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Collectanea Mathematica-Collectanea Mathematica-Collectanea Mathematica (Collect. Math.) is a mathematical journal of the Institute of Mathematics of the University of Barcelona (IMUB), published by Springer since 2011, with a periodicity of three issues per year. It publishes original research papers in all fields of ... | milkshake721/2.1M-wiki-STEM |
Collectanea Mathematica-History-Collectanea Mathematica was founded in 1948 by José M. Orts (it is the oldest mathematical journal in Spain). Thanks to the contribution of some relevant mathematicians in Catalonia, like Ferran Sunyer Balaguer, and eminent international collaborators (Wilhelm Blaschke, Hugo Hadwiger, Ga... | milkshake721/2.1M-wiki-STEM |
Collectanea Mathematica-Abstracting and indexing-Collectanea Mathematica is indexed in databases such as Current Contents (Physical Chemical and Earth Sciences) and ISI Web of Science, MathSciNet, Zentralblatt MATH, and Scopus. | milkshake721/2.1M-wiki-STEM |
Barwise compactness theorem-Barwise compactness theorem-In mathematical logic, the Barwise compactness theorem, named after Jon Barwise, is a generalization of the usual compactness theorem for first-order logic to a certain class of infinitary languages. It was stated and proved by Barwise in 1967. | milkshake721/2.1M-wiki-STEM |
Barwise compactness theorem-Statement-Let A be a countable admissible set. Let L be an A -finite relational language. Suppose Γ is a set of LA -sentences, where Γ is a Σ1 set with parameters from A , and every A -finite subset of Γ is satisfiable. Then Γ is satisfiable. | milkshake721/2.1M-wiki-STEM |
Minkowski problem for polytopes-Minkowski problem for polytopes-In the geometry of convex polytopes, the Minkowski problem for polytopes concerns the specification of the shape of a polytope by the directions and measures of its facets. The theorem that every polytope is uniquely determined up to translation by this in... | milkshake721/2.1M-wiki-STEM |
Minkowski problem for polytopes-Specification and necessary conditions-For any d -dimensional polytope, one can specify its collection of facet directions and measures by a finite set of d -dimensional nonzero vectors, one per facet, pointing perpendicularly outward from the facet, with length equal to the (d−1) -di... | milkshake721/2.1M-wiki-STEM |
Minkowski problem for polytopes-Minkowski's uniqueness theorem-It is a theorem of Hermann Minkowski that these necessary conditions are sufficient: every finite set of vectors that spans the whole space, has no two parallel with the same sign, and sums to zero describes the facet directions and measures of a polytope. ... | milkshake721/2.1M-wiki-STEM |
Minkowski problem for polytopes-Blaschke sums-The sets of vectors representing two polytopes can be added by taking the union of the two sets and, when the two sets contain parallel vectors with the same sign, replacing them by their sum. The resulting operation on polytope shapes is called the Blaschke sum. It can be ... | milkshake721/2.1M-wiki-STEM |
Minkowski problem for polytopes-Generalizations-With certain additional information (including separating the facet direction and size into a unit vector and a real number, which may be negative, providing an additional bit of information per facet) it is possible to generalize these existence and uniqueness results to... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Union-closed sets conjecture-The union-closed sets conjecture is an open problem in combinatorics posed by Péter Frankl in 1979. A family of sets is said to be union-closed if the union of any two sets from the family belongs to the family. The conjecture states: For every finite union-clos... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Union-closed sets conjecture-Professor Timothy Gowers has called this "one of the best known open problems in combinatorics" and has said that the conjecture "feels as though it ought to be easy (and as a result has attracted a lot of false proofs over the years). A good way to understand w... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Example-The family of setsconsists of five different sets and is union-closed. The element 1 is contained in three of the five sets (and so is the element 2 ), thus the conjecture holds in this case. | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Basic results-It is easy to show that if a union-closed family contains a singleton {a} (as in the example above), then the element a must occur in at least half of the sets of the family. | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Basic results-If there is a counterexample to the conjecture, then there is also a counterexample consisting only of finite sets. Therefore, without loss of generality, we will assume that all sets in the given union-closed family are finite.Given a finite non-empty set U , the power set ... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Equivalent forms-Intersection formulation The union-closed set conjecture is true if and only if a set system X which is intersection-closed contains an element of U(X) in at most half of the sets of X , where U(X) is the universe set, i.e. the union of all members of the system X The ... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Equivalent forms-We define the complement of the set system X as := {U(X)−S:S∈X} . Let X1 , X2 be arbitrary sets in X and so U(X)−X1 and U(X)−X2 are both in Xc . Since X is union-closed, X1∪X2=X3 is in X , and therefore the complement of X3 , U(X)−X3 is in Xc , the elements i... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Equivalent forms-Secondly, we show that if a set system contains an element in at least half the sets, then its complement has an element in at most half.
Lemma 2. A set system X contains an element in half of its sets if and only if the complement set system X , X∗ contains an element i... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Equivalent forms-Therefore, if X is a union-closed family of sets, the family of complement sets to sets in X relative to the universe U(X) , is closed under intersection, and an element that belongs to at least half of the sets of X belongs to at most half of the complement sets. Thus,... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Equivalent forms-Lattice formulation Although stated above in terms of families of sets, Frankl's conjecture has also been formulated and studied as a question in lattice theory. A lattice is a partially ordered set in which for two elements x and y there is a unique greatest element less t... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Equivalent forms-The lattice-theoretic version of Frankl's conjecture is that in any finite lattice there exists an element x that is not the join of any two smaller elements, and such that the number of elements greater than or equal to x totals at most half the lattice, with equality only... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Equivalent forms-Graph-theoretic formulation Another equivalent formulation of the union-closed sets conjecture uses graph theory. In an undirected graph, an independent set is a set of vertices no two of which are adjacent to each other; an independent set is maximal if it is not a subset ... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Partial results-The conjecture has been proven for many special cases of union-closed set families. In particular, it is known to be true for families of at most 46 sets.
families of sets whose union has at most 11 elements.
families of sets in which the smallest set has one or two elements... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Partial results-families of at least (12−ε)2n subsets of an n -element set, for some constant ε>0 , according to an unpublished preprint.In November 2022, a preprint was posted claiming a proof of the following statement: For every union-closed family, other than the family containing on... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-Partial results-The proof used probabilistic and entropy methods to obtain such a bound. A conjecture within this paper implied a possible improvement to a lower bound fraction of 0.38197 . The union-closed sets conjecture itself corresponds to the fraction 0.5 . A few days later, three ... | milkshake721/2.1M-wiki-STEM |
Union-closed sets conjecture-History-Péter Frankl stated the conjecture in terms of intersection-closed set families in 1979, and so the conjecture is usually credited to him and is sometimes referred to as the Frankl conjecture. The earliest publication of the union-closed version of the conjecture appears to be by Du... | milkshake721/2.1M-wiki-STEM |
Scatterplot smoothing-Scatterplot smoothing-In statistics, several scatterplot smoothing methods are available to fit a function through the points of a scatterplot to best represent the relationship between the variables. | milkshake721/2.1M-wiki-STEM |
Scatterplot smoothing-Scatterplot smoothing-Scatterplots may be smoothed by fitting a line to the data points in a diagram. This line attempts to display the non-random component of the association between the variables in a 2D scatter plot. Smoothing attempts to separate the non-random behaviour in the data from the r... | milkshake721/2.1M-wiki-STEM |
Scatterplot smoothing-Scatterplot smoothing-A straight line (simple linear regression) A quadratic or a polynomial curve Local regression Smoothing splinesThe smoothing curve is chosen so as to provide the best fit in some sense, often defined as the fit that results in the minimum sum of the squared errors (a least sq... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Theta criterion-The theta-criterion (also named θ-criterion) is a constraint on x-bar theory that was first proposed by Noam Chomsky (1981) as a rule within the system of principles of the government and binding theory, called theta-theory (θ-theory). As theta-theory is concerned with the distribution a... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Applied-Theta grid A theta-role is a status of thematic relation (Chomsky 1981, p. 35). In other words, a theta-role describes the connection of meaning between a predicate or a verb and a constituent selected by this predicate. The number, types and positions of theta-roles that a lexicon assigns is en... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Applied-In the example below the verb 'love' has two theta-roles to assign: agent (the entity who loves) and theme (the entity being loved). In accordance with the theta-criterion, each theta-role must have its argument counterpart.
In Example 1a, Megan and Kevin are the arguments that the verb assigns ... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Applied-Example 1b is ungrammatical (marked with *) because there are more theta-roles available than there are arguments. The theta-role theme does not have an argument matched to it. On the other hand, in example (1c), there are more arguments than theta-roles. Both theta-roles are matched to argument... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Applied-Consequence on movement Since trace transmits theta-role, movements resulting in non-local relations between theta-role assigners and receivers in surface structure don't violate theta-criterion. This allows us to generate sentences with DP-raising, head movement, wh-movement, etc. However, if a... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-Transitivity Verbs that can be either transitive or intransitive at the first glance could present a problem for the theta-criterion. For a transitive verb, such as "hit," we assign the theta-roles agent and theme to the arguments, as shown in (2b), (2c), and (2d): The action of hitting he... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-For an intransitive verb, such as "arrive," we assign the theta-role theme to the sole argument, since "Mary" is the one that undergoes the action: The theta-criterion assigns the theta-role in the underlying structure, as shown by (3c). The past-tense morpheme then requires a subject at t... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-A verb like "eat" can choose to take an object, as shown in (4): For this type of verb, the potential object is usually semantically limited and therefore can be inferred from the verb at a default value (Rice 1988, pp. 203–4). For instance, for (4a), the listener/reader automatically assu... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-Below is an example containing PRO in a sentence: (5) a. Jeani is likely [ti to leave].
b. Jean is reluctant [PRO to leave].
(Carnie 2012, p. 430 (1)) Example (5a) is a raising sentence, and in contrast, (5b) is a control sentence, meaning it does not involve any DP movement. The PRO, whic... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-(Carnie 2012, p. 430 (4) Similarly, example (6a) is a raising-to-object sentence; "Brian" raises to the object position of the verb want. In contrast, (6b) is an object control sentence.(Carnie 2012, p. 430) The verb persuade has three theta-roles to assign: "agent" to Jean, "theme" to Bri... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-pro pro, also known as little pro, is an empty category that occurs in a subject or object position of a finite clause (finite clauses must contain a verb which shows tense) in languages like Italian, Spanish, Portuguese, Chinese, and some Arabic dialects (Jaeggli & Safir 1989; Rizzi 1986)... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-A good psychoanalyst can give help to oneself.
'A good psychoanalyst can give help to themselves'.
(Adapted from Rizzi (1986, p. 504 (13b))) When the reflexive pronoun se stessi 'themselves' doesn't have a proper antecedent to co-refer to, the sentence can't be grammatical. This indicates ... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-(Jones 1988, p. 89 (1a)) Such a structure posed a problem for theta-criterion because normally the verb assigns only one theta-role, theme, which is already taken by the DP, "John." The sentence should be thus predicted ill-formed. To explain the phenomenon, one way is to re-categorize suc... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-(Jones 1988, p. 91 (5a)) Or John underwent a gruesome death. If the verb "die" is essentially similar to the operation-verb "meet," the cognate objects should be assigned a theta-role—one restricted to the nominal form of the verb head (Jones 1988). In other words, "die" is now classified ... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-(10) a. A gruesome death was met by John.
b. *A gruesome death was died by John.
(Jones 1988, p. 91 (6a), p=92 (11a)) As we can no longer consider verbs that take cognate objects the same as potentially transitive verbs, Jones (1988) argues, based on the framework of Zubizarreta (1982), th... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Special cases-Deverbal nouns Deverbal nouns are derived from verbs and thus assign theta-roles as their verb stems do. For example, (12) (i) the barbarians' destruction of Rome (ii) Rome's destruction (by the barbarians) (iii) the destruction of Rome (by the barbarians) (iv) *the barbarian's destruction... | milkshake721/2.1M-wiki-STEM |
Theta criterion-Alternative approaches-Theta-criterion experienced its golden age in the 1980s when people discussed its application to various languages and structures and developed many other theories from it. However, after the minimalist program challenged some cornerstones of government and binding theory, people ... | milkshake721/2.1M-wiki-STEM |
Emerald-Emerald-Emerald is a gemstone and a variety of the mineral beryl (Be3Al2(SiO3)6) colored green by trace amounts of chromium or sometimes vanadium. Beryl has a hardness of 7.5–8 on the Mohs scale. Most emeralds have lots of material trapped inside during the gem's formation, so their toughness (resistance to bre... | milkshake721/2.1M-wiki-STEM |
Emerald-Etymology-The word "emerald" is derived (via Old French: esmeraude and Middle English: emeraude), from Vulgar Latin: esmaralda/esmaraldus, a variant of Latin smaragdus, which was via Ancient Greek: σμάραγδος (smáragdos; "green gem") from a Semitic language. According to Webster's Dictionary the term emerald was... | milkshake721/2.1M-wiki-STEM |
Emerald-Properties determining value-Emeralds, like all colored gemstones, are graded using four basic parameters known as "the four Cs": color, clarity, cut and carat weight. Normally, in the grading of colored gemstones, color is by far the most important criterion. However, in the grading of emeralds, clarity is con... | milkshake721/2.1M-wiki-STEM |
Emerald-Properties determining value-Color In gemology, color is divided into three components: hue, saturation, and tone. Emeralds occur in hues ranging from yellow-green to blue-green, with the primary hue necessarily being green. Yellow and blue are the normal secondary hues found in emeralds. Only gems that are med... | milkshake721/2.1M-wiki-STEM |
Emerald-Properties determining value-Clarity Emeralds tend to have numerous inclusions and surface-breaking fissures. Unlike diamonds, where the loupe standard (i.e., 10× magnification) is used to grade clarity, emeralds are graded by eye. Thus, if an emerald has no visible inclusions to the eye (assuming normal visual... | milkshake721/2.1M-wiki-STEM |
Emerald-Properties determining value-Treatments Most emeralds are oiled as part of the post-lapidary process, in order to fill in surface-reaching cracks so that clarity and stability are improved. Cedar oil, having a similar refractive index, is often used in this widely adopted practice. Other liquids, including synt... | milkshake721/2.1M-wiki-STEM |
Emerald-Emerald mines-Emeralds in antiquity were mined in Ancient Egypt at locations on Mount Smaragdus since 1500 BC, and India and Austria since at least the 14th century AD. The Egyptian mines were exploited on an industrial scale by the Roman and Byzantine Empires, and later by Islamic conquerors. Mining in Egypt c... | milkshake721/2.1M-wiki-STEM |
Emerald-Emerald mines-Zambia is the world's second biggest producer, with its Kafubu River area deposits (Kagem Mines) about 45 km (28 mi) southwest of Kitwe responsible for 20% of the world's production of gem-quality stones in 2004. In the first half of 2011, the Kagem Mines produced 3.74 tons of emeralds.Emeralds ar... | milkshake721/2.1M-wiki-STEM |
Emerald-Emerald mines-Origin determinations Since the onset of concerns regarding diamond origins, research has been conducted to determine if the mining location could be determined for an emerald already in circulation. Traditional research used qualitative guidelines such as an emerald's color, style and quality of ... | milkshake721/2.1M-wiki-STEM |
Emerald-Synthetic emerald-Both hydrothermal and flux-growth synthetics have been produced, and a method has been developed for producing an emerald overgrowth on colorless beryl. The first commercially successful emerald synthesis process was that of Carroll Chatham, likely involving a lithium vanadate flux process, as... | milkshake721/2.1M-wiki-STEM |
Emerald-Synthetic emerald-Synthetic emeralds are often referred to as "created", as their chemical and gemological composition is the same as their natural counterparts. The U.S. Federal Trade Commission (FTC) has very strict regulations as to what can and what cannot be called a "synthetic" stone. The FTC says: "§ 23.... | milkshake721/2.1M-wiki-STEM |
Emerald-In culture and lore-Emerald is regarded as the traditional birthstone for May as well as the traditional gemstone for the astrological sign of Cancer (June/July) Traditional alchemical lore ascribes several uses and characteristics to emeralds: The virtue of the Emerald is to counteract poison. They say that if... | milkshake721/2.1M-wiki-STEM |
Emerald-In culture and lore-According to French writer Brantôme (c. 1540-1614) Hernán Cortés had one of the emeralds which he had looted from Mexico text engraved, Inter Natos Mulierum non surrexit major ("Among those born of woman there hath not arisen a greater," Matthew 11:11), in reference to John the Baptist. Bran... | milkshake721/2.1M-wiki-STEM |
Emerald-In culture and lore-The chief deity of one of India's most famous temples, the Meenakshi Amman Temple in Madurai, is the goddess Meenakshi, whose idol is traditionally thought to be made of emerald. | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-High Efficiency Video Coding-High Efficiency Video Coding (HEVC), also known as H.265 and MPEG-H Part 2, is a video compression standard designed as part of the MPEG-H project as a successor to the widely used Advanced Video Coding (AVC, H.264, or MPEG-4 Part 10). In comparison to AVC, HEVC... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-High Efficiency Video Coding-While AVC uses the integer discrete cosine transform (DCT) with 4×4 and 8×8 block sizes, HEVC uses both integer DCT and discrete sine transform (DST) with varied block sizes between 4×4 and 32×32. The High Efficiency Image Format (HEIF) is based on HEVC. | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Concept-In most ways, HEVC is an extension of the concepts in H.264/MPEG-4 AVC. Both work by comparing different parts of a frame of video to find areas that are redundant, both within a single frame and between consecutive frames. These redundant areas are then replaced with a short descri... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Concept-HEVC was standardized by the Joint Collaborative Team on Video Coding (JCT-VC), a collaboration between the ISO/IEC MPEG and ITU-T Study Group 16 VCEG. The ISO/IEC group refers to it as MPEG-H Part 2 and the ITU-T as H.265. The first version of the HEVC standard was ratified in Janu... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Concept-The combined licensing fees currently offered by all of the patent licensing bodies are higher than for AVC. The licensing fees are one of the main reasons HEVC adoption has been low on the web and is why some of the largest tech companies (Amazon, AMD, Apple, ARM, Cisco, Google, In... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-History-The HEVC format was jointly developed by more than a dozen organisations across the world. The majority of active patent contributions towards the development of the HEVC format came from five organizations: Samsung Electronics (4,249 patents), General Electric (1,127 patents), M&K ... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-History-Previous work In 2004, the ITU-T Video Coding Experts Group (VCEG) began a major study of technology advances that could enable creation of a new video compression standard (or substantial compression-oriented enhancements of the H.264/MPEG-4 AVC standard). In October 2004, various ... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-History-Joint Collaborative Team on Video Coding MPEG and VCEG established a Joint Collaborative Team on Video Coding (JCT-VC) to develop the HEVC standard. | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-History-Standardization A formal joint Call for Proposals on video compression technology was issued in January 2010 by VCEG and MPEG, and proposals were evaluated at the first meeting of the MPEG & VCEG Joint Collaborative Team on Video Coding (JCT-VC), which took place in April 2010. A to... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-History-Patent licensing On September 29, 2014, MPEG LA announced their HEVC license which covers the essential patents from 23 companies. The first 100,000 "devices" (which includes software implementations) are royalty free, and after that the fee is $0.20 per device up to an annual cap o... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-History-Patent holders The following organizations currently hold the most active patents in the HEVC patent pools listed by MPEG LA and HEVC Advance: Versions Versions of the HEVC/H.265 standard using the ITU-T approval dates.
Version 1: (April 13, 2013) First approved version of the HEVC/... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-2012 On February 29, 2012, at the 2012 Mobile World Congress, Qualcomm demonstrated a HEVC decoder running on an Android tablet, with a Qualcomm Snapdragon S4 dual-core processor running at 1.5 GHz, showing H.264/MPEG-4 AVC and HEVC versions of the same video co... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-2013 On February 11, 2013, researchers from MIT demonstrated the world's first published HEVC ASIC decoder at the International Solid-State Circuits Conference (ISSCC) 2013. Their chip was capable of decoding a 3840×2160p at 30 fps video stream in real time, con... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-2014 On April 5, 2014, at the NAB show, eBrisk Video, Inc. and Altera Corporation demonstrated an FPGA-accelerated HEVC Main10 encoder that encoded 4Kp60/10-bit video in real-time, using a dual-Xeon E5-2697-v2 platform.On August 13, 2014, Ittiam Systems announce... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-2015 On January 5, 2015, ViXS Systems announced the XCode 6800 which is the first SoC to support the Main 12 profile of HEVC.On January 5, 2015, Nvidia officially announced the Tegra X1 SoC with full fixed-function HEVC hardware decoding.On January 22, 2015, Nvi... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-On March 31, 2015, VITEC announced the MGW Ace which was the first 100% hardware-based portable HEVC encoder that provides mobile HEVC encoding.On August 5, 2015, Intel launched Skylake products with full fixed function Main/8-bit decoding/encoding and hybrid/pa... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-2016 On April 11, 2016, full HEVC (H.265) support was announced in the newest MythTV version (0.28).On August 30, 2016, Intel officially announced 7th generation Core CPUs (Kaby Lake) products with full fixed function HEVC Main10 hardware decoding support.On Sep... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-2017 On June 5, 2017, Apple announced HEVC H.265 support in macOS High Sierra, iOS 11, tvOS, HTTP Live Streaming and Safari.On June 25, 2017, Microsoft released a free HEVC app extension for Windows 10, enabling some Windows 10 devices with HEVC decoding hardwar... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-On September 28, 2017, GoPro released the Hero6 Black action camera, with 4K60P HEVC video encoding.On October 17, 2017, Microsoft removed HEVC decoding support from Windows 10 with the Version 1709 Fall Creators Update, making HEVC available instead as a separa... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-2018 On September 20, 2018, Nvidia released the GeForce RTX 2080 (TU104), which includes full fixed function HEVC Main 4:4:4 12 hardware decoder.
2022 On October 25, 2022, Chrome released version 107, which starts supporting HEVC hardware decoding for all platfo... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Implementations and products-Browser support HEVC is implemented in these web browsers: Android browser (since version 5 from November 2014) Safari (since version 11 from September 2017) Edge (since version 77 from July 2017, supported on Windows 10 1709+ for devices with supported hardware... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Coding efficiency-The design of most video coding standards is primarily aimed at having the highest coding efficiency. Coding efficiency is the ability to encode video at the lowest possible bit rate while maintaining a certain level of video quality. There are two standard ways to measure... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Coding efficiency-In a video encoder comparison released in December 2013, the HM-10.0 HEVC encoder was compared with the x264 encoder (version r2334) and the VP9 encoder (version v1.2.0-3088-ga81bd12). The comparison used the Bjøntegaard-Delta bit-rate (BD-BR) measurement method, in which ... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Coding efficiency-In a subjective video performance comparison released in May 2014, the JCT-VC compared the HEVC Main profile to the H.264/MPEG-4 AVC High profile. The comparison used mean opinion score values and was conducted by the BBC and the University of the West of Scotland. The vid... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-HEVC was designed to substantially improve coding efficiency compared with H.264/MPEG-4 AVC HP, i.e. to reduce bitrate requirements by half with comparable image quality, at the expense of increased computational complexity. HEVC was designed with the goal of allowing video content... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Video coding layer The HEVC video coding layer uses the same "hybrid" approach used in all modern video standards, starting from H.261, in that it uses inter-/intra-picture prediction and 2D transform coding. A HEVC encoder first proceeds by splitting a picture into block shaped re... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Color spacesThe HEVC standard supports color spaces such as generic film, NTSC, PAL, Rec. 601, Rec. 709, Rec. 2020, Rec. 2100, SMPTE 170M, SMPTE 240M, sRGB, sYCC, xvYCC, XYZ, and externally specified color spaces. HEVC supports color encoding representations such as RGB, YCbCr, and... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Coding tools Coding tree unit HEVC replaces 16×16 pixel macroblocks, which were used with previous standards, with coding tree units (CTUs) which can use larger block structures of up to 64×64 samples and can better sub-partition the picture into variable sized structures. HEVC ini... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Inverse transforms HEVC specifies four transform units (TUs) sizes of 4×4, 8×8, 16×16, and 32×32 to code the prediction residual. A CTB may be recursively partitioned into 4 or more TUs. TUs use integer basis functions based on the discrete cosine transform (DCT). In addition, 4×4 ... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Parallel processing tools Tiles allow for the picture to be divided into a grid of rectangular regions that can independently be decoded/encoded. The main purpose of tiles is to allow for parallel processing. Tiles can be independently decoded and can even allow for random access t... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Wavefront parallel processing (WPP) is when a slice is divided into rows of CTUs in which the first row is decoded normally but each additional row requires that decisions be made in the previous row. WPP has the entropy encoder use information from the preceding row of CTUs and al... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Tiles and WPP are allowed, but are optional. If tiles are present, they must be at least 64 pixels high and 256 pixels wide with a level specific limit on the number of tiles allowed. | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Slices can, for the most part, be decoded independently from each other with the main purpose of tiles being the re-synchronization in case of data loss in the video stream. Slices can be defined as self-contained in that prediction is not made across slice boundaries. When in-loop... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Dependent slices can allow for data related to tiles or WPP to be accessed more quickly by the system than if the entire slice had to be decoded. The main purpose of dependent slices is to allow for low-delay video encoding due to its lower latency. | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Other coding tools Entropy codingHEVC uses a context-adaptive binary arithmetic coding (CABAC) algorithm that is fundamentally similar to CABAC in H.264/MPEG-4 AVC. CABAC is the only entropy encoder method that is allowed in HEVC while there are two entropy encoder methods allowed ... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Intra predictionHEVC specifies 33 directional modes for intra prediction compared with the 8 directional modes for intra prediction specified by H.264/MPEG-4 AVC. HEVC also specifies DC intra prediction and planar prediction modes. The DC intra prediction mode generates a mean valu... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Motion compensationFor the interpolation of fractional luma sample positions HEVC uses separable application of one-dimensional half-sample interpolation with an 8-tap filter or quarter-sample interpolation with a 7-tap filter while, in comparison, H.264/MPEG-4 AVC uses a two-stage... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Motion vector predictionHEVC defines a signed 16-bit range for both horizontal and vertical motion vectors (MVs). This was added to HEVC at the July 2012 HEVC meeting with the mvLX variables. HEVC horizontal/vertical MVs have a range of −32768 to 32767 which given the quarter pixel... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Loop filters HEVC specifies two loop filters that are applied sequentially, with the deblocking filter (DBF) applied first and the sample adaptive offset (SAO) filter applied afterwards. Both loop filters are applied in the inter-picture prediction loop, i.e. the filtered image is ... | milkshake721/2.1M-wiki-STEM |
High Efficiency Video Coding-Features-Deblocking filterThe DBF is similar to the one used by H.264/MPEG-4 AVC but with a simpler design and better support for parallel processing. In HEVC the DBF only applies to a 8×8 sample grid while with H.264/MPEG-4 AVC the DBF applies to a 4×4 sample grid. DBF uses a 8×8 sample gr... | milkshake721/2.1M-wiki-STEM |
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