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Sequential auction	Revenue maximization	2. If the objects are sold by means of a sequence of open ascending auctions, then it is always optimal to sell the more valuable object first (assuming the objects' values are common knowledge).Moreover, budget constraints may arise endogenously. I.e, a bidding company may tell its representative "you may spend at most X on this auction", although the company itself has much more money to spend. Limiting the budget in advance gives the bidders some strategic advantages.
Sequential auction	Revenue maximization	When multiple objects are sold, budget constraints can have some other unanticipated consequences. For example, a reserve price can raise the seller's revenue even though it is set at such a low level that it is never binding in equilibrium.
Sequential auction	Composeable mechanisms	Sequential-auctions and simultaneous-auctions are both special case of a more general setting, in which the same bidders participate in several different mechanisms. Syrgkanis and Tardos suggest a general framework for efficient mechanism design with guaranteed good properties even when players participate in multiple mechanisms simultaneously or sequentially. The class of smooth mechanisms – mechanisms that generate approximately market clearing prices – result in high-quality outcome both in equilibrium and in learning outcomes in the full information setting, as well as in Bayesian equilibrium with uncertainty about participants. Smooth mechanisms compose well: smoothness locally at each mechanism implies global efficiency. For mechanisms where good performance requires that bidders do not bid above their value, weakly smooth mechanisms can be used, such as the Vickrey auction. They are approximately efficient under the no-overbidding assumption, and the weak smoothness property is also maintained by composition. Some of the results are valid also when participants have budget constraints.
Mitotic recombination	Mitotic recombination	Mitotic recombination is a type of genetic recombination that may occur in somatic cells during their preparation for mitosis in both sexual and asexual organisms. In asexual organisms, the study of mitotic recombination is one way to understand genetic linkage because it is the only source of recombination within an individual. Additionally, mitotic recombination can result in the expression of recessive genes in an otherwise heterozygous individual. This expression has important implications for the study of tumorigenesis and lethal recessive genes.
Mitotic recombination	Mitotic recombination	Mitotic homologous recombination occurs mainly between sister chromatids subsequent to replication (but prior to cell division). Inter-sister homologous recombination is ordinarily genetically silent. During mitosis the incidence of recombination between non-sister homologous chromatids is only about 1% of that between sister chromatids.
Mitotic recombination	Discovery	The discovery of mitotic recombination came from the observation of twin spotting in Drosophila melanogaster. This twin spotting, or mosaic spotting, was observed in D. melanogaster as early as 1925, but it was only in 1936 that Curt Stern explained it as a result of mitotic recombination. Prior to Stern's work, it was hypothesized that twin spotting happened because certain genes had the ability to eliminate the chromosome on which they were located. Later experiments uncovered when mitotic recombination occurs in the cell cycle and the mechanisms behind recombination.
Mitotic recombination	Occurrence	Mitotic recombination can happen at any locus but is observable in individuals that are heterozygous at a given locus. If a crossover event between non-sister chromatids affects that locus, then both homologous chromosomes will have one chromatid containing each genotype. The resulting phenotype of the daughter cells depends on how the chromosomes line up on the metaphase plate. If the chromatids containing different alleles line up on the same side of the plate, then the resulting daughter cells will appear heterozygous and be undetectable, despite the crossover event. However, if chromatids containing the same alleles line up on the same side, the daughter cells will be homozygous at that locus. This results in twin spotting, where one cell presents the homozygous recessive phenotype and the other cell has the homozygous wild type phenotype. If those daughter cells go on to replicate and divide, the twin spots will continue to grow and reflect the differential phenotype.
Mitotic recombination	Occurrence	Mitotic recombination takes place during interphase. It has been suggested that recombination takes place during G1, when the DNA is in its 2-strand phase, and replicated during DNA synthesis. It is also possible to have the DNA break leading to mitotic recombination happen during G1, but for the repair to happen after replication.
Mitotic recombination	Occurrence	Response to DNA damage In the budding yeast Saccharomyces cerevisiae, mutations in several genes needed for mitotic (and meiotic) recombination cause increased sensitivity to inactivation by radiation and/or genotoxic chemicals. For example, gene rad52 is required for mitotic recombination as well as meiotic recombination. Rad52 mutant yeast cells have increased sensitivity to killing by X-rays, methyl methanesulfonate and the DNA crosslinking agent 8-methoxypsoralen-plus-UV light, suggesting that mitotic recombinational repair is required for removal of the different DNA damages caused by these agents.
Mitotic recombination	Mechanisms	The mechanisms behind mitotic recombination are similar to those behind meiotic recombination. These include sister chromatid exchange and mechanisms related to DNA double strand break repair by homologous recombination such as single-strand annealing, synthesis-dependent strand annealing (SDSA), and gene conversion through a double-Holliday Junction intermediate or SDSA. In addition, non-homologous mitotic recombination is a possibility and can often be attributed to non-homologous end joining.
Mitotic recombination	Method	There are several theories on how mitotic crossover occurs. In the simple crossover model, the two homologous chromosomes overlap on or near a common Chromosomal fragile site (CFS). This leads to a double-strand break, which is then repaired using one of the two strands. This can lead to the two chromatids switching places. In another model, two overlapping sister chromatids form a double Holliday junction at a common repeat site and are later sheared in such a way that they switch places. In either model, the chromosomes are not guaranteed to trade evenly, or even to rejoin on opposite sides thus most patterns of cleavage do not result in any crossover event. Uneven trading introduces many of the deleterious effects of mitotic crossover.
Mitotic recombination	Method	Alternatively, a crossover can occur during DNA repair if, due to extensive damage, the homologous chromosome is chosen to be the template over the sister chromatid. This leads to gene synthesis since one copy of the allele is copied across from the homologous chromosome and then synthesized into the breach on the damaged chromosome. The net effect of this would be one heterozygous chromosome and one homozygous chromosome.
Mitotic recombination	Advantages and disadvantages	Mitotic crossover is known to occur in D. melanogaster, some asexually reproducing fungi and in normal human cells, where the event may allow normally recessive cancer-causing genes to be expressed and thus predispose the cell in which it occurs to the development of cancer. Alternately, a cell may become a homozygous mutant for a tumor-suppressing gene, leading to the same result. For example, Bloom's syndrome is caused by a mutation in RecQ helicase, which plays a role in DNA replication and repair. This mutation leads to high rates of mitotic recombination in mice, and this recombination rate is in turn responsible for causing tumor susceptibility in those mice. At the same time, mitotic recombination may be beneficial: it may play an important role in repairing double stranded breaks, and it may be beneficial to the organism if having homozygous dominant alleles is more functional than the heterozygous state. For use in experimentation with genomes in model organisms such as Drosophila melanogaster, mitotic recombination can be induced via X-ray and the FLP-FRT recombination system.
Penile implant	Penile implant	A penile implant is an implanted device intended for the treatment of erectile dysfunction, Peyronie's disease, ischemic priapism, deformity and any traumatic injury of the penis, and for phalloplasty or metoidioplasty, including in gender-affirming surgery. Men also opt for penile implants for aesthetic purposes. Men's satisfaction and sexual function is influenced by discomfort over genital size which leads to seek surgical and non-surgical solutions for penis alteration. Although there are many distinct types of implants, most fall into one of two categories: malleable and inflatable transplants.
Penile implant	History	The first modern prosthetic reconstruction of a penis is attributed to NA Borgus, a German physician who performed the first surgical attempts in 1936 on soldiers with traumatic amputations of the penis. He used rib cartilages as prosthetic material and reconstructed the genitals for both micturition and intercourse purposes. Willard E. Goodwin and William Wallace Scott were the first to describe the placement of synthetic penile implants using acrylic prosthesis in 1952. Silicone-based penile implants were developed by Harvey Lash and the first case series were published in 1964. The development of a high-grade silicone that is currently used in penile implants is credited to NASA. The prototypes of the contemporary inflatable and malleable penile implants were presented in 1973 during the annual meeting of the American Urological Association by two groups of physicians from Baylor University (Gerald Timm, William E. Bradley and F. Brantley Scott) and University of Miami (Michael P. Small and Hernan M. Carrion). Small and Carrion pioneered the popularization of semi-rigid penile implants with the introduction of Small-Carrion prosthesis (Mentor, USA) in 1975. Brantley Scott described the initial device as composed of two inflatable cylindrical bodies made up of silicone, a reservoir containing radiopaque fluid and two pumping units. The first generation products were marketed through American Medical Systems (AMS; currently Boston Scientific), with which Brantley Scott was associated. Many device updates have been released by AMS since the first generation implants. In 1983, Mentor (currently Coloplast) joined the market. In 2017, there were more than ten manufacturers of penile implants in the world, however only a few now remain in the market. The latest additions to the market are Zephyr Surgical Implants and Rigicon Innovative Urological Solutions. Zephyr Surgical Implants, along with penile implants for biological men, introduced the first line of inflatable and malleable penile implants designed for sex reassignment for trans men. In recent years, Rigicon Innovative Urological Solutions, a US-based company, has made significant advancements in the field of penile implants. In 2017, they released the 'Rigi10,' a malleable implant that expanded the market's options. Following this, in 2019, they introduced both the 'Infla10' series, which includes the Infla10 AX, Infla10 X, and Infla10 models, and the 'Rigi10 Hydrophilic.' These inflatable and hydrophilic-coated malleable models respectively were important additions to the range of penile implant technologies available. These advancements have contributed to the diversity and progress in the development of penile implants, offering patients more varied and tailored treatment solutions. According to analysis of the 5% Medicare Public Use Files from 2001 to 2010 approximately 3% of patients diagnosed with erectile dysfunction opt for penile implantation. Each year nearly 25,000 inflatable penile prostheses are implanted in the USA.The list shows penile implants available in the market in 2020.
Penile implant	Types	Malleable penile implant The malleable (also known as non-inflatable or semi-rigid) penile prosthesis is a pair of rods implanted into the corpora of the penis. The rods are hard, but 'malleable' in the sense that they can be adjusted manually into the erect position. There are two types of malleable implants: one that is made of silicone and does not have a rod inside, also called soft implants, and another with a silver or steel spiral wire core inside coated with silicone. Some of the models have trimmable tails intended for length adjustment. Currently, a variety of malleable penile implants are available worldwide.
Penile implant	Types	Inflatable penile implant The inflatable penile implant (IPP), more recently developed, is a set of inflatable cylinders and a pump system. Based on the differences in structure, there are two types of inflatable penile implants: two-piece and three-piece IPPs. Both types of inflatable devices are filled with sterile saline solution which is pumped into cylinders when in process. The cylinders are implanted into the cavernous body of the penis. The pump system is attached to the cylinders and placed in the scrotum. Three-piece implants have a separate large reservoir connected to the pump. The reservoir is commonly placed in the retropubic space (Retzius' space), however other locations have also been described, such as between the transverse muscle and rectus muscle. Three-piece implants provide more desirable rigidity and girth of the penis resembling natural erection. Additionally, due to the presence of a large reservoir, three-piece implants provide full flaccidity of the penis when deflated, thus bringing more comfort than two-piece inflatable and malleable implants.The saline solution is pumped manually from the reservoir into bilateral chambers of cylinders implanted in the shaft of the penis, which replaces the non- or minimally-functioning erectile tissue. This produces an erection. The glans of the penis, however, remains unaffected. Ninety to ninety-five percent of inflatable prostheses produce erections suitable for sexual intercourse. In the United States, the inflatable prosthesis has largely replaced the malleable one, due to its lower rate of infections, high device survival rate and 80–90% satisfaction rate.The first IPP prototype presented in 1975 by Scott and colleagues was a three-piece prosthesis (two cylinders, two pumps and a fluid reservoir). Since then, the IPP has undergone multiple modifications and improvements for device reliability and durability, including change in the chemical material used in implant manufacturing, using hydrophilic and antibiotic eluting coatings to reduce the rates of infections, introducing one-touch release etc. Surgical techniques used for the implantation of penile prostheses have also improved along with evolution of the device. Inflatable penile implants were one of the first interventions in urology where the "no-touch" surgical technique was introduced. This has significantly reduced the rates of post-operative infections.
Penile implant	Medical use	Erectile dysfunction In spite of recent rapid and extensive development of non-surgical management options for erectile dysfunction, especially novel targeted medications and gene therapy, the penile implants remain the mainstay and the gold standard choice for the treatment of erectile dysfunction refractory to oral medications and injectable therapy. Additionally, penile implants can be a relevant option for those with erectile dysfunction who wants to proceed with a permanent solution without medical therapy. Penile implants have been used for the treatment of erectile dysfunction with various etiologies, including vascular, cavernosal, neurogenic, psychological and post-surgical (e.g. prostatectomy). The American Urological Association recommends informing all men with erectile dysfunction about penile implants as a choice of treatment and discussing the potential outcomes with them.
Penile implant	Medical use	Penile deformity Penile implants can help recover the natural shape of the penis in various conditions that have led to penile deformity. These can be traumatic injuries, penile surgeries, disfiguring and fibrosing diseases of the penis, such as Peyronie's disease. In Peyronie's disease, the change in penile curvature affects normal sexual intercourse as well as causing erectile dysfunction due to disruption of blood flow in the cavernous bodies of the penis. Therefore, implantation of penile prosthesis in Peyronie's disease addresses several mechanisms involved in the pathophysiology of the disease.
Penile implant	Medical use	Female-to-male sex reassignment Although different models of penile prostheses have been reported to be implanted after phalloplasty procedures, with the first case described in 1978 by Pucket and Montie, the first penile implants designed and produced specifically for female-to-male gender reassignment surgery for trans men were introduced in 2015 by Zephyr Surgical Implants. Both malleable and inflatable models are available. These implants have more realistic shape with an ergonomic glans at the tip of the prosthesis. The inflatable model has an attached pump resembling a testicle. The prosthesis is implanted with a sturdy fixation on pubic bone. Another, thinner malleable implant is intended for metoidioplasty.
Penile implant	Outcomes	Satisfaction The overall satisfaction rate with penile implants reaches over 90%. Both self and partner-reported satisfaction rates are evaluated to assess the outcomes. It has been shown that implantation of inflatable penile prosthesis brings more patient and partner satisfaction than medication therapy with PDE5 inhibitors or intracavernosal injections. Satisfaction rates are reported to be higher with inflatable rather than malleable implants, but there are no difference between two-piece and three-piece devices. The most frequent reasons for dissatisfaction are reduced penis length and girth, failed expectations and difficulties with device use. Thus, it is vital to provide patients and their partners with detailed preoperative counselling and instructions.
Penile implant	Outcomes	Curvature correction 33% to 90% of cases of patients with Peyronie's disease that have had an inflatable PI procedure have successfully corrected their penile deformity. The residual curvature after penile implant placement usually requires intraoperative surgical intervention.
Penile implant	Complications	The most common complication associated with penile implant placement appears to be infections with reported rates of 1–3%. Both surgical site and device infections are reported. When the infection involves the penile implant itself, implant removal is required and irrigation of the cavities with antiseptic solutions. In this scenario, placement of a new implant is needed to avoid further tissue fibrosis and shortening of the penis. The rate of repeat surgeries or device replacements ranges from 6% to 13%. Other reported complications include perforation of the corpus cavernosum and urethra (0.1–3%), commonly occurring in patients with previous fibrosis, prosthesis erosion or extrusion, change in glans shape, hematoma, shortening of penis length, and device malfunction. Due to continuous improvement of surgical techniques and modifications of implants, complication rates have dramatically decreased over time.To overcome post-operative penile shortening and to increase the perceived length of the penis and patient satisfaction, ventral and dorsal phalloplasty procedures in combination with penile implants have been described. Modified glanulopexy has been proposed to prevent supersonic transporter deformity and glandular hypermobility which are possible complications of penile implants. Sliding techniques in which the penis is cut and elongated with penile implants have been performed in cases of severe penile shortening. However, these techniques had higher rates of complications and are currently avoided.
Singmaster's conjecture	Singmaster's conjecture	Singmaster's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times). It is clear that the only number that appears infinitely many times in Pascal's triangle is 1, because any other number x can appear only within the first x + 1 rows of the triangle.
Singmaster's conjecture	Statement	Let N(a) be the number of times the number a > 1 appears in Pascal's triangle. In big O notation, the conjecture is: N(a)=O(1).
Singmaster's conjecture	Known bound	Singmaster (1971) showed that log ⁡a). Abbot, Erdős, and Hanson (1974) (see References) refined the estimate to: log log log ⁡a).
Singmaster's conjecture	Known bound	The best currently known (unconditional) bound is log log log log log log ⁡a)3), and is due to Kane (2007). Abbot, Erdős, and Hanson note that conditional on Cramér's conjecture on gaps between consecutive primes that log ⁡a)2/3+ε) holds for every ε>0 Singmaster (1975) showed that the Diophantine equation (n+1k+1)=(nk+2) has infinitely many solutions for the two variables n, k. It follows that there are infinitely many triangle entries of multiplicity at least 6: For any non-negative i, a number a with six appearances in Pascal's triangle is given by either of the above two expressions with n=F2i+2F2i+3−1, k=F2iF2i+3−1, where Fj is the jth Fibonacci number (indexed according to the convention that F0 = 0 and F1 = 1). The above two expressions locate two of the appearances; two others appear symmetrically in the triangle with respect to those two; and the other two appearances are at (a1) and (aa−1).
Singmaster's conjecture	Elementary examples	2 appears just once; all larger positive integers appear more than once; 3, 4, 5 each appear two times; infinitely many appear exactly twice; all odd prime numbers appear two times; 6 appears three times, as do all central binomial coefficients except for 1 and 2; (it is in principle not excluded that such a coefficient would appear 5, 7 or more times, but no such example is known) all numbers of the form (p2) for prime p>3 appear four times; Infinitely many appear exactly six times, including each of the following: 120 120 120 119 16 16 14 10 10 7) 210 210 210 209 21 21 19 10 10 6) 1540 1540 1540 1539 56 56 54 22 22 19 ) 7140 7140 7140 7139 120 120 118 36 36 33 ) 11628 11628 11628 11627 153 153 151 19 19 14 ) 24310 24310 24310 24309 221 221 219 17 17 9) The next number in Singmaster's infinite family (given in terms of Fibonacci numbers), and the next smallest number known to occur six or more times, is 61218182743304701891431482520 104 39 104 65 103 40 103 63 ) The smallest number to appear eight times – indeed, the only number known to appear eight times – is 3003, which is also a member of Singmaster's infinite family of numbers with multiplicity at least 6: 3003 3003 78 15 14 14 15 10 78 76 3003 3002 ) It is not known whether infinitely many numbers appear eight times, nor even whether any other numbers than 3003 appear eight times.The number of times n appears in Pascal's triangle is ∞, 1, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 3, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 4, 2, 2, ... (sequence A003016 in the OEIS)By Abbott, Erdős, and Hanson (1974), the number of integers no larger than x that appear more than twice in Pascal's triangle is O(x1/2).
Singmaster's conjecture	Elementary examples	The smallest natural number (above 1) that appears (at least) n times in Pascal's triangle is 2, 3, 6, 10, 120, 120, 3003, 3003, ... (sequence A062527 in the OEIS)The numbers which appear at least five times in Pascal's triangle are 1, 120, 210, 1540, 3003, 7140, 11628, 24310, 61218182743304701891431482520, ... (sequence A003015 in the OEIS)Of these, the ones in Singmaster's infinite family are 1, 3003, 61218182743304701891431482520, ... (sequence A090162 in the OEIS)
Singmaster's conjecture	Open questions	It is not known whether any number appears more than eight times, nor whether any number besides 3003 appears that many times. The conjectured finite upper bound could be as small as 8, but Singmaster thought it might be 10 or 12. It is also unknown whether numbers appear exactly five or seven times.
H.262/MPEG-2 Part 2	H.262/MPEG-2 Part 2	H.262 or MPEG-2 Part 2 (formally known as ITU-T Recommendation H.262 and ISO/IEC 13818-2, also known as MPEG-2 Video) is a video coding format standardised and jointly maintained by ITU-T Study Group 16 Video Coding Experts Group (VCEG) and ISO/IEC Moving Picture Experts Group (MPEG), and developed with the involvement of many companies. It is the second part of the ISO/IEC MPEG-2 standard. The ITU-T Recommendation H.262 and ISO/IEC 13818-2 documents are identical.
H.262/MPEG-2 Part 2	H.262/MPEG-2 Part 2	The standard is available for a fee from the ITU-T and ISO. MPEG-2 Video is very similar to MPEG-1, but also provides support for interlaced video (an encoding technique used in analog NTSC, PAL and SECAM television systems). MPEG-2 video is not optimized for low bit-rates (e.g., less than 1 Mbit/s), but somewhat outperforms MPEG-1 at higher bit rates (e.g., 3 Mbit/s and above), although not by a large margin unless the video is interlaced. All standards-conforming MPEG-2 Video decoders are also fully capable of playing back MPEG-1 Video streams.
H.262/MPEG-2 Part 2	History	The ISO/IEC approval process was completed in November 1994. The first edition was approved in July 1995 and published by ITU-T and ISO/IEC in 1996. Didier LeGall of Bellcore chaired the development of the standard and Sakae Okubo of NTT was the ITU-T coordinator and chaired the agreements on its requirements.The technology was developed with contributions from a number of companies. Hyundai Electronics (now SK Hynix) developed the first MPEG-2 SAVI (System/Audio/Video) decoder in 1995.The majority of patents that were later asserted in a patent pool to be essential for implementing the standard came from three companies: Sony (311 patents), Thomson (198 patents) and Mitsubishi Electric (119 patents).In 1996, it was extended by two amendments to include the registration of copyright identifiers and the 4:2:2 Profile. ITU-T published these amendments in 1996 and ISO in 1997.There are also other amendments published later by ITU-T and ISO/IEC. The most recent edition of the standard was published in 2013 and incorporates all prior amendments.
H.262/MPEG-2 Part 2	Video coding	Picture sampling An HDTV camera with 8-bit sampling generates a raw video stream of 25 × 1920 × 1080 × 3 = 155,520,000 bytes per second for 25 frame-per-second video (using the 4:4:4 sampling format). This stream of data must be compressed if digital TV is to fit in the bandwidth of available TV channels and if movies are to fit on DVDs. Video compression is practical because the data in pictures is often redundant in space and time. For example, the sky can be blue across the top of a picture and that blue sky can persist for frame after frame. Also, because of the way the eye works, it is possible to delete or approximate some data from video pictures with little or no noticeable degradation in image quality.
H.262/MPEG-2 Part 2	Video coding	A common (and old) trick to reduce the amount of data is to separate each complete "frame" of video into two "fields" upon broadcast/encoding: the "top field", which is the odd numbered horizontal lines, and the "bottom field", which is the even numbered lines. Upon reception/decoding, the two fields are displayed alternately with the lines of one field interleaving between the lines of the previous field; this format is called interlaced video. The typical field rate is 50 (Europe/PAL) or 59.94 (US/NTSC) fields per second, corresponding to 25 (Europe/PAL) or 29.97 (North America/NTSC) whole frames per second. If the video is not interlaced, then it is called progressive scan video and each picture is a complete frame. MPEG-2 supports both options.
H.262/MPEG-2 Part 2	Video coding	Digital television requires that these pictures be digitized so that they can be processed by computer hardware. Each picture element (a pixel) is then represented by one luma number and two chroma numbers. These describe the brightness and the color of the pixel (see YCbCr). Thus, each digitized picture is initially represented by three rectangular arrays of numbers.
H.262/MPEG-2 Part 2	Video coding	Another common practice to reduce the amount of data to be processed is to subsample the two chroma planes (after low-pass filtering to avoid aliasing). This works because the human visual system better resolves details of brightness than details in the hue and saturation of colors. The term 4:2:2 is used for video with the chroma subsampled by a ratio of 2:1 horizontally, and 4:2:0 is used for video with the chroma subsampled by 2:1 both vertically and horizontally. Video that has luma and chroma at the same resolution is called 4:4:4. The MPEG-2 Video document considers all three sampling types, although 4:2:0 is by far the most common for consumer video, and there are no defined "profiles" of MPEG-2 for 4:4:4 video (see below for further discussion of profiles).
H.262/MPEG-2 Part 2	Video coding	While the discussion below in this section generally describes MPEG-2 video compression, there are many details that are not discussed, including details involving fields, chrominance formats, responses to scene changes, special codes that label the parts of the bitstream, and other pieces of information. Aside from features for handling fields for interlaced coding, MPEG-2 Video is very similar to MPEG-1 Video (and even quite similar to the earlier H.261 standard), so the entire description below applies equally well to MPEG-1.
H.262/MPEG-2 Part 2	Video coding	I-frames, P-frames, and B-frames MPEG-2 includes three basic types of coded frames: intra-coded frames (I-frames), predictive-coded frames (P-frames), and bidirectionally-predictive-coded frames (B-frames).
H.262/MPEG-2 Part 2	Video coding	An I-frame is a separately-compressed version of a single uncompressed (raw) frame. The coding of an I-frame takes advantage of spatial redundancy and of the inability of the eye to detect certain changes in the image. Unlike P-frames and B-frames, I-frames do not depend on data in the preceding or the following frames, and so their coding is very similar to how a still photograph would be coded (roughly similar to JPEG picture coding). Briefly, the raw frame is divided into 8 pixel by 8 pixel blocks. The data in each block is transformed by the discrete cosine transform (DCT). The result is an 8×8 matrix of coefficients that have real number values. The transform converts spatial variations into frequency variations, but it does not change the information in the block; if the transform is computed with perfect precision, the original block can be recreated exactly by applying the inverse cosine transform (also with perfect precision). The conversion from 8-bit integers to real-valued transform coefficients actually expands the amount of data used at this stage of the processing, but the advantage of the transformation is that the image data can then be approximated by quantizing the coefficients. Many of the transform coefficients, usually the higher frequency components, will be zero after the quantization, which is basically a rounding operation. The penalty of this step is the loss of some subtle distinctions in brightness and color. The quantization may either be coarse or fine, as selected by the encoder. If the quantization is not too coarse and one applies the inverse transform to the matrix after it is quantized, one gets an image that looks very similar to the original image but is not quite the same. Next, the quantized coefficient matrix is itself compressed. Typically, one corner of the 8×8 array of coefficients contains only zeros after quantization is applied. By starting in the opposite corner of the matrix, then zigzagging through the matrix to combine the coefficients into a string, then substituting run-length codes for consecutive zeros in that string, and then applying Huffman coding to that result, one reduces the matrix to a smaller quantity of data. It is this entropy coded data that is broadcast or that is put on DVDs. In the receiver or the player, the whole process is reversed, enabling the receiver to reconstruct, to a close approximation, the original frame.
H.262/MPEG-2 Part 2	Video coding	The processing of B-frames is similar to that of P-frames except that B-frames use the picture in a subsequent reference frame as well as the picture in a preceding reference frame. As a result, B-frames usually provide more compression than P-frames. B-frames are never reference frames in MPEG-2 Video. Typically, every 15th frame or so is made into an I-frame. P-frames and B-frames might follow an I-frame like this, IBBPBBPBBPBB(I), to form a Group Of Pictures (GOP); however, the standard is flexible about this. The encoder selects which pictures are coded as I-, P-, and B-frames.
H.262/MPEG-2 Part 2	Video coding	Macroblocks P-frames provide more compression than I-frames because they take advantage of the data in a previous I-frame or P-frame – a reference frame. To generate a P-frame, the previous reference frame is reconstructed, just as it would be in a TV receiver or DVD player. The frame being compressed is divided into 16 pixel by 16 pixel macroblocks. Then, for each of those macroblocks, the reconstructed reference frame is searched to find a 16 by 16 area that closely matches the content of the macroblock being compressed. The offset is encoded as a "motion vector". Frequently, the offset is zero, but if something in the picture is moving, the offset might be something like 23 pixels to the right and 4-and-a-half pixels up. In MPEG-1 and MPEG-2, motion vector values can either represent integer offsets or half-integer offsets. The match between the two regions will often not be perfect. To correct for this, the encoder takes the difference of all corresponding pixels of the two regions, and on that macroblock difference then computes the DCT and strings of coefficient values for the four 8×8 areas in the 16×16 macroblock as described above. This "residual" is appended to the motion vector and the result sent to the receiver or stored on the DVD for each macroblock being compressed. Sometimes no suitable match is found. Then, the macroblock is treated like an I-frame macroblock.
H.262/MPEG-2 Part 2	Video profiles and levels	MPEG-2 video supports a wide range of applications from mobile to high quality HD editing. For many applications, it is unrealistic and too expensive to support the entire standard. To allow such applications to support only subsets of it, the standard defines profiles and levels. A profile defines sets of features such as B-pictures, 3D video, chroma format, etc. The level limits the memory and processing power needed, defining maximum bit rates, frame sizes, and frame rates. A MPEG application then specifies the capabilities in terms of profile and level. For example, a DVD player may say it supports up to main profile and main level (often written as MP@ML). It means the player can play back any MPEG stream encoded as MP@ML or less. The tables below summarizes the limitations of each profile and level, though there are constraints not listed here.: Annex E Note that not all profile and level combinations are permissible, and scalable modes modify the level restrictions. A few common MPEG-2 Profile/Level combinations are presented below, with particular maximum limits noted:
H.262/MPEG-2 Part 2	Applications	Some applications are listed below. DVD-Video - a standard definition consumer video format. Uses 4:2:0 color subsampling and variable video data rate up to 9.8 Mbit/s. MPEG IMX - a standard definition professional video recording format. Uses intraframe compression, 4:2:2 color subsampling and user-selectable constant video data rate of 30, 40 or 50 Mbit/s. HDV - a tape-based high definition video recording format. Uses 4:2:0 color subsampling and 19.4 or 25 Mbit/s total data rate.
H.262/MPEG-2 Part 2	Applications	XDCAM - a family of tapeless video recording formats, which, in particular, includes formats based on MPEG-2 Part 2. These are: standard definition MPEG IMX (see above), high definition MPEG HD, high definition MPEG HD422. MPEG IMX and MPEG HD422 employ 4:2:2 color subsampling, MPEG HD employs 4:2:0 color subsampling. Most subformats use selectable constant video data rate from 25 to 50 Mbit/s, although there is also a variable bitrate mode with maximum 18 Mbit/s data rate.
H.262/MPEG-2 Part 2	Applications	XF Codec - a professional tapeless video recording format, similar to MPEG HD and MPEG HD422 but stored in a different container file. HD DVD - defunct high definition consumer video format. Blu-ray Disc - high definition consumer video format. Broadcast TV - in some countries MPEG-2 Part 2 is used for digital broadcast in high definition. For example, ATSC specifies both several scanning formats (480i, 480p, 720p, 1080i, 1080p) and frame/field rates at 4:2:0 color subsampling, with up to 19.4 Mbit/s data rate per channel. Digital cable TV Satellite TV
H.262/MPEG-2 Part 2	Patent holders	The following organizations have held patents for MPEG-2 video technology, as listed at MPEG LA. All of these patents are now expired.
Silver halide	Silver halide	A silver halide (or silver salt) is one of the chemical compounds that can form between the element silver (Ag) and one of the halogens. In particular, bromine (Br), chlorine (Cl), iodine (I) and fluorine (F) may each combine with silver to produce silver bromide (AgBr), silver chloride (AgCl), silver iodide (AgI), and four forms of silver fluoride, respectively. As a group, they are often referred to as the silver halides, and are often given the pseudo-chemical notation AgX. Although most silver halides involve silver atoms with oxidation states of +1 (Ag+), silver halides in which the silver atoms have oxidation states of +2 (Ag2+) are known, of which silver(II) fluoride is the only known stable one.
Silver halide	Silver halide	Silver halides are light-sensitive chemicals, and are commonly used in photographic film and paper.
Silver halide	Applications	Light sensitivity Silver halides are used in photographic film and photographic paper, including graphic art film and paper, where silver halide crystals in gelatin are coated on to a film base, glass or paper substrate. The gelatin is a vital part of the emulsion as the protective colloid of appropriate physical and chemical properties. The gelatin may also contain trace elements (such as sulfur) which increase the light sensitivity of the emulsion, although modern practice uses gelatin without such components. When a silver halide crystal is exposed to light, a sensitivity speck on the surface of the crystal is turned into a speck of metallic silver (these comprise the invisible or latent image). If the speck of silver contains approximately four or more atoms, it is rendered developable - meaning that it can undergo development which turns the entire crystal into metallic silver. Areas of the emulsion receiving larger amounts of light (reflected from a subject being photographed, for example) undergo the greatest development and therefore results in the highest optical density.
Silver halide	Applications	Silver bromide and silver chloride may be used separately or combined, depending on the sensitivity and tonal qualities desired in the product. Silver iodide is always combined with silver bromide or silver chloride, except in the case of some historical processes such as the collodion wet plate and daguerreotype, in which the iodide is sometimes used alone (generally regarded as necessary if a daguerreotype is to be developed by the Becquerel method, in which exposure to strong red light, which affects only the crystals bearing latent image specks, is substituted for exposure to mercury fumes). Silver fluoride is not used in photography.
Silver halide	Applications	The mechanism of the formation of the speck of metallic silver is as follows. When absorbed by an AgX crystal, photons cause electrons to be promoted to a conduction band (de-localized electron orbital with higher energy than a valence band) which can be attracted by a sensitivity speck, which is a shallow electron trap, which may be a crystalline defect or a cluster of silver sulfide, gold, other trace elements (dopant), or combination thereof, and then combined with an interstitial silver ion to form a silver metal speck.Silver halides are also used to make corrective lenses darken when exposed to ultraviolet light (see photochromism).
Silver halide	Applications	Chemistry Silver halides, except for silver fluoride, are very insoluble in water. Silver nitrate can be used to precipitate halides; this application is useful in quantitative analysis of halides. The three main silver halide compounds have distinctive colours that can be used to quickly identify halide ions in a solution. The silver chloride compound forms a white precipitate, silver bromide a creamy coloured precipitate and silver iodide a yellow coloured precipitate.
Silver halide	Applications	However, close attention is necessary for other compounds in the test solution. Some compounds can considerably increase or decrease the solubility of AgX. Examples of compounds that increase the solubility include: cyanide, thiocyanate, thiosulfate, thiourea, amines, ammonia, sulfite, thioether, crown ether. Examples of compounds that reduces the solubility include many organic thiols and nitrogen compounds that do not possess solubilizing group other than mercapto group or the nitrogen site, such as mercaptooxazoles, mercaptotetrazoles, especially 1-phenyl-5-mercaptotetrazole, benzimidazoles, especially 2-mercaptobenzimidazole, benzotriazole, and these compounds further substituted by hydrophobic groups. Compounds such as thiocyanate and thiosulfate enhance solubility when they are present in a sufficiently large quantity, due to formation of highly soluble complex ions, but they also significantly depress solubility when present in a very small quantity, due to formation of sparingly soluble complex ions.
Silver halide	Applications	Archival Use Silver Halide can be used to deposit fine details of metallic silver on surfaces, such as film. Because of the chemical stability of metallic silver, this can be used for archival purposes. For example, the Arctic World Archive uses film developed with Silver Halides to store data of historical and cultural interest, such as a snapshot of the Open Source code in all active GitHub repositories as of 2020. Medical technology and use Scientists from Tel Aviv University are experimenting with silver halide optical fibers for transmitting mid-infrared light from carbon dioxide lasers. The fibers allow laser welding of human tissue, as an alternative to traditional sutures.
Wide character	Wide character	A wide character is a computer character datatype that generally has a size greater than the traditional 8-bit character. The increased datatype size allows for the use of larger coded character sets.
Wide character	History	During the 1960s, mainframe and mini-computer manufacturers began to standardize around the 8-bit byte as their smallest datatype. The 7-bit ASCII character set became the industry standard method for encoding alphanumeric characters for teletype machines and computer terminals. The extra bit was used for parity, to ensure the integrity of data storage and transmission. As a result, the 8-bit byte became the de facto datatype for computer systems storing ASCII characters in memory.
Wide character	History	Later, computer manufacturers began to make use of the spare bit to extend the ASCII character set beyond its limited set of English alphabet characters. 8-bit extensions such as IBM code page 37, PETSCII and ISO 8859 became commonplace, offering terminal support for Greek, Cyrillic, and many others. However, such extensions were still limited in that they were region specific and often could not be used in tandem. Special conversion routines had to be used to convert from one character set to another, often resulting in destructive translation when no equivalent character existed in the target set.
Wide character	History	In 1989, the International Organization for Standardization began work on the Universal Character Set (UCS), a multilingual character set that could be encoded using either a 16-bit (2-byte) or 32-bit (4-byte) value. These larger values required the use of a datatype larger than 8-bits to store the new character values in memory. Thus the term wide character was used to differentiate them from traditional 8-bit character datatypes.
Wide character	Relation to UCS and Unicode	A wide character refers to the size of the datatype in memory. It does not state how each value in a character set is defined. Those values are instead defined using character sets, with UCS and Unicode simply being two common character sets that encode more characters than an 8-bit wide numeric value (255 total) would allow.
Wide character	Relation to multibyte characters	Just as earlier data transmission systems suffered from the lack of an 8-bit clean data path, modern transmission systems often lack support for 16-bit or 32-bit data paths for character data. This has led to character encoding systems such as UTF-8 that can use multiple bytes to encode a value that is too large for a single 8-bit symbol. The C standard distinguishes between multibyte encodings of characters, which use a fixed or variable number of bytes to represent each character (primarily used in source code and external files), from wide characters, which are run-time representations of characters in single objects (typically, greater than 8 bits).
Wide character	Size of a wide character	Early adoption of UCS-2 ("Unicode 1.0") led to common use of UTF-16 in a number of platforms, most notably Microsoft Windows, .NET and Java. In these systems, it is common to have a "wide character" (wchar_t in C/C++; char in Java) type of 16-bits. These types do not always map directly to one "character", as surrogate pairs are required to store the full range of Unicode (1996, Unicode 2.0).Unix-like generally use a 32-bit wchar_t to fit the 21-bit Unicode code point, as C90 prescribed.The size of a wide character type does not dictate what kind of text encodings a system can process, as conversions are available. (Old conversion code commonly overlook surrogates, however.) The historical circumstances of their adoption does also decide what types of encoding they prefer. A system influenced by Unicode 1.0, such as Windows, tends to mainly use "wide strings" made out of wide character units. Other systems such as the Unix-likes, however, tend to retain the 8-bit "narrow string" convention, using a multibyte encoding (almost universally UTF-8) to handle "wide" characters.
Wide character	Programming specifics	C/C++ The C and C++ standard libraries include a number of facilities for dealing with wide characters and strings composed of them. The wide characters are defined using datatype wchar_t, which in the original C90 standard was defined as "an integral type whose range of values can represent distinct codes for all members of the largest extended character set specified among the supported locales" (ISO 9899:1990 §4.1.5)Both C and C++ introduced fixed-size character types char16_t and char32_t in the 2011 revisions of their respective standards to provide unambiguous representation of 16-bit and 32-bit Unicode transformation formats, leaving wchar_t implementation-defined. The ISO/IEC 10646:2003 Unicode standard 4.0 says that: "The width of wchar_t is compiler-specific and can be as small as 8 bits. Consequently, programs that need to be portable across any C or C++ compiler should not use wchar_t for storing Unicode text. The wchar_t type is intended for storing compiler-defined wide characters, which may be Unicode characters in some compilers." Python According to Python 2.7's documentation, the language sometimes uses wchar_t as the basis for its character type Py_UNICODE. It depends on whether wchar_t is "compatible with the chosen Python Unicode build variant" on that system. This distinction has been deprecated since Python 3.3, which introduced a flexibly-sized UCS1/2/4 storage for strings and formally aliased Py_UNICODE to wchar_t.
Glomus cell	Glomus cell	Glomus cells are the cell type mainly located in the carotid bodies and aortic bodies. Glomus type I cells are peripheral chemoreceptors which sense the oxygen, carbon dioxide and pH levels of the blood. When there is a decrease in the blood's pH, a decrease in oxygen (pO2), or an increase in carbon dioxide (pCO2), the carotid bodies and the aortic bodies signal the dorsal respiratory group in the medulla oblongata to increase the volume and rate of breathing. The glomus cells have a high metabolic rate and good blood perfusion and thus are sensitive to changes in arterial blood gas tension. Glomus type II cells are sustentacular cells having a similar supportive function to glial cells.
Glomus cell	Structure	The signalling within the chemoreceptors is thought to be mediated by the release of neurotransmitters by the glomus cells, including dopamine, noradrenaline, acetylcholine, substance P, vasoactive intestinal peptide and enkephalins. Vasopressin has been found to inhibit the response of glomus cells to hypoxia, presumably because the usual response to hypoxia is vasodilation, which in case of hypovolemia should be avoided. Furthermore, glomus cells are highly responsive to angiotensin II through AT1 receptors, providing information about the body's fluid and electrolyte status.
Glomus cell	Function	Glomus type I cells are chemoreceptors which monitor arterial blood for the partial pressure of oxygen (pO2), partial pressure of carbon dioxide (pCO2) and pH. Glomus type I cells are secretory sensory neurons that release neurotransmitters in response to hypoxemia (low pO2), hypercapnia (high pCO2) or acidosis (low pH). Signals are transmitted to the afferent nerve fibers of the sinus nerve and may include dopamine, acetylcholine, and adenosine. This information is sent to the respiratory center and helps the brain to regulate breathing.
Glomus cell	Innervation	The glomus type I cells of the carotid body are innervated by the sensory neurons found in the inferior ganglion of the glossopharyngeal nerve. The carotid sinus nerve is the branch of the glossopharyngeal nerve which innervates them. Alternatively, the glomus type I cells of the aortic body are innervated by sensory neurons found in the inferior ganglion of the vagus nerve. Centrally the axons of neurons which innervate glomus type I cells synapse in the caudal portion of the solitary nucleus in the medulla. Glomus type II cells are not innervated.
Glomus cell	Development	Glomus type I cells are embryonically derived from the neural crest. In the carotid body the respiratory chemoreceptors need a period of time postnatally in order to reach functional maturity. This maturation period is known as resetting. At birth the chemorecptors express a low sensitivity for lack of oxygen but this increases over the first few days or weeks of life. The mechanisms underlying the postnatal maturity of chemotransduction are obscure.
Glomus cell	Clinical significance	Clusters of glomus cells, of which the carotid bodies and aortic bodies are the most important, are called non-chromaffin or parasympathetic paraganglia. They are also present along the vagus nerve, in the inner ears, in the lungs, and at other sites. Neoplasms of glomus cells are known as paraganglioma, among other names, they are generally non-malignant.
Glomus cell	Research	The autotransplantation of glomus cells of the carotid body into the striatum – a nucleus in the forebrain, has been investigated as a cell-based therapy for people with Parkinson's disease.
Immirzi parameter	Immirzi parameter	The Immirzi parameter (also known as the Barbero–Immirzi parameter) is a numerical coefficient appearing in loop quantum gravity (LQG), a nonperturbative theory of quantum gravity. The Immirzi parameter measures the size of the quantum of area in Planck units. As a result, its value is currently fixed by matching the semiclassical black hole entropy, as calculated by Stephen Hawking, and the counting of microstates in loop quantum gravity.
Immirzi parameter	The reality conditions	The Immirzi parameter arises in the process of expressing a Lorentz connection with noncompact group SO(3,1) in terms of a complex connection with values in a compact group of rotations, either SO(3) or its double cover SU(2). Although named after Giorgio Immirzi, the possibility of including this parameter was first pointed out by Fernando Barbero. The significance of this parameter remained obscure until the spectrum of the area operator in LQG was calculated. It turns out that the area spectrum is proportional to the Immirzi parameter.
Immirzi parameter	Black hole thermodynamics	In the 1970s Stephen Hawking, motivated by the analogy between the law of increasing area of black hole event horizons and the second law of thermodynamics, performed a semiclassical calculation showing that black holes are in equilibrium with thermal radiation outside them, and that black hole entropy (that is, the entropy of the black hole itself, not the entropy of the radiation in equilibrium with the black hole, which is infinite) equals S=A/4 (in Planck units)In 1997, Ashtekar, Baez, Corichi and Krasnov quantized the classical phase space of the exterior of a black hole in vacuum General Relativity. They showed that the geometry of spacetime outside a black hole is described by spin networks, some of whose edges puncture the event horizon, contributing area to it, and that the quantum geometry of the horizon can be described by a U(1) Chern–Simons theory. The appearance of the group U(1) is explained by the fact that two-dimensional geometry is described in terms of the rotation group SO(2), which is isomorphic to U(1). The relationship between area and rotations is explained by Girard's theorem relating the area of a spherical triangle to its angular excess.
Immirzi parameter	Black hole thermodynamics	By counting the number of spin-network states corresponding to an event horizon of area A, the entropy of black holes is seen to be S=γ0A/4γ. Here γ is the Immirzi parameter and either ln ⁡(2)/3π or ln ⁡(3)/8π, depending on the gauge group used in loop quantum gravity. So, by choosing the Immirzi parameter to be equal to γ0 , one recovers the Bekenstein–Hawking formula. This computation appears independent of the kind of black hole, since the given Immirzi parameter is always the same. However, Krzysztof Meissner and Marcin Domagala with Jerzy Lewandowski have corrected the assumption that only the minimal values of the spin contribute. Their result involves the logarithm of a transcendental number instead of the logarithms of integers mentioned above. The Immirzi parameter appears in the denominator because the entropy counts the number of edges puncturing the event horizon and the Immirzi parameter is proportional to the area contributed by each puncture.
Immirzi parameter	Immirzi parameter in spin foam theory	In late 2006, independent from the definition of isolated horizon theory, Ansari reported that in loop quantum gravity the eigenvalues of the area operator are symmetric by the ladder symmetry. Corresponding to each eigenvalue there are a finite number of degenerate states. One application could be if the classical null character of a horizon is disregarded in the quantum sector, in the lack of energy condition and presence of gravitational propagation the Immirzi parameter tunes to: ln ⁡(3)/8π, by the use of Olaf Dreyer's conjecture for identifying the evaporation of minimal area cell with the corresponding area of the highly damping quanta. This proposes a kinematical picture for defining a quantum horizon via spin foam models, however the dynamics of such a model has not yet been studied.
Immirzi parameter	Scale-invariant theory	For scale-invariant dilatonic theories of gravity with standard model-type matter couplings, Charles Wang and co-workers show that their loop quantization lead to a conformal class of Ashtekar–Barbero connection variables using the Immirzi parameter as a conformal gauge parameter without a preferred value. Accordingly, a different choice of the value for the Immirzi parameter for such a theory merely singles out a conformal frame without changing the physical descriptions.
Immirzi parameter	Interpretation	The parameter may be viewed as a renormalization of Newton's constant. Various speculative proposals to explain this parameter have been suggested: for example, an argument due to Olaf Dreyer based on quasinormal modes.Another more recent interpretation is that it is the measure of the value of parity violation in quantum gravity, analogous to the theta parameter of QCD, and its positive real value is necessary for the Kodama state of loop quantum gravity. As of today (2004), no alternative calculation of this constant exists. If a second match with experiment or theory (for example, the value of Newton's force at long distance) were found requiring a different value of the Immirzi parameter, it would constitute evidence that loop quantum gravity cannot reproduce the physics of general relativity at long distances. On the other hand, the Immirzi parameter seems to be the only free parameter of vacuum LQG, and once it is fixed by matching one calculation to an "experimental" result, it could in principle be used to predict other experimental results. Unfortunately, no such alternative calculations have been made so far.
Null hypersurface	Null hypersurface	In relativity and in pseudo-Riemannian geometry, a null hypersurface is a hypersurface whose normal vector at every point is a null vector (has zero length with respect to the local metric tensor). A light cone is an example. An alternative characterization is that the tangent space at every point of a hypersurface contains a nonzero vector such that the metric applied to such a vector and any vector in the tangent space is zero. Another way of saying this is that the pullback of the metric onto the tangent space is degenerate.
Null hypersurface	Null hypersurface	For a Lorentzian metric, all the vectors in such a tangent space are space-like except in one direction, in which they are null. Physically, there is exactly one lightlike worldline contained in a null hypersurface through each point that corresponds to the worldline of a particle moving at the speed of light, and no contained worldlines that are time-like. Examples of null hypersurfaces include a light cone, a Killing horizon, and the event horizon of a black hole.
Virtual Pro Wrestling	Virtual Pro Wrestling	Virtual Pro Wrestling (Japanese: バーチャル・プロレスリング) is a professional wrestling video game series developed by AKI Corporation and published by Asmik Ace exclusively in Japan. The series started in 1996 with the release of the first Virtual Pro Wrestling for the PlayStation. It was localized in the West as WCW vs. the World. Two other games in the series were released exclusively for the Nintendo 64, Virtual Pro Wrestling 64 and Virtual Pro Wrestling 2.All games in the series feature characters largely based on real-life wrestlers working for Japanese professional wrestling promotions. The series has been highly regarded for its gameplay engine, featuring weak/strong attacks and maneuvers and the Nintendo 64 games have been popular import titles.The games served as the basis for several games published by THQ and based on the American wrestling promotions World Championship Wrestling (WCW) and the World Wrestling Federation (WWF). The first game in the series was released outside Japan as WCW vs. the World. The last two games in the series had Western counterparts in WCW vs. nWo: World Tour and WWF WrestleMania 2000.Although AKI stopped producing Virtual Pro Wrestling titles, they continued to use tweaked versions of the gameplay system in newer titles such as Def Jam Vendetta, Def Jam: Fight for NY and games based on the Ultimate Muscle franchise such as Ultimate Muscle: Legends vs. New Generation.
S3 Texture Compression	S3 Texture Compression	S3 Texture Compression (S3TC) (sometimes also called DXTn, DXTC, or BCn) is a group of related lossy texture compression algorithms originally developed by Iourcha et al. of S3 Graphics, Ltd. for use in their Savage 3D computer graphics accelerator. The method of compression is strikingly similar to the previously published Color Cell Compression, which is in turn an adaptation of Block Truncation Coding published in the late 1970s. Unlike some image compression algorithms (e.g. JPEG), S3TC's fixed-rate data compression coupled with the single memory access (cf. Color Cell Compression and some VQ-based schemes) made it well-suited for use in compressing textures in hardware-accelerated 3D computer graphics. Its subsequent inclusion in Microsoft's DirectX 6.0 and OpenGL 1.3 (via the GL_EXT_texture_compression_s3tc extension) led to widespread adoption of the technology among hardware and software makers. While S3 Graphics is no longer a competitor in the graphics accelerator market, license fees have been levied and collected for the use of S3TC technology until October 2017, for example in game consoles and graphics cards. The wide use of S3TC has led to a de facto requirement for OpenGL drivers to support it, but the patent-encumbered status of S3TC presented a major obstacle to open source implementations, while implementation approaches which tried to avoid the patented parts existed.
S3 Texture Compression	Patent	Some (e.g. US 5956431 A) of the multiple USPTO patents on S3 Texture Compression expired on October 2, 2017. At least one continuation patent, US6,775,417, however had a 165-day extension. This continuation patent expired on March 16, 2018.
S3 Texture Compression	Codecs	There are five variations of the S3TC algorithm (named DXT1 through DXT5, referring to the FourCC code assigned by Microsoft to each format), each designed for specific types of image data. All convert a 4×4 block of pixels to a 64-bit or 128-bit quantity, resulting in compression ratios of 6:1 with 24-bit RGB input data or 4:1 with 32-bit RGBA input data. S3TC is a lossy compression algorithm, resulting in image quality degradation, an effect which is minimized by the ability to increase texture resolutions while maintaining the same memory requirements. Hand-drawn cartoon-like images do not compress well, nor do normal map data, both of which usually generate artifacts. ATI's 3Dc compression algorithm is a modification of DXT5 designed to overcome S3TC's shortcomings with regard to normal maps. id Software worked around the normalmap compression issues in Doom 3 by moving the red component into the alpha channel before compression and moving it back during rendering in the pixel shader.Like many modern image compression algorithms, S3TC only specifies the method used to decompress images, allowing implementers to design the compression algorithm to suit their specific needs, although the patent still covers compression algorithms. The nVidia GeForce 256 through to GeForce 4 cards also used 16-bit interpolation to render DXT1 textures, which resulted in banding when unpacking textures with color gradients. Again, this created an unfavorable impression of texture compression, not related to the fundamentals of the codec itself.
S3 Texture Compression	DXT1	DXT1 (also known as Block Compression 1 or BC1) is the smallest variation of S3TC, storing 16 input pixels in 64 bits of output, consisting of two 16-bit RGB 5:6:5 color values c0 and c1 , and a 4×4 two-bit lookup table.
S3 Texture Compression	DXT1	If c0>c1 (compare these colors by interpreting them as two 16-bit unsigned numbers), then two other colors are calculated, such that for each component, {\textstyle c_{2}={2 \over 3}c_{0}+{1 \over 3}c_{1}} and {\textstyle c_{3}={1 \over 3}c_{0}+{2 \over 3}c_{1}} This mode operates similarly to mode 0xC0 of the original Apple Video codec.Otherwise, if c0≤c1 , then {\textstyle c_{2}={1 \over 2}c_{0}+{1 \over 2}c_{1}} and c3 is transparent black corresponding to a premultiplied alpha format. This color sometimes causes a black border surrounding the transparent area when linear texture filtering and alpha test is used, due to colors being interpolated between the color of opaque texel and neighbouring black transparent texel.
S3 Texture Compression	DXT1	The lookup table is then consulted to determine the color value for each pixel, with a value of 0 corresponding to c0 and a value of 3 corresponding to c3
S3 Texture Compression	DXT2 and DXT3	DXT2 and DXT3 (collectively also known as Block Compression 2 or BC2) converts 16 input pixels (corresponding to a 4x4 pixel block) into 128 bits of output, consisting of 64 bits of alpha channel data (4 bits for each pixel) followed by 64 bits of color data, encoded the same way as DXT1 (with the exception that the 4-color version of the DXT1 algorithm is always used instead of deciding which version to use based on the relative values of c0 and c1 ).
S3 Texture Compression	DXT2 and DXT3	In DXT2, the color data is interpreted as being premultiplied by alpha, in DXT3 it is interpreted as not having been premultiplied by alpha. Typically DXT2/3 are well suited to images with sharp alpha transitions, between translucent and opaque areas.
S3 Texture Compression	DXT4 and DXT5	DXT4 and DXT5 (collectively also known as Block Compression 3 or BC3) converts 16 input pixels into 128 bits of output, consisting of 64 bits of alpha channel data (two 8-bit alpha values and a 4×4 3-bit lookup table) followed by 64 bits of color data (encoded the same way as DXT1).
S3 Texture Compression	DXT4 and DXT5	If α0>α1 , then six other alpha values are calculated, such that {\textstyle \alpha _{2}={{6\alpha _{0}+1\alpha _{1}} \over 7}} , {\textstyle \alpha _{3}={{5\alpha _{0}+2\alpha _{1}} \over 7}} , {\textstyle \alpha _{4}={{4\alpha _{0}+3\alpha _{1}} \over 7}} , {\textstyle \alpha _{5}={{3\alpha _{0}+4\alpha _{1}} \over 7}} , {\textstyle \alpha _{6}={{2\alpha _{0}+5\alpha _{1}} \over 7}} , and {\textstyle \alpha _{7}={{1\alpha _{0}+6\alpha _{1}} \over 7}} Otherwise, if {\textstyle \alpha _{0}\leq \alpha _{1}} , four other alpha values are calculated such that {\textstyle \alpha _{2}={{4\alpha _{0}+1\alpha _{1}} \over 5}} , {\textstyle \alpha _{3}={{3\alpha _{0}+2\alpha _{1}} \over 5}} , {\textstyle \alpha _{4}={{2\alpha _{0}+3\alpha _{1}} \over 5}} , and {\textstyle \alpha _{5}={{1\alpha _{0}+4\alpha _{1}} \over 5}} with α6=0 and 255 The lookup table is then consulted to determine the alpha value for each pixel, with a value of 0 corresponding to α0 and a value of 7 corresponding to α7 . DXT4's color data is premultiplied by alpha, whereas DXT5's is not. Because DXT4/5 use an interpolated alpha scheme, they generally produce superior results for alpha (transparency) gradients than DXT2/3.
S3 Texture Compression	Further variants	BC4 and BC5 BC4 and BC5 (Block Compression 4 and 5) are added in Direct3D 10. They reuse the alpha channel encoding found in DXT4/5 (BC3). BC4 stores 16 input single-channel (e.g. greyscale) pixels into 64 bits of output, encoded in nearly the same way as BC3 alphas. The expanded palette provides higher quality. BC5 stores 16 input double-channel (e.g. tangent space normal map) pixels into 128 bits of output, consisting of two halves each encoded like BC4. BC6H and BC7 BC6H (sometimes BC6) and BC7 (Block Compression 6H and 7) are added in Direct3D 11. BC6H encodes 16 input RGB HDR (float16) pixels into 128 bits of output. It essentially treats float16 as 16 sign-magnitude integer value and interpolates such integers linearly. It works well for blocks without sign changes. A total of 14 modes are defined, though most differ minimally: only two prediction modes are really used.
S3 Texture Compression	Further variants	BC7 encodes 16 input RGB8/RGBA8 pixels into 128 bits of output. It can be understood as a much-enhanced BC3.BC6H and BC7 have a much more complex algorithm with a selection of encoding modes. The quality is much better as a result. These two modes are also specified much more exactly, with ranges of accepted deviation. Earlier BCn modes decode slightly differently among GPU vendors.
S3 Texture Compression	Data preconditioning	BCn textures can be further compressed for on-disk storage and distribution. An application would decompress this extra layer and send the BCn data to the GPU as usual.
S3 Texture Compression	Data preconditioning	BCn can be combined with Oodle Texture, a lossy preprocessor that modifies the input texture so that the BCn output is more easily compressed by a LZ77 compressor (rate-distortion optimization). BC7 specifically can also use "bc7prep", a lossless pass to re-encode the texture in a more compressible form (requiring its inverse at decompression).crunch is another tool that performs RDO and optionally further re-encoding.In 2021, Microsoft produced a "BCPack" compression algorithm specifically for BCn-compressed textures. Xbox series X and S have hardware support for decompressing BCPack streams.
Nuclear timescale	Nuclear timescale	In astrophysics, the nuclear timescale is an estimate of the lifetime of a star based solely on its rate of fuel consumption. Along with the thermal and free-fall (aka dynamical) time scales, it is used to estimate the length of time a particular star will remain in a certain phase of its life and its lifespan if hypothetical conditions are met. In reality, the lifespan of a star is greater than what is estimated by the nuclear time scale because as one fuel becomes scarce, another will generally take its place—hydrogen burning gives way to helium burning, etc. However, all the phases after hydrogen burning combined typically add up to less than 10% of the duration of hydrogen burning.
Nuclear timescale	Stellar astrophysics	Hydrogen generally determines a star's nuclear lifetime because it is used as the main source of fuel in a main sequence star. Hydrogen becomes helium in the nuclear reaction that takes place within stars; when the hydrogen has been exhausted, the star moves on to another phase of its life and begins burning the helium. total mass of fuel available rate of fuel consumption fraction of star over which fuel is burned =MXLQ×F where M is the mass of the star, X is the fraction of the star (by mass) that is composed of the fuel, L is the star's luminosity, Q is the energy released per mass of the fuel from nuclear fusion (the chemical equation should be examined to get this value), and F is the fraction of the star where the fuel is burned (F is generally equal to .1 or so). As an example, the Sun's nuclear time scale is approximately 10 billion years.
Bayesian structural time series	Bayesian structural time series	Bayesian structural time series (BSTS) model is a statistical technique used for feature selection, time series forecasting, nowcasting, inferring causal impact and other applications. The model is designed to work with time series data.
Bayesian structural time series	Bayesian structural time series	The model has also promising application in the field of analytical marketing. In particular, it can be used in order to assess how much different marketing campaigns have contributed to the change in web search volumes, product sales, brand popularity and other relevant indicators. Difference-in-differences models and interrupted time series designs are alternatives to this approach. "In contrast to classical difference-in-differences schemes, state-space models make it possible to (i) infer the temporal evolution of attributable impact, (ii) incorporate empirical priors on the parameters in a fully Bayesian treatment, and (iii) flexibly accommodate multiple sources of variation, including the time-varying influence of contemporaneous covariates, i.e., synthetic controls."
Bayesian structural time series	General model description	The model consists of three main components: Kalman filter. The technique for time series decomposition. In this step, a researcher can add different state variables: trend, seasonality, regression, and others. Spike-and-slab method. In this step, the most important regression predictors are selected.
Bayesian structural time series	General model description	Bayesian model averaging. Combining the results and prediction calculation.The model could be used to discover the causations with its counterfactual prediction and the observed data.A possible drawback of the model can be its relatively complicated mathematical underpinning and difficult implementation as a computer program. However, the programming language R has ready-to-use packages for calculating the BSTS model, which do not require strong mathematical background from a researcher.

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