AI Assistant Quest 3

AI Assistant Quest 3 — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Autonomic networking

Autonomic networking follows the concept of Autonomic Computing, an initiative started by IBM in 2001. Its ultimate aim is to create self-managing networks to overcome the rapidly growing complexity of the Internet and other networks and to enable their further growth, far beyond the size of today. == Increasing size and complexity == The ever-growing management complexity of the Internet caused by its rapid growth is seen by some experts as a major problem that limits its usability in the future. What's more, increasingly popular smartphones, PDAs, networked audio and video equipment, and game consoles need to be interconnected. Pervasive Computing not only adds features, but also burdens existing networking infrastructure with more and more tasks that sooner or later will not be manageable by human intervention alone. Another important aspect is the price of manually controlling huge numbers of vitally important devices of current network infrastructures. == Autonomic nervous system == The autonomic nervous system (ANS) is the part of complex biological nervous systems that is not consciously controlled. It regulates bodily functions and the activity of specific organs. As proposed by IBM, future communication systems might be designed in a similar way to the ANS. == Components of autonomic networking == As autonomics conceptually derives from biological entities such as the human autonomic nervous system, each of the areas can be metaphorically related to functional and structural aspects of a living being. In the human body, the autonomic system facilitates and regulates a variety of functions including respiration, blood pressure and circulation, and emotive response. The autonomic nervous system is the interconnecting fabric that supports feedback loops between internal states and various sources by which internal and external conditions are monitored. === Autognostics === Autognostics includes a range of self-discovery, awareness, and analysis capabilities that provide the autonomic system with a view on high-level state. In metaphor, this represents the perceptual sub-systems that gather, analyze, and report on internal and external states and conditions – for example, this might be viewed as the eyes, visual cortex and perceptual organs of the system. Autognostics, or literally "self-knowledge", provides the autonomic system with a basis for response and validation. A rich autognostic capability may include many different "perceptual senses". For example, the human body gathers information via the usual five senses, the so-called sixth sense of proprioception (sense of body position and orientation), and through emotive states that represent the gross wellness of the body. As conditions and states change, they are detected by the sensory monitors and provide the basis for adaptation of related systems. Implicit in such a system are imbedded models of both internal and external environments such that relative value can be assigned to any perceived state - perceived physical threat (e.g. a snake) can result in rapid shallow breathing related to fight-flight response, a phylogenetically effective model of interaction with recognizable threats. In the case of autonomic networking, the state of the network may be defined by inputs from: individual network elements such as switches and network interfaces including specification and configuration historical records and current state traffic flows end-hosts application performance data logical diagrams and design specifications Most of these sources represent relatively raw and unprocessed views that have limited relevance. Post-processing and various forms of analysis must be applied to generate meaningful measurements and assessments against which current state can be derived. The autognostic system interoperates with: configuration management - to control network elements and interfaces policy management - to define performance objectives and constraints autodefense - to identify attacks and accommodate the impact of defensive responses === Configuration management === Configuration management is responsible for the interaction with network elements and interfaces. It includes an accounting capability with historical perspective that provides for the tracking of configurations over time, with respect to various circumstances. In the biological metaphor, these are the hands and, to some degree, the memory of the autonomic system. On a network, remediation and provisioning are applied via configuration setting of specific devices. Implementation affecting access and selective performance with respect to role and relationship are also applied. Almost all the "actions" that are currently taken by human engineers fall under this area. With only a few exceptions, interfaces are set by hand, or by extension of the hand, through automated scripts. Implicit in the configuration process is the maintenance of a dynamic population of devices under management, a historical record of changes and the directives which invoked change. Typical to many accounting functions, configuration management should be capable of operating on devices and then rolling back changes to recover previous configurations. Where change may lead to unrecoverable states, the sub-system should be able to qualify the consequences of changes prior to issuing them. As directives for change must originate from other sub-systems, the shared language for such directives must be abstracted from the details of the devices involved. The configuration management sub-system must be able to translate unambiguously between directives and hard actions or to be able to signal the need for further detail on a directive. An inferential capacity may be appropriate to support sufficient flexibility (i.e. configuration never takes place because there is no unique one-to-one mapping between directive and configuration settings). Where standards are not sufficient, a learning capacity may also be required to acquire new knowledge of devices and their configuration. Configuration management interoperates with all of the other sub-systems including: autognostics - receives direction for and validation of changes policy management - implements policy models through mapping to underlying resources security - applies access and authorization constraints for particular policy targets autodefense - receives direction for changes === Policy management === Policy management includes policy specification, deployment, reasoning over policies, updating and maintaining policies, and enforcement. Policy-based management is required for: constraining different kinds of behavior including security, privacy, resource access, and collaboration configuration management describing business processes and defining performance defining role and relationship, and establishing trust and reputation It provides the models of environment and behavior that represent effective interaction according to specific goals. In the human nervous system metaphor, these models are implicit in the evolutionary "design" of biological entities and specific to the goals of survival and procreation. Definition of what constitutes a policy is necessary to consider what is involved in managing it. A relatively flexible and abstract framework of values, relationships, roles, interactions, resources, and other components of the network environment is required. This sub-system extends far beyond the physical network to the applications in use and the processes and end-users that employ the network to achieve specific goals. It must express the relative values of various resources, outcomes, and processes and include a basis for assessing states and conditions. Unless embodied in some system outside the autonomic network or implicit to the specific policy implementation, the framework must also accommodate the definition of process, objectives and goals. Business process definitions and descriptions are then an integral part of the policy implementation. Further, as policy management represents the ultimate basis for the operation of the autonomic system, it must be able to report on its operation with respect to the details of its implementation. The policy management sub-system interoperates (at least) indirectly with all other sub-systems but primarily interacts with: autognostics - providing the definition of performance and accepting reports on conditions configuration management - providing constraints on device configuration security - providing definitions of roles, access and permissions === Autodefense === Autodefense represents a dynamic and adaptive mechanism that responds to malicious and intentional attacks on the network infrastructure, or use of the network infrastructure to attack IT resources. As defensive measures tend to impede the operation of IT, it is optimally capable of balancing performance objectives with typically over-riding threat management actions. In the
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Open-source software security

Open-source software security is the measure of assurance or guarantee in the freedom from danger and risk inherent to an open-source software system. == Implementation debate == === Benefits === Proprietary software forces the user to accept the level of security that the software vendor is willing to deliver and to accept the rate that patches and updates are released. It is assumed that any compiler that is used creates code that can be trusted, but it has been demonstrated by Ken Thompson that a compiler can be subverted using a compiler backdoor to create faulty executables that are unwittingly produced by a well-intentioned developer. With access to the source code for the compiler, the developer has at least the ability to discover if there is any mal-intention. Kerckhoffs' principle is based on the idea that an enemy can steal a secure military system and not be able to compromise the information. His ideas were the basis for many modern security practices, and followed that security through obscurity is a bad practice. === Drawbacks === Simply making source code available does not guarantee review. An example of this occurring is when Marcus Ranum, an expert on security system design and implementation, released his first public firewall toolkit. At one time, there were over 2,000 sites using his toolkit, but only 10 people gave him any feedback or patches. Having a large amount of eyes reviewing code can "lull a user into a false sense of security". Having many users look at source code does not guarantee that security flaws will be found and fixed. == Metrics and models == There are a variety of models and metrics to measure the security of a system. These are a few methods that can be used to measure the security of software systems. === Number of days between vulnerabilities === It is argued that a system is most vulnerable after a potential vulnerability is discovered, but before a patch is created. By measuring the number of days between the vulnerability and when the vulnerability is fixed, a basis can be determined on the security of the system. There are a few caveats to such an approach: not every vulnerability is equally bad, and fixing a lot of bugs quickly might not be better than only finding a few and taking a little bit longer to fix them, taking into account the operating system, or the effectiveness of the fix. === Poisson process === The Poisson process can be used to measure the rates at which different people find security flaws between open and closed source software. The process can be broken down by the number of volunteers Nv and paid reviewers Np. The rates at which volunteers find a flaw is measured by λv and the rate that paid reviewers find a flaw is measured by λp. The expected time that a volunteer group is expected to find a flaw is 1/(Nv λv) and the expected time that a paid group is expected to find a flaw is 1/(Np λp). === Morningstar model === By comparing a large variety of open source and closed source projects a star system could be used to analyze the security of the project similar to how Morningstar, Inc. rates mutual funds. With a large enough data set, statistics could be used to measure the overall effectiveness of one group over the other. An example of such as system is as follows: 1 Star: Many security vulnerabilities. 2 Stars: Reliability issues. 3 Stars: Follows best security practices. 4 Stars: Documented secure development process. 5 Stars: Passed independent security review. === Coverity scan === Coverity in collaboration with Stanford University has established a new baseline for open-source quality and security. The development is being completed through a contract with the Department of Homeland Security. They are utilizing innovations in automated defect detection to identify critical types of bugs found in software. The level of quality and security is measured in rungs. Rungs do not have a definitive meaning, and can change as Coverity releases new tools. Rungs are based on the progress of fixing issues found by the Coverity Analysis results and the degree of collaboration with Coverity. They start with Rung 0 and currently go up to Rung 2. Rung 0 The project has been analyzed by Coverity's Scan infrastructure, but no representatives from the open-source software have come forward for the results. Rung 1 At rung 1, there is collaboration between Coverity and the development team. The software is analyzed with a subset of the scanning features to prevent the development team from being overwhelmed. Rung 2 There are 11 projects that have been analyzed and upgraded to the status of Rung 2 by reaching zero defects in the first year of the scan. These projects include: AMANDA, ntp, OpenPAM, OpenVPN, Overdose, Perl, PHP, Postfix, Python, Samba, and Tcl.
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Ware report

Security Controls for Computer Systems, commonly called the Ware report, is a 1970 text by Willis Ware that was foundational in the field of computer security. == Development == A defense contractor in St. Louis, Missouri, had bought an IBM mainframe computer, which it was using for classified work on a fighter aircraft. To provide additional income, the contractor asked the Department of Defense (DoD) for permission to sell computer time on the mainframe to local businesses via remote terminals, while the classified work continued. At the time, the DoD did not have a policy to cover this. The DoD's Advanced Research Projects Agency (DARPA) asked Ware - a RAND employee - to chair a committee to examine and report on the feasibility of security controls for computer systems. The committee's report was a classified document given in January 1970 to the Defense Science Board (DSB), which had taken over the project from ARPA. After declassification, the report was published by RAND in October 1979. == Influence == The IEEE Computer Society said the report was widely circulated, and the IEEE Annals of the History of Computing said that it, together with Ware's 1967 Spring Joint Computer Conference session, marked the start of the field of computer security. The report influenced security certification standards and processes, especially in the banking and defense industries, where the report was instrumental in creating the Orange Book.
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Radioplayer

Radioplayer is a radio technology platform, owned by UK radio broadcasters and operated under licence in some other countries. It operates an internet radio web tuner, a set of mobile phone apps, an in-car adaptor, and a growing range of integrations with other connected devices and platforms. Radioplayer is operated by UK Radioplayer Ltd which is a not-for-profit organisation owned by UK radio broadcasters. Initial shareholders were the BBC, Global Radio, GMG Radio, Absolute Radio and RadioCentre. After consolidation in the radio market, current shareholders are the BBC, Global Radio, Bauer Media Group and RadioCentre. == History == Launched in the UK on 31 March 2011, Radioplayer set out to offer a simple and accessible way to listen to radio via the internet. It contained 157 stations at launch. Initially working internally at the BBC for Tim Davie, then Director of BBC Audio & Music, Michael Hill led the project since March 2009; he was made Managing Director of UK Radioplayer Ltd on 28 July 2010. At launch, Radioplayer was a simple and straightforward Flash-based radio player, linked-to by radio stations on their own website. The player included searching and bookmarking across all of UK radio station content. On 5 October 2012, Radioplayer launched a mobile app on iOS phones with an Android version following shortly afterwards. The apps are unavailable for download outside the United Kingdom. This was followed by a tablet app on 25 September 2013. The apps also support Android Wear, Android Auto, Smart Device Link, Apple Watch and Apple CarPlay. They are also compatible with Chromecast and Airplay. In September 2016, Radioplayer announced it had been chosen by Amazon to integrate with their new voice-controlled 'Echo' device, ahead of its UK launch. In July 2017, Radioplayer integrated with the Sonos and Bose multi-room speaker platforms. UK Radioplayer currently contains around 500 UK stations, from Ofcom-licensed broadcasters. Online-only 'sister-stations' can also be added, but only by broadcasters with Ofcom licences which have been on the platform for over a year. == Radioplayer Car == Radioplayer Car was announced in September 2014 as a hybrid radio receiver that switches between FM, DAB and streaming to find the strongest signal. Speaking in Oslo in June 2015, Michael Hill said that he hoped to launch the product in the UK and Norway during the summer of 2015. In February 2017, Radioplayer Car was launched. It was marketed as the world’s first voice-controlled hybrid radio adaptor for car stereos. A small box, fitted behind the dashboard, links to the auxiliary input on an existing car radio. It connects wirelessly via Bluetooth to the driver’s smartphone by an app. The adaptor enabled drivers to listen to their own smartphone music collections using Bluetooth, take hands-free calls, listen to inbound text messages and receive instant audio travel news, customised by GPS to their location and direction of travel. The hardware was manufactured under licence by car audio interfaces supplier Connects2, and Hyde Park Corner was promoted as the preferred installer of the audio equipment. There were several spin-off benefits of the Radioplayer Car project, including the creation of the hybrid radio metadata API for cars, known as the 'WRAPI' (Worldwide Radioplayer API). == International == Through a separate company called Radioplayer Worldwide, Radioplayer technology is licensed to a number of different territories.
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Description logic

Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems. There are general, spatial, temporal, spatiotemporal, and fuzzy description logics, and each description logic features a different balance between expressive power and reasoning complexity by supporting different sets of mathematical constructors. DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as terminological knowledge). It is of particular importance in providing a logical formalism for ontologies and the Semantic Web: the Web Ontology Language (OWL) and its profiles are based on DLs. A major area of application of DLs and OWL is in biomedical informatics, where they assist in the codification of biomedical knowledge. DLs and OWL are also applied in other domains, including defense, climate modeling, and large-scale industrial knowledge graphs. == Introduction == A DL models concepts, roles and individuals, and their relationships. The fundamental modeling concept of a DL is the axiom—a logical statement relating roles and/or concepts. This is a key difference from the frames paradigm where a frame specification declares and completely defines a class. == Nomenclature == === Terminology compared to FOL and OWL === The description logic community uses different terminology than the first-order logic (FOL) community for operationally equivalent notions; some examples are given below. The Web Ontology Language (OWL) uses again a different terminology, also given in the table below. === Naming convention === There are many varieties of description logics and there is an informal naming convention, roughly describing the operators allowed. The expressivity is encoded in the label for a logic starting with one of the following basic logics: Followed by any of the following extensions: ==== Exceptions ==== Some canonical DLs that do not exactly fit this convention are: ==== Examples ==== As an example, A L C {\displaystyle {\mathcal {ALC}}} is a centrally important description logic from which comparisons with other varieties can be made. A L C {\displaystyle {\mathcal {ALC}}} is simply A L {\displaystyle {\mathcal {AL}}} with complement of any concept allowed, not just atomic concepts. A L C {\displaystyle {\mathcal {ALC}}} is used instead of the equivalent A L U E {\displaystyle {\mathcal {ALUE}}} . A further example, the description logic S H I Q {\displaystyle {\mathcal {SHIQ}}} is the logic A L C {\displaystyle {\mathcal {ALC}}} plus extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic A L C O I N {\displaystyle {\mathcal {ALCOIN}}} might be referred to as A L C N I O {\displaystyle {\mathcal {ALCNIO}}} and other abbreviations are also made where possible. The Protégé ontology editor supports S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} . Three major biomedical informatics terminology bases, SNOMED CT, GALEN, and GO, are expressible in E L {\displaystyle {\mathcal {EL}}} (with additional role properties). OWL 2 provides the expressiveness of S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} , OWL-DL is based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} , and for OWL-Lite it is S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} . == History == Description logic was given its current name in the 1980s. Previous to this it was called (chronologically): terminological systems, and concept languages. === Knowledge representation === Frames and semantic networks lack formal (logic-based) semantics. DL was first introduced into knowledge representation (KR) systems to overcome this deficiency. The first DL-based KR system was KL-ONE (by Ronald J. Brachman and Schmolze, 1985). During the '80s other DL-based systems using structural subsumption algorithms were developed including KRYPTON (1983), LOOM (1987), BACK (1988), K-REP (1991) and CLASSIC (1991). This approach featured DL with limited expressiveness but relatively efficient (polynomial time) reasoning. In the early '90s, the introduction of a new tableau based algorithm paradigm allowed efficient reasoning on more expressive DL. DL-based systems using these algorithms — such as KRIS (1991) — show acceptable reasoning performance on typical inference problems even though the worst case complexity is no longer polynomial. From the mid '90s, reasoners were created with good practical performance on very expressive DL with high worst case complexity. Examples from this period include FaCT, RACER (2001), CEL (2005), and KAON 2 (2005). DL reasoners, such as FaCT, FaCT++, RACER, DLP and Pellet, implement the method of analytic tableaux. KAON2 is implemented by algorithms which reduce a SHIQ(D) knowledge base to a disjunctive datalog program. === Semantic web === The DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ontology languages for the Semantic Web can be viewed as syntactic variants of DL. In particular, the formal semantics and reasoning in OIL use the S H I Q {\displaystyle {\mathcal {SHIQ}}} DL. The DAML+OIL DL was developed as a submission to—and formed the starting point of—the World Wide Web Consortium (W3C) Web Ontology Working Group. In 2004, the Web Ontology Working Group completed its work by issuing the OWL recommendation. The design of OWL is based on the S H {\displaystyle {\mathcal {SH}}} family of DL with OWL DL and OWL Lite based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} and S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} respectively. The W3C OWL Working Group began work in 2007 on a refinement of - and extension to - OWL. In 2009, this was completed by the issuance of the OWL2 recommendation. OWL2 is based on the description logic S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} . Practical experience demonstrated that OWL DL lacked several key features necessary to model complex domains. == Modeling == === TBox vs Abox === In DL, a distinction is drawn between the so-called TBox (terminological box) and the ABox (assertional box). In general, the TBox contains sentences describing concept hierarchies (i.e., relations between concepts) while the ABox contains ground sentences stating where in the hierarchy, individuals belong (i.e., relations between individuals and concepts). For example, the statement: belongs in the TBox, while the statement: belongs in the ABox. Note that the TBox/ABox distinction is not significant, in the same sense that the two "kinds" of sentences are not treated differently in first-order logic (which subsumes most DL). When translated into first-order logic, a subsumption axiom like (1) is simply a conditional restriction to unary predicates (concepts) with only variables appearing in it. Clearly, a sentence of this form is not privileged or special over sentences in which only constants ("grounded" values) appear like (2). === Motivation for having Tbox and Abox === So why was the distinction introduced? The primary reason is that the separation can be useful when describing and formulating decision-procedures for various DL. For example, a reasoner might process the TBox and ABox separately, in part because certain key inference problems are tied to one but not the other one ('classification' is related to the TBox, 'instance checking' to the ABox). Another example is that the complexity of the TBox can greatly affect the performance of a given decision-procedure for a certain DL, independently of the ABox. Thus, it is useful to have a way to talk about that specific part of the knowledge base. The secondary reason is that the distinction can make sense from the knowledge base modeler's perspective. It is plausible to distinguish between our conception of terms/concepts in the world (class axioms in the TBox) and particular manifestations of those terms/concepts (instance assertions in the ABox). In the above example: when the hierarchy within a company is the same in every branch but the assignment to employees is different in every department (because there are other people working there), it makes sense to reuse the TBox for different branches that do not use the same ABox. There are two features of description logic that are not shared by most other data description formalisms: DL does not make the unique name assumption (UNA) or the closed-world assumption (CWA). Not having UNA means that two concepts with different names may be allowed by some inference to be shown to be equivalent. Not having CWA, or rather having the open world assumption (OWA) means that
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Supertoroid

In geometry and computer graphics, a supertoroid or supertorus is usually understood to be a family of doughnut-like surfaces (technically, a topological torus) whose shape is defined by mathematical formulas similar to those that define the superellipsoids. The plural of "supertorus" is either supertori or supertoruses. The family was described and named by Alan Barr in 1994. Barr's supertoroids have been fairly popular in computer graphics as a convenient model for many objects, such as smooth frames for rectangular things. One quarter of a supertoroid can provide a smooth and seamless 90-degree joint between two superquadric cylinders. However, they are not algebraic surfaces (except in special cases). == Formulas == Alan Barr's supertoroids are defined by parametric equations similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u, v) of the surface is given by P ( u , v ) = ( X ( u , v ) Y ( u , v ) Z ( u , v ) ) = ( ( a + C u s ) C v t ( b + C u s ) S v t S u s ) {\displaystyle P(u,v)=\left({\begin{array}{c}X(u,v)\\Y(u,v)\\Z(u,v)\end{array}}\right)=\left({\begin{array}{c}(a+C_{u}^{s})C_{v}^{t}\\(b+C_{u}^{s})S_{v}^{t}\\S_{u}^{s}\end{array}}\right)} where C θ ε = sgn ⁡ ( cos ⁡ θ ) | cos ⁡ θ | ε , S θ ε = sgn ⁡ ( sin ⁡ θ ) | sin ⁡ θ | ε , {\displaystyle {\begin{aligned}C_{\theta }^{\varepsilon }&=\operatorname {sgn} (\cos \theta )\,\left|\,\cos \theta \,\right|^{\varepsilon },\\S_{\theta }^{\varepsilon }&=\operatorname {sgn} (\sin \theta )\ \left|\,\sin \theta \ \right|^{\varepsilon },\end{aligned}}} sgn is the sign function, and the parameters u, v range from 0 to 360 degrees (0 to 2π radians). In these formulas, the parameter s > 0 controls the "squareness" of the vertical sections, t > 0 controls the squareness of the horizontal sections, and a, b ≥ 1 are the major radii in the x and y directions. With s = t = 1 and a = b = R one obtains the ordinary torus with major radius R and minor radius 1, with the center at the origin and rotational symmetry about the z-axis. In general, the supertorus defined as above spans the intervals: − ( a + 1 ) ≤ x ≤ + ( a + 1 ) − ( b + 1 ) ≤ y ≤ + ( b + 1 ) − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}-(a+1)&\leq &x&\leq &+(a+1)\\[4pt]-(b+1)&\leq &y&\leq &+(b+1)\\[4pt]-1&\leq &z&\leq &+1\end{array}}} The whole shape is symmetric about the planes x = 0, y = 0, and z = 0. The hole runs in the z direction and spans the intervals − ( a − 1 ) ≤ x ≤ + ( a − 1 ) − ( b − 1 ) ≤ y ≤ + ( b − 1 ) − ∞ ≤ z ≤ + ∞ {\displaystyle {\begin{array}{rcccl}-(a-1)&\leq &x&\leq &+(a-1)\\[4pt]-(b-1)&\leq &y&\leq &+(b-1)\\[4pt]-\infty &\leq &z&\leq &+\infty \end{array}}} A curve of constant u on this surface is a horizontal Lamé curve with exponent ⁠ 2 t , {\displaystyle {\tfrac {2}{t}},} ⁠ scaled in x and y and displaced in z. A curve of constant v, projected on the plane x = 0 or y = 0, is a Lamé curve with exponent ⁠ 2 s , {\displaystyle {\tfrac {2}{s}},} ⁠ scaled and horizontally shifted. If v = 0, the curve is planar and spans the intervals: a − 1 ≤ x ≤ a + 1 − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}a-1&\leq &x&\leq &a+1\\[4pt]-1&\leq &z&\leq &+1\end{array}}} and similarly if v = 90°, 180°, 270°. The curve is also planar if a = b. In general, if a ≠ b and v is not a multiple of 90 degrees, the curve of constant v will not be planar; and, conversely, a vertical plane section of the supertorus will not be a Lamé curve. The basic supertoroid shape defined above is often modified by non-uniform scaling to yield supertoroids of specific width, length, and vertical thickness. == Plotting code == The following GNU Octave code generates plots of a supertorus:
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Zolostays

Zolostays is a real-tech co-living focused startup that provides ready-to-move rooms/beds. It was founded in 2015 by Nikhil Sikri, Akhil Sikri and Sneha Choudhry. == Overview == During the pandemic, Zolo provided 75 of rent-free accommodation to those who lost their jobs. Zolo uses bulk inventory in usually residential township and ties up with real estate companies to make the rooms/beds available. Zolostays has both revenue sharing and leased model. == History == Zolostays was founded in 2015 to solve the problem of students and young professionals who would move to temporarily go to other cities to study and work and look for affordable housing. In 2020, it was operating in 10 Indian cities. It has four round of funding, with total $98 million.
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PenTile matrix family

PenTile matrix is a family of patented subpixel matrix schemes used in electronic device displays. PenTile is a trademark of Samsung. PenTile matrices are used in AMOLED and LCD displays. These subpixel layouts are specifically designed to operate with proprietary algorithms for subpixel rendering embedded in the display driver, allowing plug and play compatibility with conventional RGB (Red-Green-Blue) stripe panels. == Overview == "PenTile Matrix" (a neologism from penta-, meaning "five" in Greek and tile) describes the geometric layout of the prototypical subpixel arrangement developed in the early 1990s. The layout consists of a quincunx comprising two red subpixels, two green subpixels, and one central blue subpixel in each unit cell. It was inspired by biomimicry of the human retina, which has nearly equal numbers of L and M type cone cells, but significantly fewer S cones. As the S cones are primarily responsible for perceiving blue colors, which do not appreciably affect the perception of luminance, reducing the number of blue subpixels with respect to the red and green subpixels in a display does not reduce the image quality. However, the layout may cause color leakage image distortion, which can be reduced by filters. In some cases the layout causes reduced moiré and blockiness compared to conventional RGB layouts. The PenTile layout is specifically designed to work with and be dependent upon subpixel rendering that uses only one and a quarter subpixel per pixel, on average, to render an image. That is, that any given input pixel is mapped to either a red-centered logical pixel, or a green-centered logical pixel. === History === PenTile was invented by Candice H. Brown Elliott, for which she was awarded the Society for Information Display's Otto Schade Prize in 2014. The technology was licensed by the company Clairvoyante from 2000 until 2008, during which time several prototype PenTile displays were developed by a number of Asian liquid crystal display (LCD) manufacturers. In March 2008, Samsung Electronics acquired Clairvoyante's PenTile IP assets. Samsung then funded a new company, Nouvoyance, Inc. to continue development of the PenTile technology. == PenTile RGBG == PenTile RGBG layout used in AMOLED and plasma displays uses green pixels interleaved with alternating red and blue pixels. The human eye is most sensitive to green, especially for high resolution luminance information. The green subpixels are mapped to input pixels on a one-to-one basis. The red and blue subpixels are subsampled, reconstructing the chroma signal at a lower resolution. The luminance signal is processed using adaptive subpixel rendering filters to optimize reconstruction of high spatial frequencies from the input image, wherein the green subpixels provide the majority of the reconstruction. The red and blue subpixels are capable of reconstructing the horizontal and vertical spatial frequencies, but not the highest of the diagonal. Diagonal high spatial frequency information in the red and blue channels of the input image are transferred to the green subpixels for image reconstruction. Thus the RG-BG scheme creates a color display with one third fewer subpixels than a traditional RGB-RGB scheme but with the same measured luminance display resolution. This is similar to the Bayer filter commonly used in digital cameras. === Devices === As of 2021, "almost all" OLED screens in portable consumer devices use some form of Pentile subpixel layout. == PenTile RGBW == PenTile RGBW technology, used in LCD, adds an extra subpixel to the traditional red, green and blue subpixels that is a clear area without color filtering material and with the only purpose of letting backlight come through, hence W for white. This makes it possible to produce a brighter image compared to an RGB-matrix while using the same amount of power, or produce an equally bright image while using less power. The PenTile RGBW layout uses each red, green, blue and white subpixel to present high-resolution luminance information to the human eyes' red-sensing and green-sensing cone cells, while using the combined effect of all the color subpixels to present lower-resolution chroma (color) information to all three cone cell types. Combined, this optimizes the match of display technology to the biological mechanisms of human vision. The layout uses one third fewer subpixels for the same resolution as the RGB stripe (RGB-RGB) layout, in spite of having four color primaries instead of the conventional three, using subpixel rendering combined with metamer rendering. Metamer rendering optimizes the energy distribution between the white subpixel and the combined red, green, and blue subpixels: W <> RGB, to improve image sharpness. The display driver chip has an RGB to RGBW color vector space converter and gamut mapping algorithm, followed by metamer and subpixel rendering algorithms. In order to maintain saturated color quality, to avoid simultaneous contrast error between saturated colors and peak white brightness, while simultaneously reducing backlight power requirements, the display backlight brightness is under control of the PenTile driver engine. When the image is mostly desaturated colors, those near white or grey, the backlight brightness is significantly reduced, often to less than 50% peak, while the LCD levels are increased to compensate. When the image has very bright saturated colors, the backlight brightness is maintained at higher levels. The PenTile RGBW also has an optional high-brightness mode that doubles the brightness of the desaturated color image areas, such as black-and-white text, for improved outdoor viewability. === Devices === Motorola MC65 Motorola ES55 Motorola ES400 Motorola Atrix 4G Samsung Galaxy Note 10.1 2014 version Lenovo Yoga 2 Pro Lenovo Yoga 3 Pro HP ENVY TouchSmart 14-k022tx Sleekbook MSI GS60 Ghost Pro 4K Lenovo IdeaPad Y50 4K Asus ZenBook UX303LN 4K Asus ZenBook Pro UX501JW LG UH7500/6500/6100 LG ThinQ G7/G7+ Oculus Quest 1 == Controversy == An ongoing controversy regarding the definition or measurement of resolution of color subpixelated flat panel displays led many people to question the resolution claims of PenTile display products. Journalists have noted that in "just about every flat-panel TV in existence, each pixel is composed of one red, one green, and one blue subpixel (RGB), all of uniform size". In traditional flat-panel screens, the resolution is defined by the number of red, green, and blue subpixels, in groups of three, in an array in each axis. As a result, each pixel or group of subpixels can render any colour on the screen, regardless of neighbouring pixels. This is not the case with PenTile screens. The Video Electronics Standards Association (VESA) method of measuring and defining resolution in color displays is to measure the contrast of line pairs, requiring a minimum of 50% Michelson contrast for displays intended for rendering text. The developers of PenTile displays use this VESA criterion for contrast of line pairs to calculate the resolutions specified. In the RGBG layout the alternate red and blue subpixels are 'shared' or sub-sampled with neighboring pixels. Due to the one third lower subpixel density on PenTile displays the pixel structure may be more visible when compared to RGB stripe displays with the same pixel density. The loss of subpixels for a given resolution specification has led some journalists to describe the use of PenTile as "shady practice" and "sort of cheating". For a given size and resolution specification, the PenTile screen can appear grainy, pixelated, speckled, with blurred text on some saturated colors and backgrounds when compared to RGB stripe color. This effect is understood to be caused by the restriction of the number of subpixels that may participate in the image reconstruction when colors are highly saturated to primaries. In the RGBW case, this is caused as the W subpixel will not be available in order to maintain the saturated color. In the RGBG case, this effect will occur when the color boundary is primarily red or blue, as the fully populated (one green per pixel) sub-pixel cannot contribute. For all other cases, text and especially full color images are effectively reconstructed. == Advantages and disadvantages == The PenTile layout reduces the number of subpixels needed to create a specified resolution. Consequently it is possible to achieve an HD resolution on a PenTile AMOLED screen at lower cost than other technologies, and most reviewers note that "300 ppi" (as per VESA - not full pixels) resolution displays (such as Samsung Galaxy S III) make the PenTile effect less obvious than lower resolution PenTile displays (Droid Razr). The second advantage is lower power consumption: the HTC One S's use of a PenTile display makes it more energy efficient and thinner than equivalent LCD screens, giving it better battery life than the HTC One X's IPS LCD. A PenTile AMOLED screen is also
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List of monochrome and RGB color formats

This list of monochrome and RGB palettes includes generic repertoires of colors (color palettes) to produce black-and-white and RGB color pictures by a computer's display hardware. RGB is the most common method to produce colors for displays; so these complete RGB color repertoires have every possible combination of R-G-B triplets within any given maximum number of levels per component. Each palette is represented by a series of color patches. When the number of colors is low, a 1-pixel-size version of the palette appears below it, for easily comparing relative palette sizes. Huge palettes are given directly in one-color-per-pixel color patches. For each unique palette, an image color test chart and sample image (truecolor original follows) rendered with that palette (without dithering) are given. The test chart shows the full 256 levels of the red, green, and blue (RGB) primary colors and cyan, magenta, and yellow complementary colors, along with a full 256-level grayscale. Gradients of RGB intermediate colors (orange, lime green, sea green, sky blue, violet, and fuchsia), and a full hue spectrum are also present. Color charts are not gamma corrected. These elements illustrate the color depth and distribution of the colors of any given palette, and the sample image indicates how the color selection of such palettes could represent real-life images. These images are not necessarily representative of how the image would be displayed on the original graphics hardware, as the hardware may have additional limitations regarding the maximum display resolution, pixel aspect ratio and color placement. Implementation of these formats is specific to each machine. Therefore, the number of colors that can be simultaneously displayed in a given text or graphic mode might be different. Also, the actual displayed colors are subject to the output format used - PAL or NTSC, composite or component video, etc. - and might be slightly different. For simulated images and specific hardware and alternate methods to produce colors other than RGB (ex: composite), see the List of 8-bit computer hardware palettes, the List of 16-bit computer hardware palettes and the List of video game console palettes. For various software arrangements and sorts of colors, including other possible full RGB arrangements within 8-bit color depth displays, see the List of software palettes. == Monochrome palettes == These palettes only have some shades of gray, from black to white (considered the darkest and lightest "grays", respectively). The general rule is that those palettes have 2n different shades of gray, where n is the number of bits needed to represent a single pixel. === Monochrome (1-bit grayscale) === Monochrome graphics displays typically have a black background with a white or light gray image, though green and amber monochrome monitors were also common. Such a palette requires only one bit per pixel. Where photo-realism was desired, these early computer systems had a heavy reliance on dithering to make up for the limits of the technology. In some systems, as Hercules and CGA graphic cards for the IBM PC, a bit value of 1 represents white pixels (light on) and a value of 0 the black ones (light off); others, like the Playdate and Atari ST and Apple Macintosh with monochrome monitors, a bit value of 0 means a white pixel (no ink) and a value of 1 means a black pixel (dot of ink), which it approximates to the printing logic. === 2-bit Grayscale === In a 2-bit color palette each pixel's value is represented by 2 bits resulting in a 4-value palette (22 = 4). 2-bit dithering: It has black, white and two intermediate levels of gray as follows: A monochrome 2-bit palette is used on: The Monochrome Display Adapter for the IBM PC NeXT Computer, NeXTcube and NeXTstation monochrome graphic displays. Original Game Boy system portable video game console. Macintosh PowerBook 150 monochrome LC displays. Amiga with A2024 monochrome monitor in high-resolution mode. The original Amazon Kindle The original WonderSwan The Tiger Electronics Game.com portable video game console The original Neo Geo Pocket. === 4-bit Grayscale === In a 4-bit color palette each pixel's value is represented by 4 bits resulting in a 16-value palette (24 = 16): 4-bit grayscale dithering does a fairly good job of reducing visible banding of the level changes: A monochrome 4-bit palette is used on: MOS Technology VDC (on the Commodore 128 with monochrome monitor) Amstrad CPC series with a GT64/GT65 Green Monitor (16 unique green shades) Amstrad CPC Plus series with the MM12 Monochrome monitor (16 shades of grey) Some Apple PowerBooks equipped with monochrome displays like the PowerBook 5300 The original VideoNow === 8-bit Grayscale === In an 8-bit color palette each pixel's value is represented by 8 bits resulting in a 256-value palette (28 = 256). This is usually the maximum number of grays in ordinary monochrome systems; each image pixel occupies a single memory byte. Most scanners can capture images in 8-bit grayscale, and image file formats like TIFF and JPEG natively support this monochrome palette size. Alpha channels employed for video overlay also use (conceptually) this palette. The gray level indicates the opacity of the blended image pixel over the background image pixel. == Dichrome palettes == === 16-bit RG palette === The RG or red–green color space is a color space that uses only two primary colors: red and green. It was used on early color processes for films. It was used as an additive format, similar to the RGB color model but without a blue channel, on processes such as Kinemacolor, Prizma, Technicolor I, Raycol, etc., producing shades of black, red, green and yellow. Alternatively, it was used as a subtractive format on Brewster Color I, Kodachrome I, Prizma II, Technicolor II, etc., producing shades of transparent, red, green and black. Until recently, its primary use was in low-cost light-emitting diode displays in which red and green tended to be far more common than the still nascent blue LED technology, but full-color LEDs with blue have become more common in recent years. ColorCode 3-D, a anaglyph stereoscopic color scheme, uses the RG color space to simulate a broad spectrum of color in one eye, while the blue portion of the spectrum transmits a black-and-white (black-and-blue) image to the other eye to give depth perception. === 16-bit RB palette === === 16-bit GB palette === == Regular RGB palettes == Here are grouped those full RGB hardware palettes that have the same number of binary levels (i.e., the same number of bits) for every red, green and blue components using the full RGB color model. Thus, the total number of colors are always the number of possible levels by component, n, raised to a power of 3: n×n×n = n3. === 3-bit RGB === 3-bit RGB dithering: Systems with a 3-bit RGB palette use 1 bit for each of the red, green and blue color components. That is, each component is either "on" or "off" with no intermediate states. This results in an 8-color palette ((21)3 = 23 = 8) that has black, white, the three RGB primary colors red, green and blue and their correspondent complementary colors cyan, magenta and yellow as follows: The color indices vary between implementations; therefore, index numbers are not given. The 3-bit RGB palette is used by: Text terminals following the ECMA-48 standard (sometimes known as the "ANSI standard", although ANSI X3.128 does not define colors) World System Teletext Level 1/1.5 Videotex Oric computers BBC Micro PC-8801 (up to the MkII) PC-9801 (with original 8086 CPU, before the VM/VX models) Sharp X1 (models before the X1 Turbo Z) Sharp MZ 700 FM-7, FM New 7, FM 77 (before the FM77AV) Sinclair QL Space Invaders Part II (arcade hardware) Macintosh SE (with a color printer or external monitor) Atari 2600 (SECAM version) Color Maximite (PIC32 based microcomputer) Arcadia 2001 PV-1000 Monkey Magic (arcade hardware) VIC-20 (high-res mode) Mouse Trap (arcade hardware) Sanyo MBC-550 series Windows 1.0 (includes dithering) === 6-bit RGB === Systems with a 6-bit RGB palette use 2 bits for each of the red, green, and blue color components. This results in a (22)3 = 43 = 64-color palette as follows: 6-bit RGB systems include the following: Enhanced Graphics Adapter (EGA) for IBM PC/AT (16 colors at once) Sega Master System video game console (32 colors at once) GIME for TRS-80 Color Computer 3 (16 colors at once) Pebble Time smartwatch which has a 6-bit (64 color) e-paper display Parallax Propeller using the reference VGA circuit === 9-bit RGB === Systems with a 9-bit RGB palette use 3 bits for each of the red, green, and blue color components. This results in a (23)3 = 83 = 512-color palette as follows: 9-bit RGB systems include the following: Atari ST (Normally 4 to 16 at once without tricks) MSX2 computers (up to 16 at once) Sega Genesis video game console, (64 colors at once) Sega Nomad TurboGrafx-16 (NEC PC-Engine) ZX Spectrum Next The NEC PC-88
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National Cyber Security Policy 2013

National Cyber Security Policy is a policy framework by Department of Electronics and Information Technology (DeitY) It aims at protecting the public and private infrastructure from cyber attacks. The policy also intends to safeguard "information, such as personal information (of web users), financial and banking information and sovereign data". This was particularly relevant in the wake of US National Security Agency (NSA) leaks that suggested the US government agencies are spying on Indian users, who have no legal or technical safeguards against it. Ministry of Communications and Information Technology (India) defines Cyberspace as a complex environment consisting of interactions between people, software services supported by worldwide distribution of information and communication technology. == Reason for Cyber Security policies == India had no Cyber security policy before 2013. In 2013, The Hindu newspaper, citing documents leaked by NSA whistle-blower Edward Snowden, has alleged that much of the NSA surveillance was focused on India's domestic politics and its strategic and commercial interests. This sparked a furore among people. Under pressure, the government unveiled a National Cyber Security Policy 2013 on 2 July 2013. == Vision == To build a secure and resilient cyberspace for citizens, business, and government and also to protect anyone from intervening in user's privacy.It mentioned a five year target of training five lakh cyber security personnel by 2018. == Mission == To protect information and information infrastructure in cyberspace, build capabilities to prevent and respond to cyber threat, reduce vulnerabilities and minimize damage from cyber incidents through a combination of institutional structures, people, processes, technology, and cooperation. == Objective == Ministry of Communications and Information Technology (India) define objectives as follows: To create a secure cyber ecosystem in the country, generate adequate trust and confidence in IT system and transactions in cyberspace and thereby enhance adoption of IT in all sectors of the economy. To create an assurance framework for the design of security policies and promotion and enabling actions for compliance to global security standards and best practices by way of conformity assessment (Product, process, technology & people). To strengthen the Regulatory Framework for ensuring a SECURE CYBERSPACE ECOSYSTEM. To enhance and create National and Sectoral level 24x7 mechanism for obtaining strategic information regarding threats to ICT infrastructure, creating scenarios for response, resolution and crisis management through effective predictive, preventive, protective response and recovery actions. -To improve visibility of integrity of ICT products and services by establishing infrastructure for testing & validation of security of such product. To create workforce for 500,000 professionals skilled in next 5 years through capacity building skill development and training. To provide fiscal benefit to businesses for adoption of standard security practices and processes. To enable Protection of information while in process, handling, storage & transit so as to safeguard privacy of citizen's data and reducing economic losses due to cyber crime or data theft. To enable effective prevention, investigation and prosecution of cybercrime and enhancement of law enforcement capabilities through appropriate legislative intervention. == Strategies == Creating a secured Ecosystem. Creating an assurance framework. Encouraging Open Standards. Strengthening The regulatory Framework. Creating a mechanism for Security Threats Early Warning, Vulnerability management, and response to security threats. Securing E-Governance services. Protection and resilience of Critical Information Infrastructure. Promotion of Research and Development in cyber security. Reducing supply chain risks Human Resource Development (fostering education and training programs both in formal and informal sectors to Support the Nation's cyber security needs and build capacity. Creating cyber security awareness. Developing effective Public-Private partnerships. To develop bilateral and multilateral relationships in the area of cyber security with another country. (Information sharing and cooperation) a Prioritized approach for implementation.
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Texture atlas

In computer graphics, a texture atlas (also called a spritesheet or an image sprite in 2D game development) is an image containing multiple smaller images, usually packed together to reduce overall dimensions. An atlas can consist of uniformly-sized images or images of varying dimensions. A sub-image is drawn using custom texture coordinates to pick it out of the atlas. == Benefits == In an application where many small textures are used frequently, it is often more efficient to store the textures in a texture atlas which is treated as a single unit by the graphics hardware. This reduces both the disk I/O overhead and the overhead of a context switch by increasing memory locality. Careful alignment may be needed to avoid bleeding between sub textures when used with mipmapping and texture compression. In web development, images are packed into a sprite sheet to reduce the number of image resources that need to be fetched in order to display a page. == Gallery ==
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Sprayprinter

SprayPrinter is a device that attaches to aerosol paint cans whereby users can print images via Bluetooth from a smartphone onto a wall or almost any surface. == History == The technology behind SprayPrinter was developed by Mihkel Joala. He explained in a 2016 interview with New Atlas that his idea was inspired by the modern car engine and the Nintendo Wii console. "Engines nowadays use extremely fast valves to spray fuel to [the] combustion chamber," says Joala. "I realized I can use them to shoot paint with pinpoint accuracy." As of December 2021, the company appears to be no longer selling products. == Awards and Recognitions == In 2015, SprayPrinter received €8,000 from the Estonian prototyping contest Prototron for its initial prototype. In 2016, the SprayPrinter team won the grand prize of €30,000 from the televised pitching competition Ajujaht.
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Carrenza

Carrenza was a cloud-computing company based in London, United Kingdom. The company was acquired by Six Degrees Technology Group in 2016. == Operations == Carrenza was a UK-based IT company that provides Cloud computing technologies. It offered a range of public cloud, private cloud and hybrid cloud services, including Infrastructure as a Service (IaaS), Platform as a Service (PaaS), enterprise application integration and system integration. Carrenza partnered with several enterprise IT providers and was an accredited VMware Enterprise Service Partner and HP (Hewlett-Packard) Cloud Agile Partner. The company was based on Commercial Street, in the heart of the East London Tech City district, which is host to a large number of technology companies. == History == Carrenza was formed in 2001 as a consultancy by chief executive and founder Dan Sutherland. It began trading in 2004 and launched its first enterprise cloud computing platform in 2006, becoming one of the first companies in Europe to provide this type of hosting service. In 2009, it formed a partnership with Comic Relief and its affiliated campaigns Red Nose Day Sport Relief to provide IT infrastructure services to the charity, an arrangement that has won industry recognition. In 2013 it launched its first overseas services, with a mainland Europe cloud node based in Amsterdam. == Partnerships and customers == Carrenza had formed partnerships with a range of IT providers. It was one of the first companies in Europe to become a HP Cloud Agile partner., using HP blade servers and HP 3PAR SAN technology to power its cloud computing services. The company's products also use VMware vCloud IaaS tools and it is taking part in the VMware lighthouse initiative helping develop the next generation of VMware products and services. Other technology companies that Carrenza has worked closely with include Cisco, for enterprise security and loadblancing services, and Oracle. The company was the first to deploy Oracle Database 11g stretched RAC in production. It has also won two Oracle partner awards, including a Special Recognition award for its work with Comic Relief. The company has also been recognised by the UK IT Industry, receiving awards in 2009 for Community Project of the Year and in 2010 for best small business project for its Monopoly City Streets Work. Other companies that have partnered with Carrenza for their cloud-based IT services include Age UK, Haymarket Media Group, the World Wide Fund for Nature, Royal Bank of Scotland, eBay and Cineworld. == Accreditations == Carrenza's services are accredited for their compliance with several key international IT security and quality standards. These include: ISO27001:2005, Information Security Management System for all Carrenza services. UK Government G-Cloud, Carrenza has been awarded a place on the UK government's G-Cloud iii framework as an Infrastructure as a Service provider.
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Digital video effect

Digital video effects (DVEs) are visual effects that provide comprehensive live video image manipulation, in the same form as optical printer effects in film. DVEs differ from standard video switcher effects (often referred to as analog effects) such as wipes or dissolves, in that they deal primarily with resizing, distortion or movement of the image. Modern video switchers often contain internal DVE functionality. Modern DVE devices are incorporated in high-end broadcast video switchers. Early examples of DVE devices found in the broadcast post-production industry include the Ampex Digital Optics (ADO), Quantel DPE-5000, Vital Squeezoom, NEC E-Flex and the Abekas A5x series of DVEs. By 1988, Grass Valley Group caught up with the competition with their Kaleidoscope, which integrated ADO-type effects with their widely used line of broadcast switching gear. DVEs are used by the broadcast television industry in live television production environments like television studios and outside broadcasts. They are commonly used in video post-production.
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Swizzling (computer graphics)

In computer graphics, swizzles are a class of operations that transform vectors by rearranging components. Swizzles can also project from a vector of one dimensionality to a vector of another dimensionality, such as taking a three-dimensional vector and creating a two-dimensional or five-dimensional vector using components from the original vector. For example, if A = {1,2,3,4}, where the components are x, y, z, and w respectively, one could compute B = A.wwxy, whereupon B would equal {4,4,1,2}. Additionally, one could create a two-dimensional vector with A.wx or a five-dimensional vector with A.xyzwx. Combining vectors and swizzling can be employed in various ways. This is common in GPGPU applications. In terms of linear algebra, this is equivalent to multiplying by a matrix whose rows are standard basis vectors. If A = ( 1 , 2 , 3 , 4 ) T {\displaystyle A=(1,2,3,4)^{T}} , then swizzling A {\displaystyle A} as above looks like A . w w x y = [ 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 ] [ 1 2 3 4 ] = [ 4 4 1 2 ] . {\displaystyle A.\!wwxy={\begin{bmatrix}0&0&0&1\\0&0&0&1\\1&0&0&0\\0&1&0&0\end{bmatrix}}{\begin{bmatrix}1\\2\\3\\4\end{bmatrix}}={\begin{bmatrix}4\\4\\1\\2\end{bmatrix}}.}
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