In computer graphics, tessellation is the dividing of datasets of polygons (sometimes called vertex sets) presenting objects in a scene into suitable structures for rendering. Especially for real-time rendering, data is tessellated into triangles, for example in OpenGL 4.0 and Direct3D 11. == In graphics rendering == A key advantage of tessellation for realtime graphics is that it allows detail to be dynamically added and subtracted from a 3D polygon mesh and its silhouette edges based on control parameters (often camera distance). In previously leading realtime techniques such as parallax mapping and bump mapping, surface details could be simulated at the pixel level, but silhouette edge detail was fundamentally limited by the quality of the original dataset. In Direct3D 11 pipeline (a part of DirectX 11), the graphics primitive is the patch. The tessellator generates a triangle-based tessellation of the patch according to tessellation parameters such as the TessFactor, which controls the degree of fineness of the mesh. The tessellation, along with shaders such as a Phong shader, allows for producing smoother surfaces than would be generated by the original mesh. By offloading the tessellation process onto the GPU hardware, smoothing can be performed in real time. Tessellation can also be used for implementing subdivision surfaces, level of detail scaling and fine displacement mapping. OpenGL 4.0 uses a similar pipeline, where tessellation into triangles is controlled by the Tessellation Control Shader and a set of four tessellation parameters. == In computer-aided design == In computer-aided design the constructed design is represented by a boundary representation topological model, where analytical 3D surfaces and curves, limited to faces, edges, and vertices, constitute a continuous boundary of a 3D body. Arbitrary 3D bodies are often too complicated to analyze directly. So they are approximated (tessellated) with a mesh of small, easy-to-analyze pieces of 3D volume—usually either irregular tetrahedra, or irregular hexahedra. The mesh is used for finite element analysis. The mesh of a surface is usually generated per individual faces and edges (approximated to polylines) so that original limit vertices are included into mesh. To ensure that approximation of the original surface suits the needs of further processing, three basic parameters are usually defined for the surface mesh generator: The maximum allowed distance between the planar approximation polygon and the surface (known as "sag"). This parameter ensures that mesh is similar enough to the original analytical surface (or the polyline is similar to the original curve). The maximum allowed size of the approximation polygon (for triangulations it can be maximum allowed length of triangle sides). This parameter ensures enough detail for further analysis. The maximum allowed angle between two adjacent approximation polygons (on the same face). This parameter ensures that even very small humps or hollows that can have significant effect to analysis will not disappear in mesh. An algorithm generating a mesh is typically controlled by the above three and other parameters. Some types of computer analysis of a constructed design require an adaptive mesh refinement, which is a mesh made finer (using stronger parameters) in regions where the analysis needs more detail.
Rule-based machine translation
Rule-based machine translation (RBMT) is a classical approach of machine translation systems based on linguistic information about source and target languages. Such information is retrieved from (unilingual, bilingual or multilingual) dictionaries and grammars covering the main semantic, morphological, and syntactic regularities of each language. Having input sentences, an RBMT system generates output sentences on the basis of analysis of both the source and the target languages involved. RBMT has been progressively superseded by more efficient methods, particularly neural machine translation. == History == The first RBMT systems were developed in the early 1970s. The most important steps of this evolution were the emergence of the following RBMT systems: Systran Japanese MT systems Today, other common RBMT systems include: Apertium GramTrans == Types of RBMT == There are three different types of rule-based machine translation systems: Direct Systems (Dictionary Based Machine Translation) map input to output with basic rules. Transfer RBMT Systems (Transfer Based Machine Translation) employ morphological and syntactical analysis. Interlingual RBMT Systems (Interlingua) use an abstract meaning. RBMT systems can also be characterized as the systems opposite to Example-based Systems of Machine Translation (Example Based Machine Translation), whereas Hybrid Machine Translations Systems make use of many principles derived from RBMT. == Basic principles == The main approach of RBMT systems is based on linking the structure of the given input sentence with the structure of the demanded output sentence, necessarily preserving their unique meaning. The following example can illustrate the general frame of RBMT: A girl eats an apple. Source Language = English; Demanded Target Language = German Minimally, to get a German translation of this English sentence one needs: A dictionary that will map each English word to an appropriate German word. Rules representing regular English sentence structure. Rules representing regular German sentence structure. And finally, we need rules according to which one can relate these two structures together. Accordingly, we can state the following stages of translation: 1st: getting basic part-of-speech information of each source word: a = indef.article; girl = noun; eats = verb; an = indef.article; apple = noun 2nd: getting syntactic information about the verb "to eat": NP-eat-NP; here: eat – Present Simple, 3rd Person Singular, Active Voice 3rd: parsing the source sentence: (NP an apple) = the object of eat Often only partial parsing is sufficient to get to the syntactic structure of the source sentence and to map it onto the structure of the target sentence. 4th: translate English words into German a (category = indef.article) => ein (category = indef.article) girl (category = noun) => Mädchen (category = noun) eat (category = verb) => essen (category = verb) an (category = indef. article) => ein (category = indef.article) apple (category = noun) => Apfel (category = noun) 5th: Mapping dictionary entries into appropriate inflected forms (final generation): A girl eats an apple. => Ein Mädchen isst einen Apfel. == Ontologies == An ontology is a formal representation of knowledge that includes the concepts (such as objects, processes etc.) in a domain and some relations between them. If the stored information is of linguistic nature, one can speak of a lexicon. In NLP, ontologies can be used as a source of knowledge for machine translation systems. With access to a large knowledge base, rule-based systems can be enabled to resolve many (especially lexical) ambiguities on their own. In the following classic examples, as humans, we are able to interpret the prepositional phrase according to the context because we use our world knowledge, stored in our lexicons:I saw a man/star/molecule with a microscope/telescope/binoculars.Since the syntax does not change, a traditional rule-based machine translation system may not be able to differentiate between the meanings. With a large enough ontology as a source of knowledge however, the possible interpretations of ambiguous words in a specific context can be reduced. === Building ontologies === The ontology generated for the PANGLOSS knowledge-based machine translation system in 1993 may serve as an example of how an ontology for NLP purposes can be compiled: A large-scale ontology is necessary to help parsing in the active modules of the machine translation system. In the PANGLOSS example, about 50,000 nodes were intended to be subsumed under the smaller, manually-built upper (abstract) region of the ontology. Because of its size, it had to be created automatically. The goal was to merge the two resources LDOCE online and WordNet to combine the benefits of both: concise definitions from Longman, and semantic relations allowing for semi-automatic taxonomization to the ontology from WordNet. A definition match algorithm was created to automatically merge the correct meanings of ambiguous words between the two online resources, based on the words that the definitions of those meanings have in common in LDOCE and WordNet. Using a similarity matrix, the algorithm delivered matches between meanings including a confidence factor. This algorithm alone, however, did not match all meanings correctly on its own. A second hierarchy match algorithm was therefore created which uses the taxonomic hierarchies found in WordNet (deep hierarchies) and partially in LDOCE (flat hierarchies). This works by first matching unambiguous meanings, then limiting the search space to only the respective ancestors and descendants of those matched meanings. Thus, the algorithm matched locally unambiguous meanings (for instance, while the word seal as such is ambiguous, there is only one meaning of seal in the animal subhierarchy). Both algorithms complemented each other and helped constructing a large-scale ontology for the machine translation system. The WordNet hierarchies, coupled with the matching definitions of LDOCE, were subordinated to the ontology's upper region. As a result, the PANGLOSS MT system was able to make use of this knowledge base, mainly in its generation element. == Components == The RBMT system contains: a SL morphological analyser - analyses a source language word and provides the morphological information; a SL parser - is a syntax analyser which analyses source language sentences; a translator - used to translate a source language word into the target language; a TL morphological generator - works as a generator of appropriate target language words for the given grammatica information; a TL parser - works as a composer of suitable target language sentences; Several dictionaries - more specifically a minimum of three dictionaries: a SL dictionary - needed by the source language morphological analyser for morphological analysis, a bilingual dictionary - used by the translator to translate source language words into target language words, a TL dictionary - needed by the target language morphological generator to generate target language words. The RBMT system makes use of the following: a Source Grammar for the input language which builds syntactic constructions from input sentences; a Source Lexicon which captures all of the allowable vocabulary in the domain; Source Mapping Rules which indicate how syntactic heads and grammatical functions in the source language are mapped onto domain concepts and semantic roles in the interlingua; a Domain Model/Ontology which defines the classes of domain concepts and restricts the fillers of semantic roles for each class; Target Mapping Rules which indicate how domain concepts and semantic roles in the interlingua are mapped onto syntactic heads and grammatical functions in the target language; a Target Lexicon which contains appropriate target lexemes for each domain concept; a Target Grammar for the target language which realizes target syntactic constructions as linearized output sentences. == Advantages == No bilingual texts are required. This makes it possible to create translation systems for languages that have no texts in common, or even no digitized data whatsoever. Domain independent. Rules are usually written in a domain independent manner, so the vast majority of rules will "just work" in every domain, and only a few specific cases per domain may need rules written for them. No quality ceiling. Every error can be corrected with a targeted rule, even if the trigger case is extremely rare. This is in contrast to statistical systems where infrequent forms will be washed away by default. Total control. Because all rules are hand-written, you can easily debug a rule-based system to see exactly where a given error enters the system, and why. Reusability. Because RBMT systems are generally built from a strong source language analysis that is fed to a transfer step and target language generator, the source language analysis and targe
Allen's interval algebra
Allen's interval algebra is a calculus for temporal reasoning that was introduced by James F. Allen in 1983. The calculus defines possible relations between time intervals and provides a composition table that can be used as a basis for reasoning about temporal descriptions of events. == Formal description == === Relations === The following 13 base relations capture the possible relations between two intervals. To see that the 13 relations are exhaustive, note that each point of X {\displaystyle X} can be at 5 possible locations relative to Y {\displaystyle Y} : before, at the start, within, at the end, after. These give 5 + 4 + 3 + 2 + 1 = 15 {\displaystyle 5+4+3+2+1=15} possible relative positions for the start and the end of X {\displaystyle X} . Of these, we cannot have X 0 = X 1 = Y 0 {\displaystyle X_{0}=X_{1}=Y_{0}} since X 0 < X 1 {\displaystyle X_{0} Comet is an AI-powered web browser based on Chromium. It was released by Perplexity AI for Microsoft Windows and macOS on July 9, 2025, for Android on November 20, 2025, and for iOS on March 18, 2026. Initial access to the browser was limited to users subscribed to Perplexity's most expensive tier, with broader availability expected over time. The browser was released for free download in October 2025. == Features == Comet is integrated with Perplexity's AI-assisted search engine. The browser features an assistant which enables users to perform a variety of tasks such as generating article summaries, sending emails, or buying products. == Security concerns == Researchers at LayerX Security identified a malicious attack vector which they call CometJacking. The exploit could possibly exfiltrate a user's personal sensitive data to a remote server controlled by the attacker. LayerX attempted to responsibly disclose their findings to Comet's developer Perplexity AI in August 2025. Perplexity responded that they saw no security impact and marked the disclosure as not applicable. Tractable is a technology company specializing in the development of Artificial Intelligence (AI) to assess damage to property and vehicles. The AI allows users to appraise damage digitally. == Technology == Tractable's technology uses computer vision and deep learning to automate the appraisal of visual damage in accident and disaster recovery, for example to a vehicle. Drivers can be directed to use the application by their insurer after an accident, with the aim of settling their claim more quickly. The AI evaluates the damage from images, and therefore doesn't assess what isn't visible (such as, for example, interior damage to a vehicle or property). == History == Alexandre Dalyac and Razvan Ranca founded Tractable in 2014, and Adrien Cohen joined as co-founder in 2015. The company employs more than 300 staff members, largely in the United Kingdom. Tractable was named one of the 100 leading AI companies in the world in 2020 and 2021 by CB Insights. It won the Best Technology Award in the 2020 British Insurance Awards. In June 2021, Tractable announced a venture round that valued the company at $1 billion. Tractable was the UK's 100th billion-dollar tech company, or unicorn. In July 2023, the company received a $65 million investment from SoftBank Group, through its Vision Fund 2. LTX is a family of open source artificial intelligence video foundation models developed by Lightricks, and first released in November 2024. The latest models, LTX-2, create videos based on user prompts. They were preceded by LTX Video, which was released in 2024 as the company's first text-to-video model. LTX-2 is part of the LTX family of video generation models, which form the core technology, alongside LTX Studio, of the LTX ecosystem. == History == === Origins: LTX Video (2024–2025) === In November 2024 Lightricks publicly released its first text-to-video model, LTX Video. It was a 2-billion parameter model, available as open source. In May 2025 Lightricks launched LTXV-13b, a version with 13-billion parameters. Two months later, the model broke the 60 second barrier for generated video. === Release of LTX-2 (2025) === In October 2025 Lightricks announced its latest model, and renamed it LTX-2. The model was described as capable of generating synchronized audio and video at native 4K resolution and up to 50 frames per second (fps), using a variety of conditions and prompts, including text-to-video and image-to-video. Google highlighted the fact that LTX-2 was trained on its infrastructure, and saying it was "The first open source AI video generation model, powered by Google Cloud". Upon its release it was ranked in the top-3 models for image-to-video creation by Artificial Analysis, behind Kling 3.5 by Kling AI and Veo 3.1 by Google. Its text-to-image option was ranked 7th. In addition to its open-source release, Lightricks offers API access to LTX-2, allowing developers to generate videos from text and image prompts through a hosted service without running the model locally. === Open Source Release (2026) === In January 2026, Lightricks officially released the full open-source version of LTX-2, making the model’s complete codebase, weights, and associated tooling publicly available. In March 2026 the company released LTX-2.3, which was accompanied by a desktop video editor enabling the entire model to run locally on consumer hardware. == Technical features == === Advancements over LTX Video === LTX-2 builds upon the LTX Video architecture with several major improvements: Unified audio-video generation producing synchronized dialogue, ambience, and motion Native 4K rendering 50-fps output for cinematic motion Three operational modes (Fast, Pro, Ultra) More efficient diffusion pipelines enabling high fidelity on consumer GPUs === Core capabilities === Text-to-video generation Image-to-video generation Multimodal audiovisual synthesis High-resolution spatial and temporal coherence Configurable quality/performance settings Open-source distribution of weights and datasets == Reception == Initial reception to LTX-2 was broadly positive, with several technology and media outlets highlighting its open-source approach and multimodal capabilities. Open Source For You described LTX-2 as “one of the first AI video systems to combine 4K output, synchronized audio, and an open model release,” noting that it positioned Lightricks as a significant competitor to proprietary systems such as OpenAI's Sora and Google's Veo. IEA Green said that the model “could rewrite the AI filmmaking game,” emphasizing that its 50-fps rendering and unified audio-video generation made it suitable for professional studios and independent creators alike. AI News characterized LTX-2 as a “major step forward in the democratization of cinematic-quality video generation,” praising its consumer-grade hardware efficiency and multi-tier generation modes, while also noting ongoing challenges in long-form temporal stability. FinancialContent reported strong interest among creative agencies, attributing the attention to Lightricks’ decision to release model weights and datasets, which reviewers said enabled “a level of transparency not typically seen in commercial AI video models.” === Benchmarks and rankings === Upon release, LTX-2 ranked third for image-to-video creation in the Artificial Analysis benchmark, behind Kling 3.5 and Veo 3.1, while its text-to-video option ranked seventh. As of early 2026, it was the highest-ranked open-source model in the benchmark. === Limitations === Some early reviewers also pointed out quality limitations. The Ray3 technical review noted occasional inconsistencies in lip-sync and motion tracking during long scenes, though it stated these were “in line with the challenges faced by all current AI video diffusion models” and expected to improve with continued iteration. Like other diffusion-based video generators, LTX-2 can produce artifacts in complex multi-person scenes and may struggle with precise text rendering within generated video. The Unified Modeling Language (UML) is a general-purpose, object-oriented, visual modeling language that provides a way to visualize the architecture and design of a system, similar to the function of a blueprint. UML defines notation for many types of diagrams which focus on aspects such as behavior, interaction, and structure. UML is both a formal metamodel and a collection of graphical templates. The metamodel defines the elements in an object-oriented model such as classes and properties. It is essentially the same thing as the metamodel in object-oriented programming (OOP), however for OOP, the metamodel is primarily used at run time to dynamically inspect and modify an application object model. The UML metamodel provides a mathematical, formal foundation for the graphic views used in the modeling language to describe an emerging system. UML was created in an attempt to define a standard language for object-oriented programming at the OOPSLA '95 Conference. Originally, Grady Booch and James Rumbaugh merged their models into a unified model. This was followed by Booch's company Rational Software purchasing Ivar Jacobson's Objectory company and merging their model into the UML. At the time Rational and Objectory were two of the dominant players in the small world of independent vendors of object-oriented tools and methods. The Object Management Group (OMG) then took ownership of UML. The creation of UML was motivated by the desire to standardize the disparate nature of notational systems and approaches to software design at the time. In 1997, UML was adopted as a standard by the Object Management Group (OMG) and has been managed by this organization ever since. In 2005, UML was also published by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC) as the ISO/IEC 19501 standard. Since then the standard has been periodically revised to cover the latest revision of UML. Most developers do not use UML per se, but instead produce more informal diagrams, often hand-drawn. These diagrams, however, often include elements from UML. == Use == UML is primarily used for software development (in any industry or domain) but also used outside elsewhere including business processes, system functions, database schemas, workflow in the legal systems, medical electronics, Health care systems, and hardware design.. The UML is used by the OMG itself to define other OMG products such as the Unified Architecture Framework (UAF) and the Systems Modelling Language (SysML) v1. UML is designed for use with many object-oriented software development methods, both today and for the methods when it was first developed – including OMT, Booch method, Objectory, and especially RUP, which it was originally intended to be used with when work began at Rational Software. Although originally intended for object-oriented design documentation, UML has been used effectively in other contexts such as modeling business process. As UML is not inherently linked to a particular programming language, it can be used for modeling a system independent of language. Some UML tools generate source code from a UML model. === Elements === UML diagrams support visualizing system aspects like: Use case diagram for specifying user interactions with systems Class diagram for specifying structures, including data structures Activity diagram for specifying business process workflows Component diagram for specifying how components interface with other components Deployment diagram for specifying how components are deployed and executed on computational nodes In addition to syntactical (notational) elements with well-defined semantics, UML diagrams also allow for free-form comments (notes) that explain aspects such as usage, constraints, and intents. === Sharing === UML models can be exchanged among UML tools via the XML Metadata Interchange (XMI) format. === Cardinality notation === As with database Chen, Bachman, and ISO ER diagrams, class models are specified to use "look-across" cardinalities, even though several authors (Merise, Elmasri & Navathe, amongst others) prefer same-side or "look-here" for roles and both minimum and maximum cardinalities. Recent researchers (Feinerer and Dullea et al.) have shown that the "look-across" technique used by UML and ER diagrams is less effective and less coherent when applied to n-ary relationships of order strictly greater than 2. Feinerer says: "Problems arise if we operate under the look-across semantics as used for UML associations. Hartmann investigates this situation and shows how and why different transformations fail.", and: "As we will see on the next few pages, the look-across interpretation introduces several difficulties which prevent the extension of simple mechanisms from binary to n-ary associations." === Artifacts === An artifact is the "specification of a physical piece of information that is used or produced by a software development process, or by deployment and operation of a system" including models, source code, scripts, executables, tables in database systems, development deliverables, a design documents, and email messages. An artifact is the physical entity that is deployed to a node. Other UML elements such as classes and components are first manifest into artifacts and instances of these artifacts are then deployed. Artifacts can be composed of other artifacts. === Metamodeling === The OMG developed a metamodeling architecture to define UML, called the Meta-Object Facility (MOF). MOF is designed as a four-layered architecture, as shown in the image at right. It provides a meta-meta model at the top, called the M3 layer. This M3-model is the language used by Meta-Object Facility to build metamodels, called M2-models. The most prominent example of a Layer 2 Meta-Object Facility model is the UML metamodel, which describes UML itself. These M2-models describe elements of the M1-layer, and thus M1-models. These would be, for example, models written in UML. The last layer is the M0-layer or data layer. It is used to describe runtime instances of the system. The metamodel can be extended using a mechanism called stereotyping. This has been criticized as being insufficient/untenable by Brian Henderson-Sellers and Cesar Gonzalez-Perez in "Uses and Abuses of the Stereotype Mechanism in UML 1.x and 2.0". == Diagrams == UML 2 defines many types of diagrams – shown as a taxonomy in the image. === Structure diagrams === Structure diagrams emphasize the structure of the system – using objects, classifiers, relationships, attributes and operations. They are used to document software architecture. Class diagram – Describes the structure of a class Component diagram – Describes how a software system is split into components and dependencies between the components Composite structure diagram Deployment diagram Object diagram Package diagram Profile diagram === Behavior diagrams === Behavior diagrams emphasize the behavior of a system by showing collaborations among objects and changes to the internal states of objects. They are used to describe the functionality of a system. Activity diagram – Describes the business and operational activities of components State machine diagram Use case diagram – Depicts of a user's interaction with a system === Interaction diagrams === Interaction diagrams, a subset of behavior diagrams, emphasize the flow of control and data between components of a system. Communication diagram – shows communication between components Interaction overview diagram Sequence diagram – shows interactions arranged in time sequence; can be drawn via tools such as Lucidchart and Draw.io Timing diagram – focuses on timing constraints === Examples === == Adoption == In 2013, UML had been marketed by OMG for many contexts, but aimed primarily at software development with limited success. It has been treated, at times, as a design silver bullet, which leads to problems. UML misuse includes overuse (designing every part of the system with it, which is unnecessary) and assuming that novices can design with it. It is considered a large language, with many constructs. Some people (including Jacobson) feel that UML's size hinders learning and therefore uptake. Visual Studio removed support for UML in 2016 due to lack of use. == History == UML has evolved since the second half of the 1990s and has its roots in the object-oriented programming methods developed in the late 1980s and early 1990s. The image shows a timeline of the history of UML and other object-oriented modeling methods and notation. === Origin === Rational Software hired James Rumbaugh from General Electric in 1994 and after that, the company became the source for two of the most popular object-oriented modeling approaches of the day: Rumbaugh's object-modeling technique (OMT) and Grady Booch's method. They were soon assisted in their efforts by Ivar Jacobson, the creator of the object-oriented software engineeriComet (browser)
Tractable (company)
LTX (text-to-video model)
Unified Modeling Language