In combinatorics and computational learning theory, a witness set is a set of elements that distinguishes a given Boolean function from a given class of other Boolean functions. Let C {\displaystyle C} be a concept class over a domain X {\displaystyle X} (that is, a family of Boolean functions over X {\displaystyle X} ) and c {\displaystyle c} be a concept in X {\displaystyle X} (a single Boolean function). A subset S {\displaystyle S} of X {\displaystyle X} is a witness set for c {\displaystyle c} in X {\displaystyle X} if S {\displaystyle S} distinguishes c {\displaystyle c} from all the other functions in C {\displaystyle C} , in the sense that no other function in C {\displaystyle C} has the same values on S {\displaystyle S} . For a concept class with | C | {\displaystyle |C|} concepts, there exists a concept that has a witness of size at most log 2 | C | {\displaystyle \log _{2}|C|} ; this bound is tight when C {\displaystyle C} consists of all Boolean functions over X {\displaystyle X} . By a result of Bondy (1972) there exists a single witness set of size at most | C | − 1 {\displaystyle |C|-1} that is valid for all concepts in C {\displaystyle C} ; this bound is tight when C {\displaystyle C} consists of the indicator functions of the empty set and some singleton sets. One way to construct this set is to interpret the concepts as bitstrings, and the domain elements as positions in these bitstrings. Then the set of positions at which a trie of the bitstrings branches forms the desired witness set. This construction is central to the operation of the fusion tree data structure. The minimum size of a witness set for c {\displaystyle c} is called the witness size or specification number and is denoted by w C ( c ) {\displaystyle w_{C}(c)} . The value max { w C ( c ) : c ∈ C } {\displaystyle \max\{w_{C}(c):c\in C\}} is called the teaching dimension of C {\displaystyle C} . It represents the number of examples of a concept that need to be presented by a teacher to a learner, in the worst case, to enable the learner to determine which concept is being presented. Witness sets have also been called teaching sets, keys, specifying sets, or discriminants. The "witness set" terminology is from Kushilevitz et al. (1996), who trace the concept of witness sets to work by Cover (1965).
Paprika (app)
Paprika is an app and website that helps users organize recipes, produce meal plans, and create grocery lists. The app is available for Android, iOS, macOS, and Windows devices. == Overview == The app allows users to import recipes from various sources, including websites and other apps. The app also allows users to automatically generate meal plans, which are also customizable, in order to achieve specific objectives such as weight loss, muscle gain, adherence to various dietary preferences, or personal taste. The app is also capable of generating grocery lists based on the daily or weekly meal plans chosen by the user. All the recipes, menus, and grocery lists of each user are accessible from smartphones, tablets, and computers. The app is part of a broader category of mobile apps focused on meal planning, recipe management, and shopping list automation, which have grown in popularity with the expansion of smartphone usage and digital cooking tools. == History == Paprika Recipe Manager for iPad version 1.0 was initially released in September 2010 by Hindsight LLC. Paprika 2.0 was released for iPhone and iPad in November 2013, and Paprika 3.0 was released for iOS and macOS in November 2017. == Reception == Paprika has been featured in technology and lifestyle publications as a recipe management and meal planning application. Coverage has noted features such as importing recipes from websites, ingredient scaling, and cross-platform synchronization. The app has also appeared in lists of cooking and meal planning tools published by outlets including The Verge and The Kitchn.
Quantum Artificial Intelligence Lab
The Quantum Artificial Intelligence Lab (also called the Quantum AI Lab or QuAIL) is a joint initiative of NASA, Universities Space Research Association, and Google (specifically, Google Research) whose goal is to pioneer research on how quantum computing might help with machine learning and other difficult computer science problems. The lab is hosted at NASA's Ames Research Center. == History == The Quantum AI Lab was announced by Google Research in a blog post on May 16, 2013. At the time of launch, the Lab was using the most advanced commercially available quantum computer, D-Wave Two from D-Wave Systems. On October 10, 2013, Google released a short film describing the current state of the Quantum AI Lab. On October 18, 2013, Google announced that it had incorporated quantum physics into Minecraft. In January 2014, Google reported results comparing the performance of the D-Wave Two in the lab with that of classical computers. The results were ambiguous and provoked heated discussion on the Internet. On 2 September 2014, it was announced that the Google Quantum AI Lab, in partnership with UC Santa Barbara, would be launching an initiative to create quantum information processors based on superconducting electronics. On the 23rd of October 2019, the Quantum AI Lab announced in a paper that it had achieved quantum supremacy with their Sycamore processor. The claim of quantum supremacy achievement has since been debated, with a far more accurate simulation on a classical computer being possible in 2.5 days as a conservative estimate. == Present == On December 9, 2024, Google introduced the Willow processor, describing it as a "state-of-the-art quantum chip". Google claims that this new chip takes just five minutes to solve a problem that takes traditional supercomputers ten septillion years. However, experts say Willow is, for now, a largely experimental device.
Oracle Database
Oracle AI Database (commonly referred to as Oracle Database, Oracle DBMS, Oracle Autonomous Database, or simply as Oracle) is a proprietary multi-model database management system produced and marketed by Oracle Corporation. It is a database commonly used for running online transaction processing (OLTP), data warehousing (DW) and mixed (OLTP & DW) database workloads. Oracle AI Database uses SQL for database updating and retrieval. Oracle Database runs on-premises, on Oracle engineered systems such as Oracle Exadata, on Oracle Cloud Infrastructure, and as a managed Autonomous Database service. It is also offered inside Microsoft Azure, Google Cloud, and Amazon Web Services data centers through Oracle's multicloud offerings. The current long-term support release, Oracle AI Database 26ai, became available in the cloud and on Oracle engineered systems in October 2025 and on-premises for Linux x86-64 in January 2026. == History == Larry Ellison and his two friends and former co-workers, Bob Miner and Ed Oates, started a consultancy called Software Development Laboratories (SDL) in 1977, later Oracle Corporation. SDL developed the original version of the Oracle software. The name Oracle comes from the code-name of a Central Intelligence Agency-funded project Ellison had worked on while formerly employed by Ampex; the CIA was Oracle's first customer, and allowed the company to use the code name for the new product. Ellison wanted his database to be compatible with IBM System R, but that company's Don Chamberlin declined to release its error codes. By 1985 Oracle advertised, however, that "Programs written for SQL/DS or DB2 will run unmodified" on the many non-IBM mainframes, minicomputers, and microcomputers its database supported "Because all versions of ORACLE are identical". Later releases introduced capabilities associated with successive eras of the product, including PL/SQL stored procedures and triggers in Oracle7 (1992), Real Application Clusters in Oracle9i (2001), grid infrastructure and automatic management in Oracle 10g (2003), the multitenant architecture and In-Memory Column Store in Oracle Database 12c (2013), and AI Vector Search and JSON Relational Duality in Oracle Database 23ai (2024). In October 2025 Oracle rebranded the 23ai line as Oracle AI Database 26ai. (see Release History) == Architecture == An Oracle Database system consists of an instance and a database. The instance is a set of memory structures and background processes; the database is the set of files that store data. The instance exists only in memory, and a single instance is associated with one multitenant container database. The principal memory structures are the System Global Area, which is shared, and the Program Global Areas, which are private to individual processes. The shared pool, database buffer cache, and redo log buffer are components of the System Global Area, and the optional In-Memory Column Store also resides there. Background processes operate on the database files and use these memory structures; they include the database writer, the log writer, the checkpoint process, and the system and process monitor processes. Server processes handle connections from client programs and run their SQL statements. Storage is organized logically and physically. Logically, data is held in tablespaces composed of segments, extents, and data blocks. Physically, the database comprises datafiles, control files, and online redo log files, with archived redo logs supporting media recovery. == High Availability and Scalability == Oracle Database includes several technologies for high availability, disaster recovery, and scale. Oracle Real Application Clusters allows multiple instances on separate servers to access one shared database concurrently; it was introduced with Oracle9i in 2001. Oracle Data Guard maintains standby databases synchronized with a primary database, and Active Data Guard additionally allows read-only workloads on a standby while it applies changes. Oracle GoldenGate performs logical replication and data integration across heterogeneous systems. Native sharding, introduced in Oracle Database 12c Release 2, distributes one logical database across independent shards. Oracle Exadata is an engineered system that pairs database servers with storage servers and offloads operations such as filtering to the storage tier; it is available on-premises, in Oracle Cloud Infrastructure, and through Cloud@Customer. == Notable Features == AI Vector Search adds a vector data type, vector indexes, and vector distance operators to the database. These allow similarity search over machine-learning embeddings to be expressed in SQL and combined with queries over relational, JSON, spatial, and graph data. It became generally available in Oracle Database 23ai. JSON Relational Duality exposes the same data both as relational tables and as JSON documents through duality views, so that an application can read and write either representation of the data. It became generally available in Oracle Database 23ai. In-Memory Column Store maintains a column-oriented copy of selected tables in memory in addition to the row-oriented format, and the optimizer can use the columnar copy for analytic queries. It was introduced in Oracle Database 12c Release 1.Partitioning divides large tables and indexes into independently managed pieces. Advanced Compression and Hybrid Columnar Compression are compression features for transactional and warehouse data respectively. == Data Types == Oracle AI Database supports a variety of data types and data models within a single system. These include traditional relational data types as well as semi-structured, unstructured, and specialized data formats, enabling different types of data to be stored and queried together. == Releases and versions == Oracle products follow a custom release-numbering and -naming convention. The "ai" in the current release, Oracle AI Database 26ai, stands for "Artificial Intelligence". Previous releases (e.g. Oracle Database 19c, 10g, and Oracle9i Database) have used suffixes of "c", "g", and "i" which stand for "Cloud", "Grid", and "Internet" respectively. Prior to the release of Oracle8i Database, no suffixes featured in Oracle AI Database naming conventions. There was no v1 of Oracle AI Database, as Ellison "knew no one would want to buy version 1". For some database releases, Oracle also provides an Express Edition (XE) that is free to use. Oracle AI Database release numbering has used the following codes: The Introduction to Oracle AI Database includes a brief history on some of the key innovations introduced with each major release of Oracle AI Database. See My Oracle Support (MOS) note Release Schedule of Current Database Releases (Doc ID 742060.1) for the current Oracle AI Database releases and their patching end dates. == Patch updates and security alerts == Prior to Oracle Database 18c, Oracle Corporation released Critical Patch Updates (CPUs) and Security Patch Updates (SPUs) and Security Alerts to close security vulnerabilities. These releases are issued quarterly; some of these releases have updates issued prior to the next quarterly release. Starting with Oracle Database 18c, Oracle Corporation releases Release Updates (RUs) and Release Update Revisions (RURs). RUs usually contain security, regression (bug), optimizer, and functional fixes which may include feature extensions as well. RURs include all fixes from their corresponding RU but only add new security and regression fixes. However, no new optimizer or functional fixes are included. == Competition == In the market for relational databases, Oracle AI Database competes against commercial products such as IBM Db2 and Microsoft SQL Server. Oracle and IBM tend to battle for the mid-range database market on Unix and Linux platforms, while Microsoft dominates the mid-range database market on Microsoft Windows platforms. However, since they share many of the same customers, Oracle and IBM tend to support each other's products in many middleware and application categories (for example: WebSphere, PeopleSoft, and Siebel Systems CRM), and IBM's hardware divisions work closely with Oracle on performance-optimizing server-technologies (for example, Linux on IBM Z). Niche commercial competitors include Teradata (in data warehousing and business intelligence), Software AG's ADABAS, Sybase, and IBM's Informix, among many others. In the cloud, Oracle AI Database competes against the database services of AWS, Microsoft Azure, and Google Cloud Platform. Increasingly, the Oracle AI Database products compete against open-source software relational and non-relational database systems such as PostgreSQL, MongoDB, Couchbase, Neo4j, ArangoDB and others. Oracle acquired Innobase, supplier of the InnoDB codebase to MySQL, in part to compete better against open source alternatives, and acquired Sun Microsystems, owner of MySQL, in 2010. Database products licensed as open
WordNet
WordNet is a lexical database of semantic relations between words that links words into semantic relations including synonyms, hyponyms, and meronyms. The synonyms are grouped into synsets with short definitions and usage examples. It can thus be seen as a combination and extension of a dictionary and thesaurus. Its primary use is in automatic text analysis and artificial intelligence applications. It was first created in the English language and the English WordNet database and software tools have been released under a BSD style license and are freely available for download. The latest official release from Princeton was released in 2011. Princeton currently has no plans to release any new versions due to staffing and funding issues. New versions are still being released annually through the Open English WordNet website. Until about 2024 an online version was previously available through wordnet.princeton.edu. That version of WordNet has been deprecated, but a new online version is available at en-word.net. There are now WordNets in more than 200 languages. == History and team members == WordNet was first created in 1985, in English only, in the Cognitive Science Laboratory of Princeton University under the direction of psychology professor George Armitage Miller. It was later directed by Christiane Fellbaum. The project was initially funded by the U.S. Office of Naval Research, and later also by other U.S. government agencies including the DARPA, the National Science Foundation, the Disruptive Technology Office (formerly the Advanced Research and Development Activity) and REFLEX. George Miller and Christiane Fellbaum received the 2006 Antonio Zampolli Prize for their work with WordNet. The Global WordNet Association is a non-commercial organization that provides a platform for discussing, sharing and connecting WordNets for all languages in the world. Christiane Fellbaum and Piek Th.J.M. Vossen are its co-presidents. == Database contents == The database contains 155,327 words organized in 175,979 synsets for a total of 207,016 word-sense pairs; in compressed form, it is about 12 megabytes in size. It includes the lexical categories nouns, verbs, adjectives and adverbs but ignores prepositions, determiners and other function words. Words from the same lexical category that are roughly synonymous are grouped into synsets, which include simplex words as well as collocations like "eat out" and "car pool." The different senses of a polysemous word form are assigned to different synsets. A synset's meaning is further clarified with a short defining gloss and one or more usage examples. An example adjective synset is: good, right, ripe – (most suitable or right for a particular purpose; "a good time to plant tomatoes"; "the right time to act"; "the time is ripe for great sociological changes") All synsets are connected by means of semantic relations. These relations, which are not all shared by all lexical categories, include: Nouns hypernym: Y is a hypernym of X if every X is a (kind of) Y (canine is a hypernym of dog) hyponym: Y is a hyponym of X if every Y is a (kind of) X (dog is a hyponym of canine) coordinate term: Y is a coordinate term of X if X and Y share a hypernym (wolf is a coordinate term of dog, and dog is a coordinate term of wolf) holonym: Y is a holonym of X if X is a part of Y (building is a holonym of window) meronym: Y is a meronym of X if Y is a part of X (window is a meronym of building) Verbs hypernym: the verb Y is a hypernym of the verb X if the activity X is a (kind of) Y (to perceive is an hypernym of to listen) troponym: the verb Y is a troponym of the verb X if the activity Y is doing X in some manner (to lisp is a troponym of to talk) entailment: the verb Y is entailed by the verb X if by doing X you must be doing Y (to sleep is entailed by to snore) coordinate term: the verb Y is a coordinate term of the verb X if X and Y share a hypernym (to lisp is a coordinate term of to yell, and to yell is a coordinate term of to lisp) These semantic relations hold among all members of the linked synsets. Individual synset members (words) can also be connected with lexical relations. For example, (one sense of) the noun "director" is linked to (one sense of) the verb "direct" from which it is derived via a "morphosemantic" link. The morphology functions of the software distributed with the database try to deduce the lemma or stem form of a word from the user's input. Irregular forms are stored in a list, and looking up "ate" will return "eat," for example. == Knowledge structure == Both nouns and verbs are organized into hierarchies, defined by hypernym or IS A relationships. For instance, one sense of the word dog is found following hypernym hierarchy; the words at the same level represent synset members. Each set of synonyms has a unique index. At the top level, these hierarchies are organized into 25 beginner "trees" for nouns and 15 for verbs (called lexicographic files at a maintenance level). All are linked to a unique beginner synset, "entity". Noun hierarchies are far deeper than verb hierarchies. Adjectives are not organized into hierarchical trees. Instead, two "central" antonyms such as "hot" and "cold" form binary poles, while 'satellite' synonyms such as "steaming" and "chilly" connect to their respective poles via a "similarity" relations. The adjectives can be visualized in this way as "dumbbells" rather than as "trees". == Psycholinguistic aspects == The initial goal of the WordNet project was to build a lexical database that would be consistent with theories of human semantic memory developed in the late 1960s. Psychological experiments indicated that speakers organized their knowledge of concepts in an economic, hierarchical fashion. Retrieval time required to access conceptual knowledge seemed to be directly related to the number of hierarchies the speaker needed to "traverse" to access the knowledge. Thus, speakers could more quickly verify that canaries can sing because a canary is a songbird, but required slightly more time to verify that canaries can fly (where they had to access the concept "bird" on the superordinate level) and even more time to verify canaries have skin (requiring look-up across multiple levels of hyponymy, up to "animal"). While such psycholinguistic experiments and the underlying theories have been subject to criticism, some of WordNet's organization is consistent with experimental evidence. For example, anomic aphasia selectively affects speakers' ability to produce words from a specific semantic category, a WordNet hierarchy. Antonymous adjectives (WordNet's central adjectives in the dumbbell structure) are found to co-occur far more frequently than chance, a fact that has been found to hold for many languages. == As a lexical ontology == WordNet is sometimes called an ontology, a persistent claim that its creators do not make. The hypernym/hyponym relationships among the noun synsets can be interpreted as specialization relations among conceptual categories. In other words, WordNet can be interpreted and used as a lexical ontology in the computer science sense. However, such an ontology should be corrected before being used, because it contains hundreds of basic semantic inconsistencies; for example there are, (i) common specializations for exclusive categories and (ii) redundancies in the specialization hierarchy. Furthermore, transforming WordNet into a lexical ontology usable for knowledge representation should normally also involve (i) distinguishing the specialization relations into subtypeOf and instanceOf relations, and (ii) associating intuitive unique identifiers to each category. Although such corrections and transformations have been performed and documented as part of the integration of WordNet 1.7 into the cooperatively updatable knowledge base of WebKB-2, most projects claiming to reuse WordNet for knowledge-based applications (typically, knowledge-oriented information retrieval) simply reuse it directly. WordNet has also been converted to a formal specification, by means of a hybrid bottom-up top-down methodology to automatically extract association relations from it and interpret these associations in terms of a set of conceptual relations, formally defined in the DOLCE foundational ontology. In most works that claim to have integrated WordNet into ontologies, the content of WordNet has not simply been corrected when it seemed necessary; instead, it has been heavily reinterpreted and updated whenever suitable. This was the case when, for example, the top-level ontology of WordNet was restructured according to the OntoClean-based approach, or when it was used as a primary source for constructing the lower classes of the SENSUS ontology. == Limitations == The most widely discussed limitation of WordNet (and related resources like ImageNet) is that some of the semantic relations are more suited to concrete concepts than to abstract concepts. For example,
Rule induction
Rule induction is an area of machine learning in which formal rules are extracted from a set of observations. The rules extracted may represent a full scientific model of the data, or merely represent local patterns in the data. Data mining in general and rule induction in detail are trying to create algorithms without human programming but with analyzing existing data structures. In the easiest case, a rule is expressed with “if-then statements” and was created with the ID3 algorithm for decision tree learning. Rule learning algorithm are taking training data as input and creating rules by partitioning the table with cluster analysis. A possible alternative over the ID3 algorithm is genetic programming which evolves a program until it fits to the data. Creating different algorithm and testing them with input data can be realized in the WEKA software. Additional tools are machine learning libraries for Python, like scikit-learn. == Paradigms == Some major rule induction paradigms are: Association rule learning algorithms (e.g., Agrawal) Decision rule algorithms (e.g., Quinlan 1987) Hypothesis testing algorithms (e.g., RULEX) Horn clause induction Version spaces Rough set rules Inductive Logic Programming Boolean decomposition (Feldman) == Algorithms == Some rule induction algorithms are: Charade Rulex Progol CN2
Automatic1111
AUTOMATIC1111 Stable Diffusion Web UI (SD WebUI, A1111, or Automatic1111) is an open source generative artificial intelligence program that allows users to generate images from a text prompt. It uses Stable Diffusion as the base model for its image capabilities together with a large set of extensions and features to customize its output. == History == SD WebUI was released on GitHub on August 22, 2022, by AUTOMATIC1111, 1 month after the initial release of Stable Diffusion. At the time, Stable Diffusion could only be run via the command line. SD WebUI quickly rose in popularity and has been described as "the most popular tool for running diffusion models locally." SD WebUI is one of the most popular user interfaces for Stable Diffusion, together with ComfyUI. In February 2024, a book was published by ja:Gijutsu Hyoronsha on using Stable Diffusion with SD WebUI in Japanese. As of July 2024, the project had 136,000 stars on GitHub. == Features == SD WebUI uses Gradio for its user interface. Each parameter in the Stable Diffusion program is exposed via a UI interface within SD WebUI. SD WebUI contains additional parameters not included in Stable Diffusion itself, such as support for Low-rank adaptations, ControlNet and custom variational autoencoders. SD WebUI supports prompt weighting, image-to-image based generation, inpainting, outpainting and image scaling. It supports over 20 samplers including DDIM, Euler, Euler a, DPM++ 2M Karras, and UniPC. It is also used for its various optimizations over the base Stable Diffusion. == Stable Diffusion WebUI Forge == Stable Diffusion WebUI Forge (Forge) is a notable fork of SD WebUI started by Lvmin Zhang, who is also the creator of ControlNet and Fooocus. The initial goal of Forge was to improve the performance and features of SD WebUI with the intention to upstream changes back to SD WebUI. One of Forge's optimizations allowed users with low VRAM to generate images faster on some versions of Stable Diffusion. It improved generation speed for users with 8GB and 6GB VRAM by 30-45% and 60-75%, respectively. Forge also includes extra features such as support for more samplers than standard SD WebUI. Some of Forge's optimizations were borrowed from ComfyUI, and others were developed by the Forge team. In August 2024, Forge added support for the Flux diffusion model developed by Black Forest Labs, which is not yet supported by SD WebUI.