of artificial intelligence (AI). OpenAI operates the service on a freemium model. Users can interact with ChatGPT through text, audio, and image prompts. ChatGPT was quickly adopted, reaching 100 million monthly active users two months after its release and 900 million weekly active users in February 2026. It has been lauded for its potential to transform numerous professional fields, and has instigated public debate about the nature of creativity and the future of knowledge work. The chatbot has also been criticized for its limitations and potential for unethical use. It can generate plausible-sounding but incorrect or nonsensical answers, known as hallucinations. Biases in its training data have been reflected in its responses. The chatbot can facilitate academic dishonesty, generate misinformation, and create malicious code. The ethics of its development, particularly the use of copyrighted content as training data, have also drawn controversy. == Features == ChatGPT is a chatbot and AI assistant built on large language model (LLM) technology. It is designed to generate human-like text and can carry out a wide variety of tasks. These include, among many others, writing and debugging computer programs, composing music, scripts, fairy tales, and essays, answering questions (sometimes at a level exceeding that of an average human test-taker), and generating business concepts. ChatGPT is frequently used for translation and summarization tasks, and can simulate interactive environments such as a Linux terminal, a multi-user chat room, or simple text-based games such as tic-tac-toe. Users interact with ChatGPT through conversations which consist of text, audio, and image inputs and outputs. The user's inputs to these conversations are referred to as prompts. An optional "Memory" feature allows users to tell ChatGPT to memorize specific information. Another option allows ChatGPT to recall old conversations. GPT-based moderation classifiers are used to reduce the risk of harmful outputs being presented to users. In March 2023, OpenAI added support for plugins for ChatGPT. This includes both plugins made by OpenAI, such as web browsing and code interpretation, and external plugins from developers such as Expedia, OpenTable, and Zapier. From October to December 2024, ChatGPT Search was deployed. It allows ChatGPT to search the web in an attempt to make more accurate and up-to-date responses. It increased OpenAI's direct competition with major search engines. OpenAI allows businesses to tailor how their content appears in the ChatGPT Search results and influence what sources are used. In December 2024, OpenAI launched a new feature allowing users to call ChatGPT with a telephone for up to 15 minutes per month for free. In September 2025, OpenAI added a feature called Pulse, which generates a daily analysis of a user's chats and connected apps such as Gmail and Google Calendar. In October 2025, OpenAI launched ChatGPT Atlas, a browser integrating the ChatGPT assistant directly into web navigation, to compete with existing browsers such as Google Chrome. It has an additional feature called "agentic mode" that allows it to take online actions for the user. === Paid tier === ChatGPT was initially free to the public and remains free in a limited capacity. In February 2023, OpenAI launched a premium service, ChatGPT Plus, that costs US$20 per month. What was offered on the paid plan versus the free tier changed as OpenAI has continued to update ChatGPT, and a Pro tier at $200/mo was introduced in December 2024. The Pro launch coincided with the release of the o1 model. In August 2025, ChatGPT Go was offered in India for ₹399 per month. The plan has higher limits than the free version. === Mobile apps === In May-July 2023, OpenAI began offering ChatGPT iOS and Android apps. ChatGPT can also power Android's assistant. An app for Windows launched on the Microsoft Store on October 15, 2024. === Languages === OpenAI met Icelandic President Guðni Th. Jóhannesson in 2022. In 2023, OpenAI worked with a team of 40 Icelandic volunteers to fine-tune ChatGPT's Icelandic conversation skills as a part of Iceland's attempts to preserve the Icelandic language. ChatGPT (based on GPT-4) was better able to translate Japanese to English when compared to Bing, Bard, and DeepL Translator in 2023. In December 2023, the Albanian government decided to use ChatGPT for the rapid translation of European Union documents and the analysis of required changes needed for Albania's accession to the EU. Several studies have shown that ChatGPT can outperform Google Translate in some mainstream translation tasks. However, as of 2024, no machine translation services match human expert performance. In August 2024, a representative of the Asia Pacific wing of OpenAI made a visit to Taiwan, during which a demonstration of ChatGPT's Chinese abilities was made. ChatGPT's Mandarin Chinese abilities were lauded, but the ability of the AI to produce content in Mandarin Chinese in a Taiwanese accent was found to be "less than ideal" due to differences between mainland Mandarin Chinese and Taiwanese Mandarin. === GPT Store === In November 2023, OpenAI released GPT Builder, a tool allowing users to customize ChatGPT's behavior for a specific use case. The customized systems are referred to as GPTs. In January 2024, OpenAI launched the GPT Store, a marketplace for GPTs. At launch, OpenAI included more than 3 million GPTs created by GPT Builder users in the GPT Store. === ChatGPT Apps === In September 2025, OpenAI added support for Model Context Protocol (MCP) to ChatGPT apps. When enabled in developer mode, this allows for improved third-party access to ChatGPT tools and servers. === Deep Research === In February 2025, OpenAI released Deep Research, a feature that generates reports based on extensive web searches. It was initially based on the reasoning model o3 and took 5 to 30 minutes per report. === Images === In October 2023, OpenAI's image generation model DALL-E 3 was integrated into ChatGPT. The integration used ChatGPT to write prompts for DALL-E guided by conversations with users. In March 2025, OpenAI updated ChatGPT to generate images using GPT Image instead of DALL-E. One of the most significant improvements was in the generation of text within images, which is especially useful for branded content. However, this ability is noticeably worse in non-Latin alphabets. The model can also generate new images based on existing ones provided in the prompt. These images are generated with C2PA metadata, which can be used to verify that they are AI-generated. OpenAI has emplaced additional safeguards to prevent what the company deems to be harmful image generation. === Agents === In 2025, OpenAI added several features to make ChatGPT more agentic (capable of autonomously performing longer tasks). In January, Operator was released. It was capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other browser-based tasks. It was controlling a software environment inside a virtual machine with limited internet connectivity and with safety restrictions. It struggled with complex user interfaces. In May 2025, OpenAI introduced an agent for coding named Codex. It is capable of writing software, answering codebase questions, running tests, and proposing pull requests. It is based on a fine-tuned version of OpenAI o3. It has two versions, one running in a virtual machine in the cloud, and one where the agent runs in the cloud, but performs actions on a local machine connected via API. In July 2025, OpenAI released ChatGPT agent, an AI agent that can perform multi-step tasks. Like Operator, it controls a virtual computer. It also inherits from Deep Research's ability to gather and summarize significant volumes of information. The user can interrupt tasks or provide additional instructions as needed. In September 2025, OpenAI partnered with Stripe, Inc. to release Agentic Commerce Protocol, enabling purchases through ChatGPT. At launch, the feature was limited to purchases on Etsy from US users with a payment method linked to their OpenAI account. OpenAI takes an undisclosed cut from the merchant's payment. === ChatGPT Health === On January 7, 2026, OpenAI introduced a feature called "ChatGPT Health", whereby ChatGPT can discuss the user's health in a way that is separate from other chats. The feature is not available for users in the United Kingdom, Switzerland, or the European Economic Area, and is available on a waitli
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Ogle app

Ogle is a free smartphone based social media application. It is available for iOS and Android. Ogle acts like a school wide forum that lets users and users' classmates share and interact. Users can share photos, videos, questions, even thoughts and watch submissions grow in popularity as other users vote and comment on them. == App Features == Campus Feed: Interact by watching and posting videos or pictures to your campus story. Photos and Videos: share what you want with many different timing options. Interact: Chat with friends and groups, or share a moment for all to see. Real-name system: choose to register an account with username and profile picture. Custom Stickers: Create stickers to add creativity and zest to your pictures. Flash Interaction: All private chat and group chat history will be deleted after 24 hours on Ogle Chat. == Controversies == Users can post anything on Ogle using text, photos, and videos. As a result, some Ogle user's sense of anonymity, posts have targeted specific schools and students with abusive and hurtful content. The Ogle app's user anonymity makes it difficult for school officials to quickly investigate issues that occur within the Ogle app. On March 28, 2016, three people were arrested after violent threats were made against an Anaheim high school. 18-year-old Miguel Meza was arrested Sunday afternoon during a traffic stop, along with his passenger, 23-year-old Johnny Aguilar. Police said both men had loaded handguns. Aguilar was also accused of violating his probation. "It is concerning the fact that they did have firearms, but we don't have a crystal ball. We can't determine if they possessed those firearms to engage in some kind of school violence or if they had it for another reason," Sgt. Daron Wyatt with the Anaheim Police Department said. Officials said Meza and Aguilar have known gang ties and detectives began investigating Meza after threats were made against the school on Ogle. On February 29, 2016, Santa Cruz County sheriff's deputies arrested a 16-year-old Aptos High School student Friday, accused of making an online threat of gun violence at Aptos High and Monte Vista Christian."He basically told detectives that it was all a joke. It's not a joke. You have multiple resources being spent to investigate these cases," said Santa Cruz County Sheriff's Sgt. Roy Morales. The schools remained open throughout the week, with a huge police presence on campus. In an anonymous emailed statement to the Daily Pilot on Thursday, the "Ogle team" said: "We are aware of the concern, and cyberbullying is absolutely NOT our intention for the app. Our goal for this app is to create a free and safe community space for students, for a better communication. We are currently working around the clock to improve the app. As a matter of fact, we are also in contact with local police departments, anti-bullying organizations and local high schools to try to help the students." In response to these incidents, Ogle expressed that they takes the safety of its users seriously and does not condone any type of behavior that is illegal or in violation of its content policies. The company also said it has instituted a content moderation team to increase review and identify and remove inappropriate content, and take action against “those who violate our community guidelines.”
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Hybrid machine translation

Hybrid machine translation is a method of machine translation that is characterized by the use of multiple machine translation approaches within a single machine translation system. The motivation for developing hybrid machine translation systems stems from the failure of any single technique to achieve a satisfactory level of accuracy. Many hybrid machine translation systems have been successful in improving the accuracy of the translations, and there are several popular machine translation systems which employ hybrid methods. == Approaches == === Multi-engine === This approach to hybrid machine translation involves running multiple machine translation systems in parallel. The final output is generated by combining the output of all the sub-systems. Most commonly, these systems use statistical and rule-based translation subsystems, but other combinations have been explored. For example, researchers at Carnegie Mellon University have had some success combining example-based, transfer-based, knowledge-based and statistical translation sub-systems into one machine translation system. === Statistical rule generation === This approach involves using statistical data to generate lexical and syntactic rules. The input is then processed with these rules as if it were a rule-based translator. This approach attempts to avoid the difficult and time-consuming task of creating a set of comprehensive, fine-grained linguistic rules by extracting those rules from the training corpus. This approach still suffers from many problems of normal statistical machine translation, namely that the accuracy of the translation will depend heavily on the similarity of the input text to the text of the training corpus. As a result, this technique has had the most success in domain-specific applications, and has the same difficulties with domain adaptation as many statistical machine translation systems. === Multi-Pass === This approach involves serially processing the input multiple times. The most common technique used in multi-pass machine translation systems is to pre-process the input with a rule-based machine translation system. The output of the rule-based pre-processor is passed to a statistical machine translation system, which produces the final output. This technique is used to limit the amount of information a statistical system need consider, significantly reducing the processing power required. It also removes the need for the rule-based system to be a complete translation system for the language, significantly reducing the amount of human effort and labor necessary to build the system. === Confidence-Based === This approach differs from the other hybrid approaches in that in most cases only one translation technology is used. A confidence metric is produced for each translated sentence from which a decision can be made whether to try a secondary translation technology or to proceed with the initial translation output. SMT is also used when common error patterns such as multiple repeat words appear in sequence, as is common with NMT when the attention mechanism is confused.
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Boyfriend Maker

Boyfriend Maker was a dating sim, romance chatbot smartphone app for iOS (iPhone) and Android devices, developed by Japanese studio 36 You Games (styled as 36You) and distributed under the freemium business model. Boyfriend Maker incorporated advanced artificial intelligence chat technology a decade before products such as ChatGPT. According to the developer's website, Boyfriend Maker is an "app that lets you interact and chat with quirky virtual boyfriends". While each virtual boyfriend has certain unique characteristics, the various instances of the boyfriend are powered by a chat engine, that (at least within a language and market) can utilise vocabulary and knowledge acquired in a chat with one user in subsequent chats with other users. == Gameplay == Users gain experience points and in-game coins. Users can customize their virtual boyfriend's appearance by selecting items such as hair, clothing, face, and a necklace. == Apple delisting and reintroduction == In late November 2012, the original iOS Boyfriend Maker app was delisted from the Apple App Store due to "ribald" chat, according to the New York Times. Boyfriend Maker was removed by Apple due to "reports of references to violent sexual acts and pedophilia". Boyfriend Maker had an age rating of 4+, even though the chat bot "responds with often strange and explicit text unsuitable for young children". User-posted chat excerpts indicate that the virtual boyfriend would sometimes transition abruptly to sexual chat in response to a seemingly innocent question. In one user-posted example, in response to the question, "what kind of wedding cake will we have" the boyfriend responds, "a good sex ima be on top of u u gonna ride oon me bitin the pillow gurrl ima fuck da shit out of u". The developer's use of the SimSimi-created third-party chat engine may be responsible for the sexual text. As the virtual boyfriend converses with human users, the SimSimi chat engine acquires vocabulary from users of the game and applies this "learned" vocabulary in chats with other users. The chat engine might also employ lines harvested from human-human chat logs, song lyrics, movies or TV shows. In April 2013, a detuned and presumably tamer version of the app, titled Boyfriend Plus, was permitted on Apple's App Store.
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Cloud-based quantum computing

Cloud-based quantum computing refers to the remote access of quantum computing resources—such as quantum emulators, simulators, or processors—via the internet. Cloud access enables users to develop, test, and execute quantum algorithms without the need for direct interaction with specialized hardware, facilitating broader participation in quantum software development and experimentation. In 2016, IBM launched the IBM Quantum Experience, one of the first publicly accessible quantum processors connected to the cloud. In early 2017, researchers at Rigetti Computing demonstrated programmable quantum cloud access through their software platform Forest, which included the pyQuil Python library. Since the early-2020s, cloud-based quantum computing has grown significantly, with multiple providers offering access to a variety of quantum hardware modalities, including superconducting qubits, trapped ions, neutral atoms, and photonic systems. Major platforms such as Amazon Braket, Azure Quantum, and qBraid aggregate quantum devices from hardware developers like IonQ, Rigetti Computing, QuEra, Pasqal, Oxford Quantum Circuits, and IBM Quantum. These platforms provide unified interfaces for users to write and execute quantum algorithms across diverse backends, often supporting open-source SDKs such as Qiskit, Cirq, and PennyLane. The proliferation of cloud-based access has played a key role in accelerating quantum education, algorithm research, and early-stage application development by lowering the barrier to experimentation with real quantum hardware. Cloud-based quantum computing has expanded access to quantum hardware and tools beyond traditional research laboratories. These platforms support educational initiatives, algorithm development, and early-stage commercial applications. == Applications == Cloud-based quantum computing is used across education, research, and software development, offering remote access to quantum systems without the need for on-site infrastructure. === Education === Quantum cloud platforms have become valuable tools in education, allowing students and instructors to engage with real quantum processors through user-friendly interfaces. Educators use these platforms to teach foundational concepts in quantum mechanics and quantum computing, as well as to demonstrate and implement quantum algorithms in a classroom or laboratory setting. === Scientific Research === Cloud-based access to quantum hardware has enabled researchers to conduct experiments in quantum information, test quantum algorithms, and compare quantum hardware platforms. Experiments such as testing Bell's theorem or evaluating quantum teleportation protocols have been performed on publicly available quantum processors. === Software Development and Prototyping === Developers use cloud-based platforms to prototype quantum software applications across fields such as optimization, machine learning, and chemistry. These platforms offer SDKs and APIs that integrate classical and quantum workflows, enabling experimentation with quantum algorithms in real-world or simulated environments. === Public Engagement and Games === Quantum cloud tools have also been used to create educational games and interactive applications aimed at increasing public understanding of quantum concepts. These efforts help bridge the gap between theoretical content and intuitive learning. == Existing platforms == qBraid Lab by qBraid is a cloud-based platform for quantum computing. It provides software tools for researchers and developers in quantum, as well as access to quantum hardware. qBraid provides cloud based access to Microsoft Azure Quantum and Amazon Braket devices including IQM, QuEra, Pasqal, Rigetti, IonQ, QIR simulators, Amazon Braket simulators, and the NEC Vector Annealer, as of August 2025. qBraid's base version is free, where unlimited hardware and simulator access is available with the purchase of credits. Quandela Cloud by Quandela is the platform to access first cloud-accessible European photonic quantum computer. The computer is interfaced using the Perceval scripting language, with tutorials and documentation available online for free. Xanadu Quantum Cloud by Xanadu is a platform with cloud-based access to three fully programmable photonic quantum computers. Forest by Rigetti Computing is a tool suite for cloud-based quantum computing. It includes a programming language, development tools and example algorithms. LIQUi> by Microsoft is a software architecture and tool suite for quantum computing. It includes a programming language, example optimization and scheduling algorithms, and quantum simulators. Q#, a quantum programming language by Microsoft on the .NET Framework seen as a successor to LIQUi|>. IBM Quantum Platform by IBM, providing access to quantum hardware as well as HPC simulators. These can be accessed programmatically using the Python-based Qiskit framework, or via graphical interface with the IBM Q Experience GUI. Both are based on the OpenQASM standard for representing quantum operations. There is also a tutorial and online community. Quantum in the Cloud by The University of Bristol, which consists of a quantum simulator and a four qubit optical quantum system. Quantum Playground by Google is an educational resource which features a simulator with a simple interface, and a scripting language and 3D quantum state visualization. Quantum in the Cloud is an experimental quantum cloud platform for access to a four-qubit nuclear magnetic resonance-NMRCloudQ computer, managed by Tsinghua University. Quantum Inspire by Qutech is the first platform in Europe providing cloud-based quantum computing to two hardware chips. Next to a 5-qubit transmon processor, Quantum Inspire is the first platform in the world to provide online access to a fully programmable 2-qubit electron spin quantum processor. Amazon Braket is a cloud-based quantum computing platform hosted by AWS which, as of June 2025, provides access to quantum computers built by IonQ, Rigetti, IQM, and QuEra. Braket also provides a quantum algorithm development environment and simulator. Forge by QC Ware is a cloud-based quantum computing platform that provides access to D-Wave hardware, as well as Google and IBM simulators. The platform offers a 30-day free trial, including one minute of quantum computing time. Quantum-as-a-Service by Scaleway is a cloud-based platform created in 2022 to access to real quantum hardware from IQM Quantum Computers, Alpine Quantum Technologies, Quandela and Pasqal. It also include access to GPU-powered emulators such as Aer, Qsim and Quandela proprietary emulation.
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Natural Language Toolkit

The Natural Language Toolkit, or more commonly NLTK, is a suite of libraries and programs for symbolic and statistical natural language processing (NLP) for English written in the Python programming language. It supports classification, tokenization, stemming, tagging, parsing, and semantic reasoning functionalities. It was developed by Steven Bird and Edward Loper in the Department of Computer and Information Science at the University of Pennsylvania. NLTK includes graphical demonstrations and sample data. It is accompanied by a book that explains the underlying concepts behind the language processing tasks supported by the toolkit, plus a cookbook. NLTK is intended to support research and teaching in NLP or closely related areas, including empirical linguistics, cognitive science, artificial intelligence, information retrieval, and machine learning. NLTK has been used successfully as a teaching tool, as an individual study tool, and as a platform for prototyping and building research systems. == Library highlights == Discourse representation Lexical analysis: Word and text tokenizer n-gram and collocations Part-of-speech tagger Tree model and Text chunker for capturing Named-entity recognition
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Ernie Bot

Ernie Bot (Chinese: 文心一言, Pinyin: wénxīn yīyán), full name Enhanced Representation through Knowledge Integration, is an artificial intelligence chatbot developed by the Chinese technology company Baidu. Ernie Bot rivals GPT models in Chinese NLP tasks. It is built on the company's ERNIE series of large language models, which have been in development since 2019. The service was first launched for invited testing on March 16, 2023, and was released to the general public on August 31, 2023, after receiving approval from Chinese regulators. Since its public launch, Ernie Bot has undergone several updates, with newer versions like ERNIE 4.0 and 4.5 released to improve its capabilities. The service has seen rapid user adoption, reportedly reaching over 200 million users by April 2024. It has been integrated into various products, notably powering AI features for the Chinese release of Samsung's Galaxy S24 smartphones. As a product operating in China, Ernie Bot is subject to the country's censorship regulations. It has been observed to refuse answers to politically sensitive questions, such as those regarding CCP general secretary Xi Jinping, the 1989 Tiananmen Square protests and massacre, and other topics deemed taboo by the government. == History == Ernie Bot was initially released for invited testing on March 16, 2023. The live release demo was reported to have been prerecorded, which caused Baidu's stock to drop 10 percent on the day of the launch. The company's stock gained 14 percent the following day after analysts from Citigroup and Bank of America tested Ernie Bot and gave it positive preliminary reviews. On August 31, 2023, Ernie Bot was released to the public after receiving approval from Chinese regulatory authorities. By December 2023, Baidu announced the service had surpassed 100 million users. In January 2024, Hong Kong newspaper South China Morning Post reported that a university research lab linked to the People's Liberation Army (PLA) had tested Ernie Bot for military response scenarios. Baidu denied the allegations, stating it had no connection with the academic paper. That same month, Ernie was integrated into Samsung's Galaxy S24 lineup for its launch in China. The user base reportedly grew to 200 million by April 2024 and 300 million by June 2024. In September 2024, Baidu changed the chatbot's Chinese name from "Wenxin Yiyan" (文心一言) to "Wenxiaoyan" (文小言) to position it as a search assistant. On March 16, 2025, Baidu announced version 4.5 and the reasoning model ERNIE X1. The following month, at the Create2025 Baidu AI Developer Conference, the company released the Wenxin 4.5 Turbo and Wenxin X1 Turbo models, designed to be faster and less expensive to operate. == Development == Ernie Bot is based on Baidu's ERNIE (Enhanced Representation through Knowledge Integration) series of foundation models. The general training process begins with pre-training on large datasets, followed by refinement using techniques like supervised fine-tuning, reinforcement learning with human feedback, and prompt engineering. === Foundation models === ==== Ernie 3.0 ==== The model powering the initial launch of Ernie Bot. It was trained with 10 billion parameters on a 4-terabyte corpus consisting of plain text and a large-scale knowledge graph. ==== Ernie 3.5 ==== Released in June 2023. At the time of release, its performance was reported as "slightly inferior" to OpenAI's GPT-4. ==== Ernie 4.0 ==== Unveiled in October 2023 and released to paying subscribers in November. According to Baidu, this version featured improved performance over its predecessor, with information updated to April 2023. ==== Ernie X1 ==== Announced in March 2025, with Ernie X1 positioned as a specialized reasoning model. Baidu stated that performance improvements were achieved through new technologies such as "FlashMask" dynamic attention masking and a heterogeneous multimodal mixture-of-experts architecture. === Turbo Models === In June 2024, Baidu announced Ernie 4.0 Turbo. In April 2025, Ernie 4.5 Turbo and X1 Turbo were released. These models are optimized for faster response times and lower operational costs. == Service == In its subscription options, the professional plan gives users access to Ernie 4.0 with a payment either for a month or with reduced payment for auto-renewal per month. Meanwhile, Ernie 3.5 is free of charge. Ernie 4.0, the language model for Ernie bot, has information updated to April 2023. == Censorship == Ernie Bot is subject to the Chinese government's censorship regime. In public tests with journalists, Ernie Bot refused to answer questions about CCP general secretary Xi Jinping, the 1989 Tiananmen Square protests and massacre, the persecution of Uyghurs in China in Xinjiang, and the 2019–2020 Hong Kong protests. When queried about the origin of SARS-CoV-2, Ernie Bot stated that it originated among American vape users.
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ChatGPT

ChatGPT is a generative artificial intelligence chatbot developed by OpenAI. Originally released in November 2022, the product uses large language models—specifically generative pre-trained transformers (GPTs)—to generate text, speech, and images in response to user prompts. ChatGPT accelerated the AI boom, an ongoing period marked by rapid investment and public attention toward the field of artificial intelligence (AI). OpenAI operates the service on a freemium model. Users can interact with ChatGPT through text, audio, and image prompts. ChatGPT was quickly adopted, reaching 100 million monthly active users two months after its release and 900 million weekly active users in February 2026. It has been lauded for its potential to transform numerous professional fields, and has instigated public debate about the nature of creativity and the future of knowledge work. The chatbot has also been criticized for its limitations and potential for unethical use. It can generate plausible-sounding but incorrect or nonsensical answers, known as hallucinations. Biases in its training data have been reflected in its responses. The chatbot can facilitate academic dishonesty, generate misinformation, and create malicious code. The ethics of its development, particularly the use of copyrighted content as training data, have also drawn controversy. == Features == ChatGPT is a chatbot and AI assistant built on large language model (LLM) technology. It is designed to generate human-like text and can carry out a wide variety of tasks. These include, among many others, writing and debugging computer programs, composing music, scripts, fairy tales, and essays, answering questions (sometimes at a level exceeding that of an average human test-taker), and generating business concepts. ChatGPT is frequently used for translation and summarization tasks, and can simulate interactive environments such as a Linux terminal, a multi-user chat room, or simple text-based games such as tic-tac-toe. Users interact with ChatGPT through conversations which consist of text, audio, and image inputs and outputs. The user's inputs to these conversations are referred to as prompts. An optional "Memory" feature allows users to tell ChatGPT to memorize specific information. Another option allows ChatGPT to recall old conversations. GPT-based moderation classifiers are used to reduce the risk of harmful outputs being presented to users. In March 2023, OpenAI added support for plugins for ChatGPT. This includes both plugins made by OpenAI, such as web browsing and code interpretation, and external plugins from developers such as Expedia, OpenTable, and Zapier. From October to December 2024, ChatGPT Search was deployed. It allows ChatGPT to search the web in an attempt to make more accurate and up-to-date responses. It increased OpenAI's direct competition with major search engines. OpenAI allows businesses to tailor how their content appears in the ChatGPT Search results and influence what sources are used. In December 2024, OpenAI launched a new feature allowing users to call ChatGPT with a telephone for up to 15 minutes per month for free. In September 2025, OpenAI added a feature called Pulse, which generates a daily analysis of a user's chats and connected apps such as Gmail and Google Calendar. In October 2025, OpenAI launched ChatGPT Atlas, a browser integrating the ChatGPT assistant directly into web navigation, to compete with existing browsers such as Google Chrome. It has an additional feature called "agentic mode" that allows it to take online actions for the user. === Paid tier === ChatGPT was initially free to the public and remains free in a limited capacity. In February 2023, OpenAI launched a premium service, ChatGPT Plus, that costs US$20 per month. What was offered on the paid plan versus the free tier changed as OpenAI has continued to update ChatGPT, and a Pro tier at $200/mo was introduced in December 2024. The Pro launch coincided with the release of the o1 model. In August 2025, ChatGPT Go was offered in India for ₹399 per month. The plan has higher limits than the free version. === Mobile apps === In May-July 2023, OpenAI began offering ChatGPT iOS and Android apps. ChatGPT can also power Android's assistant. An app for Windows launched on the Microsoft Store on October 15, 2024. === Languages === OpenAI met Icelandic President Guðni Th. Jóhannesson in 2022. In 2023, OpenAI worked with a team of 40 Icelandic volunteers to fine-tune ChatGPT's Icelandic conversation skills as a part of Iceland's attempts to preserve the Icelandic language. ChatGPT (based on GPT-4) was better able to translate Japanese to English when compared to Bing, Bard, and DeepL Translator in 2023. In December 2023, the Albanian government decided to use ChatGPT for the rapid translation of European Union documents and the analysis of required changes needed for Albania's accession to the EU. Several studies have shown that ChatGPT can outperform Google Translate in some mainstream translation tasks. However, as of 2024, no machine translation services match human expert performance. In August 2024, a representative of the Asia Pacific wing of OpenAI made a visit to Taiwan, during which a demonstration of ChatGPT's Chinese abilities was made. ChatGPT's Mandarin Chinese abilities were lauded, but the ability of the AI to produce content in Mandarin Chinese in a Taiwanese accent was found to be "less than ideal" due to differences between mainland Mandarin Chinese and Taiwanese Mandarin. === GPT Store === In November 2023, OpenAI released GPT Builder, a tool allowing users to customize ChatGPT's behavior for a specific use case. The customized systems are referred to as GPTs. In January 2024, OpenAI launched the GPT Store, a marketplace for GPTs. At launch, OpenAI included more than 3 million GPTs created by GPT Builder users in the GPT Store. === ChatGPT Apps === In September 2025, OpenAI added support for Model Context Protocol (MCP) to ChatGPT apps. When enabled in developer mode, this allows for improved third-party access to ChatGPT tools and servers. === Deep Research === In February 2025, OpenAI released Deep Research, a feature that generates reports based on extensive web searches. It was initially based on the reasoning model o3 and took 5 to 30 minutes per report. === Images === In October 2023, OpenAI's image generation model DALL-E 3 was integrated into ChatGPT. The integration used ChatGPT to write prompts for DALL-E guided by conversations with users. In March 2025, OpenAI updated ChatGPT to generate images using GPT Image instead of DALL-E. One of the most significant improvements was in the generation of text within images, which is especially useful for branded content. However, this ability is noticeably worse in non-Latin alphabets. The model can also generate new images based on existing ones provided in the prompt. These images are generated with C2PA metadata, which can be used to verify that they are AI-generated. OpenAI has emplaced additional safeguards to prevent what the company deems to be harmful image generation. === Agents === In 2025, OpenAI added several features to make ChatGPT more agentic (capable of autonomously performing longer tasks). In January, Operator was released. It was capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other browser-based tasks. It was controlling a software environment inside a virtual machine with limited internet connectivity and with safety restrictions. It struggled with complex user interfaces. In May 2025, OpenAI introduced an agent for coding named Codex. It is capable of writing software, answering codebase questions, running tests, and proposing pull requests. It is based on a fine-tuned version of OpenAI o3. It has two versions, one running in a virtual machine in the cloud, and one where the agent runs in the cloud, but performs actions on a local machine connected via API. In July 2025, OpenAI released ChatGPT agent, an AI agent that can perform multi-step tasks. Like Operator, it controls a virtual computer. It also inherits from Deep Research's ability to gather and summarize significant volumes of information. The user can interrupt tasks or provide additional instructions as needed. In September 2025, OpenAI partnered with Stripe, Inc. to release Agentic Commerce Protocol, enabling purchases through ChatGPT. At launch, the feature was limited to purchases on Etsy from US users with a payment method linked to their OpenAI account. OpenAI takes an undisclosed cut from the merchant's payment. === ChatGPT Health === On January 7, 2026, OpenAI introduced a feature called "ChatGPT Health", whereby ChatGPT can discuss the user's health in a way that is separate from other chats. The feature is not available for users in the United Kingdom, Switzerland, or the European Economic Area, and is available on a waitli
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CapCut

CapCut, known domestically as JianYing (Chinese: 剪映; pinyin: Jiǎnyìng) and formerly internationally as ViaMaker, is a video editor developed by ByteDance, available as a mobile app, desktop app, and web app. == History == The app was first released in China in 2019 and was initially available for iPhone and Android. In 2020, it was rebranded in English from ViaMaker to CapCut and became available globally. It later expanded to include web and desktop versions for Mac and Windows. In 2022, CapCut reached 200 million active users. According to The Wall Street Journal, in March 2023, it was the second-most downloaded app in the U.S., behind that of Chinese discount retailer Temu. In January 2025, CapCut had over 1 billion downloads on the Google Play Store. On February 1, 2021, CapCut Pro for Windows was launched. On November 27, the Pro version for Mac was launched. In July 2025, CapCut Pro for HarmonyOS was available on HarmonyOS NEXT tablets. In July 2024, CapCut was reported by the South China Morning Post to be a generative AI (GenAI) application that led global AI app downloads, with approximately 38.42 million downloads and 323 million monthly active users. == Features == CapCut supports basic video editing functions, including editing, trimming, and adding or splitting clips. Editing projects is limited to single-layer editing, but the app supports overlay options that enable additional effects, including multi-layer editing. The app includes a library of pre-made templates and a tool that generates editable video captions. It also provides photo editing tools, including retouch and product photo features integrated within the editing interface. CapCut's video editor includes AI-based features such as video and script generation. Users can export or save completed projects directly to different social media platforms. CapCut includes a free version and a paid Pro version with cloud storage and advanced features. == Controversies == === Illegal data collection === In July 2023, many users of CapCut accused it of illegally profiting off their personal data. A class-action lawsuit filed in the U.S. District Court for the Northern District of Illinois on July 28, 2023, alleged that CapCut illegally harvests and profits from user data including biometric information and geolocation without consent. In September 2025, a federal court excluded most of the lawsuit, which alleged that TikTok’s parent company improperly scraped private data from CapCut's video editing software, as lacking grounds, with some of the class action continuing to move forward. == Bans and restrictions == === Ban in India === As a response to border clashes with China in May 2020, the Indian government banned around 56 Chinese applications including CapCut and TikTok, which is owned by CapCut's parent company ByteDance. Indian users were unable to use and download the application. As of February 2022, around 273 Chinese applications have been banned by the Indian government under the concern of national security and Indian user privacy. === Ban in the United States === On January 18, 2025, at 10 PM EST, CapCut was banned in the United States along with TikTok and all other ByteDance apps due to the implementation of the Protecting Americans from Foreign Adversary Controlled Applications Act. Hours after the suspension of services took effect, President Donald Trump indicated on Truth Social that he would issue an executive order on the day of his inauguration "to extend the period of time before the law's prohibitions take effect". On January 21, CapCut began restoring service. On February 13, Google and Apple restored CapCut on the App Store and Google Play Store.
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Scale space

Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures. The parameter t {\displaystyle t} in this family is referred to as the scale parameter, with the interpretation that image structures of spatial size smaller than about t {\displaystyle {\sqrt {t}}} have largely been smoothed away in the scale-space level at scale t {\displaystyle t} . The main type of scale space is the linear (Gaussian) scale space, which has wide applicability as well as the attractive property of being possible to derive from a small set of scale-space axioms. The corresponding scale-space framework encompasses a theory for Gaussian derivative operators, which can be used as a basis for expressing a large class of visual operations for computerized systems that process visual information. This framework also allows visual operations to be made scale invariant, which is necessary for dealing with the size variations that may occur in image data, because real-world objects may be of different sizes and in addition the distance between the object and the camera may be unknown and may vary depending on the circumstances. == Definition == The notion of scale space applies to signals of arbitrary numbers of variables. The most common case in the literature applies to two-dimensional images, which is what is presented here. Consider a given image f {\displaystyle f} where f ( x , y ) {\displaystyle f(x,y)} is the greyscale value of the pixel at position ( x , y ) {\displaystyle (x,y)} . The linear (Gaussian) scale-space representation of f {\displaystyle f} is a family of derived signals L ( x , y ; t ) {\displaystyle L(x,y;t)} defined by the convolution of f ( x , y ) {\displaystyle f(x,y)} with the two-dimensional Gaussian kernel g ( x , y ; t ) = 1 2 π t e − ( x 2 + y 2 ) / 2 t {\displaystyle g(x,y;t)={\frac {1}{2\pi t}}e^{-(x^{2}+y^{2})/2t}\,} such that L ( ⋅ , ⋅ ; t ) = g ( ⋅ , ⋅ ; t ) ∗ f ( ⋅ , ⋅ ) , {\displaystyle L(\cdot ,\cdot ;t)\ =g(\cdot ,\cdot ;t)f(\cdot ,\cdot ),} where the semicolon in the argument of L {\displaystyle L} implies that the convolution is performed only over the variables x , y {\displaystyle x,y} , while the scale parameter t {\displaystyle t} after the semicolon just indicates which scale level is being defined. This definition of L {\displaystyle L} works for a continuum of scales t ≥ 0 {\displaystyle t\geq 0} , but typically only a finite discrete set of levels in the scale-space representation would be actually considered. The scale parameter t = σ 2 {\displaystyle t=\sigma ^{2}} is the variance of the Gaussian filter and as a limit for t = 0 {\displaystyle t=0} the filter g {\displaystyle g} becomes an impulse function such that L ( x , y ; 0 ) = f ( x , y ) , {\displaystyle L(x,y;0)=f(x,y),} that is, the scale-space representation at scale level t = 0 {\displaystyle t=0} is the image f {\displaystyle f} itself. As t {\displaystyle t} increases, L {\displaystyle L} is the result of smoothing f {\displaystyle f} with a larger and larger filter, thereby removing more and more of the details that the image contains. Since the standard deviation of the filter is σ = t {\displaystyle \sigma ={\sqrt {t}}} , details that are significantly smaller than this value are to a large extent removed from the image at scale parameter t {\displaystyle t} , see the following figures and for graphical illustrations. === Why a Gaussian filter? === When faced with the task of generating a multi-scale representation one may ask: could any filter g of low-pass type and with a parameter t which determines its width be used to generate a scale space? The answer is no, as it is of crucial importance that the smoothing filter does not introduce new spurious structures at coarse scales that do not correspond to simplifications of corresponding structures at finer scales. In the scale-space literature, a number of different ways have been expressed to formulate this criterion in precise mathematical terms. The conclusion from several different axiomatic derivations that have been presented is that the Gaussian scale space constitutes the canonical way to generate a linear scale space, based on the essential requirement that new structures must not be created when going from a fine scale to any coarser scale. Conditions, referred to as scale-space axioms, that have been used for deriving the uniqueness of the Gaussian kernel include linearity, shift invariance, semi-group structure, non-enhancement of local extrema, scale invariance and rotational invariance. In the works, the uniqueness claimed in the arguments based on scale invariance has been criticized, and alternative self-similar scale-space kernels have been proposed. The Gaussian kernel is, however, a unique choice according to the scale-space axiomatics based on causality or non-enhancement of local extrema. === Alternative definition === Equivalently, the scale-space family can be defined as the solution of the diffusion equation (for example in terms of the heat equation), ∂ t L = 1 2 ∇ 2 L , {\displaystyle \partial _{t}L={\frac {1}{2}}\nabla ^{2}L,} with initial condition L ( x , y ; 0 ) = f ( x , y ) {\displaystyle L(x,y;0)=f(x,y)} . This formulation of the scale-space representation L means that it is possible to interpret the intensity values of the image f as a "temperature distribution" in the image plane and that the process that generates the scale-space representation as a function of t corresponds to heat diffusion in the image plane over time t (assuming the thermal conductivity of the material equal to the arbitrarily chosen constant ⁠1/2⁠). Although this connection may appear superficial for a reader not familiar with differential equations, it is indeed the case that the main scale-space formulation in terms of non-enhancement of local extrema is expressed in terms of a sign condition on partial derivatives in the 2+1-D volume generated by the scale space, thus within the framework of partial differential equations. Furthermore, a detailed analysis of the discrete case shows that the diffusion equation provides a unifying link between continuous and discrete scale spaces, which also generalizes to nonlinear scale spaces, for example, using anisotropic diffusion. Hence, one may say that the primary way to generate a scale space is by the diffusion equation, and that the Gaussian kernel arises as the Green's function of this specific partial differential equation. == Motivations == The motivation for generating a scale-space representation of a given data set originates from the basic observation that real-world objects are composed of different structures at different scales. This implies that real-world objects, in contrast to idealized mathematical entities such as points or lines, may appear in different ways depending on the scale of observation. For example, the concept of a "tree" is appropriate at the scale of meters, while concepts such as leaves and molecules are more appropriate at finer scales. For a computer vision system analysing an unknown scene, there is no way to know a priori what scales are appropriate for describing the interesting structures in the image data. Hence, the only reasonable approach is to consider descriptions at multiple scales in order to be able to capture the unknown scale variations that may occur. Taken to the limit, a scale-space representation considers representations at all scales. Another motivation to the scale-space concept originates from the process of performing a physical measurement on real-world data. In order to extract any information from a measurement process, one has to apply operators of non-infinitesimal size to the data. In many branches of computer science and applied mathematics, the size of the measurement operator is disregarded in the theoretical modelling of a problem. The scale-space theory on the other hand explicitly incorporates the need for a non-infinitesimal size of the image operators as an integral part of any measurement as well as any other operation that depends on a real-world measurement. There is a close link between scale-space theory and biological vision. Many scale-space operations show a high degree of similarity with receptive field profiles recorded from the mammalian retina and the first stages in the visual cortex. In these respects, the scale-space framework can be seen as a theoretically well-founded paradigm for early vision, which in addition has been thoroughly tested by algorithms and experiments. == Gaussian derivatives == At any scale in scale space, we c
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Intrinsic dimension

In mathematics, the intrinsic dimension of a subset can be thought of as the minimal number of variables needed to represent the subset. The concept has widespread applications in geometry, dynamical systems, signal processing, statistics, and other fields. Due to its widespread applications and vague conceptualization, there are many different ways to define it rigorously. Consequently, the same set might have different intrinsic dimensions according to different definitions. The intrinsic dimension can be used as a lower bound of what dimension it is possible to compress a data set into through dimension reduction, but it can also be used as a measure of the complexity of the data set or signal. For a data set or signal of N variables, its intrinsic dimension M satisfies 0 ≤ M ≤ N, although estimators may yield higher values. == Exact dimension == === Differential === In differential geometry, given a differentiable manifold N and a submanifold M, the intrinsic dimension of M is its dimension. Suppose N has n dimensions and M has m dimensions, then that means around any point in M, there exists a local coordinate system ( x 1 , … , x m , x m + 1 , … , x n ) {\displaystyle (x_{1},\dots ,x_{m},x_{m+1},\dots ,x_{n})} of N, such that the manifold M is simply the subset of N defined by x m + 1 = 0 , … , x n = 0 {\displaystyle x_{m+1}=0,\dots ,x_{n}=0} . === Metric === Given a mere metric space, we can still define its intrinsic dimension. The most general case is the Hausdorff dimension, though for metric spaces occurring in practice, the box-counting dimension and the packing dimension often are identical to the Hausdorff dimension. Let X , d {\textstyle X,d} be a metric space and A ⊂ X {\textstyle A\subset X} be totally bounded. Define the covering number N ( A , ε ) = min { k : A ⊂ ⋃ i = 1 k B ( x i , ε ) } . {\displaystyle N(A,\varepsilon )=\min \left\{k:A\subset \bigcup _{i=1}^{k}B\left(x_{i},\varepsilon \right)\right\}.} The metric entropy is H ( A , ε ) = log ⁡ N ( A , ε ) {\textstyle H(A,\varepsilon )=\log N(A,\varepsilon )} (any log base). The upper and lower metric entropy dimensions are dim ¯ E A = lim sup ε ↓ 0 H ( A , ε ) log ⁡ ( 1 / ε ) , dim _ E A = lim inf ε ↓ 0 H ( A , ε ) log ⁡ ( 1 / ε ) . {\displaystyle {\overline {\dim }}_{E}A=\limsup _{\varepsilon \downarrow 0}{\frac {H(A,\varepsilon )}{\log(1/\varepsilon )}},\quad {\underline {\dim }}_{E}A=\liminf _{\varepsilon \downarrow 0}{\frac {H(A,\varepsilon )}{\log(1/\varepsilon )}}.} If they are equal, then dim E ⁡ A {\textstyle \operatorname {dim} _{E}A} is that common value, called the metric entropy dimension. The entropy dimensions are usually used in information theory, and especially coding theory, since entropy is involved in its definition. === Topological === If X {\displaystyle X} is merely a topological space, then we can still define its intrinsic dimension, using the topological dimension or Lebesgue covering dimension. An open cover of a topological space X is a family of open sets Uα such that their union is the whole space, ∪ α {\displaystyle \cup _{\alpha }} Uα = X. The order or ply of an open cover A {\displaystyle {\mathfrak {A}}} = {Uα} is the smallest number m (if it exists) for which each point of the space belongs to at most m open sets in the cover: in other words Uα1 ∩ ⋅⋅⋅ ∩ Uαm+1 = ∅ {\displaystyle \emptyset } for α1, ..., αm+1 distinct. A refinement of an open cover A {\displaystyle {\mathfrak {A}}} = {Uα} is another open cover B {\displaystyle {\mathfrak {B}}} = {Vβ}, such that each Vβ is contained in some Uα. The covering dimension of a topological space X is defined to be the minimum value of n such that every finite open cover A {\displaystyle {\mathfrak {A}}} of X has an open refinement B {\displaystyle {\mathfrak {B}}} with order n + 1. The refinement B {\displaystyle {\mathfrak {B}}} can always be chosen to be finite. Thus, if n is finite, Vβ1 ∩ ⋅⋅⋅ ∩ Vβn+2 = ∅ {\displaystyle \emptyset } for β1, ..., βn+2 distinct. If no such minimal n exists, the space is said to have infinite covering dimension. == Introductory example == Let f ( x 1 , x 2 ) {\textstyle f(x_{1},x_{2})} be a two-variable function (or signal) which is of the form f ( x 1 , x 2 ) = g ( x 1 ) {\textstyle f(x_{1},x_{2})=g(x_{1})} for some one-variable function g which is not constant. This means that f varies, in accordance to g, with the first variable or along the first coordinate. On the other hand, f is constant with respect to the second variable or along the second coordinate. It is only necessary to know the value of one, namely the first, variable in order to determine the value of f. Hence, it is a two-variable function but its intrinsic dimension is one. A slightly more complicated example is f ( x 1 , x 2 ) = g ( x 1 + x 2 ) {\textstyle f(x_{1},x_{2})=g(x_{1}+x_{2})} . f is still intrinsic one-dimensional, which can be seen by making a variable transformation y 1 = x 1 + x 2 {\textstyle y_{1}=x_{1}+x_{2}} and y 2 = x 1 − x 2 {\textstyle y_{2}=x_{1}-x_{2}} which gives f ( y 1 + y 2 2 , y 1 − y 2 2 ) = g ( y 1 ) {\textstyle f\left({\frac {y_{1}+y_{2}}{2}},{\frac {y_{1}-y_{2}}{2}}\right)=g\left(y_{1}\right)} . Since the variation in f can be described by the single variable y1 its intrinsic dimension is one. For the case that f is constant, its intrinsic dimension is zero since no variable is needed to describe variation. For the general case, when the intrinsic dimension of the two-variable function f is neither zero or one, it is two. In the literature, functions which are of intrinsic dimension zero, one, or two are sometimes referred to as i0D, i1D or i2D, respectively. == Signal processing == In signal processing of multidimensional signals, the intrinsic dimension of the signal describes how many variables are needed to generate a good approximation of the signal. For an N-variable function f, the set of variables can be represented as an N-dimensional vector x: f = f ( x ) where x = ( x 1 , … , x N ) {\textstyle f=f\left(\mathbf {x} \right){\text{ where }}\mathbf {x} =\left(x_{1},\dots ,x_{N}\right)} . If for some M-variable function g and M × N matrix A it is the case that for all x; f ( x ) = g ( A x ) , {\textstyle f(\mathbf {x} )=g(\mathbf {Ax} ),} M is the smallest number for which the above relation between f and g can be found, then the intrinsic dimension of f is M. The intrinsic dimension is a characterization of f, it is not an unambiguous characterization of g nor of A. That is, if the above relation is satisfied for some f, g, and A, it must also be satisfied for the same f and g′ and A′ given by g ′ ( y ) = g ( B y ) {\textstyle g'\left(\mathbf {y} \right)=g\left(\mathbf {By} \right)} and A ′ = B − 1 A {\textstyle \mathbf {A'} =\mathbf {B} ^{-1}\mathbf {A} } where B is a non-singular M × M matrix, since f ( x ) = g ′ ( A ′ x ) = g ( B A ′ x ) = g ( A x ) {\textstyle f\left(\mathbf {x} \right)=g'\left(\mathbf {A'x} \right)=g\left(\mathbf {BA'x} \right)=g\left(\mathbf {Ax} \right)} . == The Fourier transform of signals of low intrinsic dimension == An N variable function which has intrinsic dimension M < N has a characteristic Fourier transform. Intuitively, since this type of function is constant along one or several dimensions its Fourier transform must appear like an impulse (the Fourier transform of a constant) along the same dimension in the frequency domain. === A simple example === Let f be a two-variable function which is i1D. This means that there exists a normalized vector n ∈ R 2 {\textstyle \mathbf {n} \in \mathbb {R} ^{2}} and a one-variable function g such that f ( x ) = g ( n T x ) {\textstyle f(\mathbf {x} )=g(\mathbf {n} ^{\operatorname {T} }\mathbf {x} )} for all x ∈ R 2 {\textstyle \mathbf {x} \in \mathbb {R} ^{2}} . If F is the Fourier transform of f (both are two-variable functions) it must be the case that F ( u ) = G ( n T u ) ⋅ δ ( m T u ) {\textstyle F\left(\mathbf {u} \right)=G\left(\mathbf {n} ^{\mathrm {T} }\mathbf {u} \right)\cdot \delta \left(\mathbf {m} ^{\mathrm {T} }\mathbf {u} \right)} . Here G is the Fourier transform of g (both are one-variable functions), δ is the Dirac impulse function and m is a normalized vector in R 2 {\textstyle \mathbb {R} ^{2}} perpendicular to n. This means that F vanishes everywhere except on a line which passes through the origin of the frequency domain and is parallel to m. Along this line F varies according to G. === The general case === Let f be an N-variable function which has intrinsic dimension M, that is, there exists an M-variable function g and M × N matrix A such that f ( x ) = g ( A x ) ∀ x {\textstyle f(\mathbf {x} )=g(\mathbf {Ax} )\quad \forall \mathbf {x} } . Its Fourier transform F can then be described as follows: F vanishes everywhere except for a subspace of dimension M The subspace M is spanned by the rows of the matrix A In the subspace, F varies according to G the Fourier transform of g == Generalizations == The type of intrinsic dimension described above assume
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