The cerebellar model arithmetic computer (CMAC) is a type of neural network based on a model of the mammalian cerebellum. It is also known as the cerebellar model articulation controller. It is a type of associative memory. The CMAC was first proposed as a function modeler for robotic controllers by James Albus in 1975 (hence the name), but has been extensively used in reinforcement learning and also as for automated classification in the machine learning community. The CMAC is an extension of the perceptron model. It computes a function for n {\displaystyle n} input dimensions. The input space is divided up into hyper-rectangles, each of which is associated with a memory cell. The contents of the memory cells are the weights, which are adjusted during training. Usually, more than one quantisation of input space is used, so that any point in input space is associated with a number of hyper-rectangles, and therefore with a number of memory cells. The output of a CMAC is the algebraic sum of the weights in all the memory cells activated by the input point. A change of value of the input point results in a change in the set of activated hyper-rectangles, and therefore a change in the set of memory cells participating in the CMAC output. The CMAC output is therefore stored in a distributed fashion, such that the output corresponding to any point in input space is derived from the value stored in a number of memory cells (hence the name associative memory). This provides generalisation. == Building blocks == In the adjacent image, there are two inputs to the CMAC, represented as a 2D space. Two quantising functions have been used to divide this space with two overlapping grids (one shown in heavier lines). A single input is shown near the middle, and this has activated two memory cells, corresponding to the shaded area. If another point occurs close to the one shown, it will share some of the same memory cells, providing generalisation. The CMAC is trained by presenting pairs of input points and output values, and adjusting the weights in the activated cells by a proportion of the error observed at the output. This simple training algorithm has a proof of convergence. It is normal to add a kernel function to the hyper-rectangle, so that points falling towards the edge of a hyper-rectangle have a smaller activation than those falling near the centre. One of the major problems cited in practical use of CMAC is the memory size required, which is directly related to the number of cells used. This is usually ameliorated by using a hash function, and only providing memory storage for the actual cells that are activated by inputs. == One-step convergent algorithm == Initially least mean square (LMS) method is employed to update the weights of CMAC. The convergence of using LMS for training CMAC is sensitive to the learning rate and could lead to divergence. In 2004, a recursive least squares (RLS) algorithm was introduced to train CMAC online. It does not need to tune a learning rate. Its convergence has been proved theoretically and can be guaranteed to converge in one step. The computational complexity of this RLS algorithm is O(N3). == Hardware implementation infrastructure == Based on QR decomposition, an algorithm (QRLS) has been further simplified to have an O(N) complexity. Consequently, this reduces memory usage and time cost significantly. A parallel pipeline array structure on implementing this algorithm has been introduced. Overall by utilizing QRLS algorithm, the CMAC neural network convergence can be guaranteed, and the weights of the nodes can be updated using one step of training. Its parallel pipeline array structure offers its great potential to be implemented in hardware for large-scale industry usage. == Continuous CMAC == Since the rectangular shape of CMAC receptive field functions produce discontinuous staircase function approximation, by integrating CMAC with B-splines functions, continuous CMAC offers the capability of obtaining any order of derivatives of the approximate functions. == Deep CMAC == In recent years, numerous studies have confirmed that by stacking several shallow structures into a single deep structure, the overall system could achieve better data representation, and, thus, more effectively deal with nonlinear and high complexity tasks. In 2018, a deep CMAC (DCMAC) framework was proposed and a backpropagation algorithm was derived to estimate the DCMAC parameters. Experimental results of an adaptive noise cancellation task showed that the proposed DCMAC can achieve better noise cancellation performance when compared with that from the conventional single-layer CMAC. == Summary ==
Lynda Soderholm
Lynda Soderholm is a physical chemist at the U.S. Department of Energy's (DOE) Argonne National Laboratory with a specialty in f-block elements. She is a senior scientist and the lead of the Actinide, Geochemistry & Separation Sciences Theme within Argonne's Chemical Sciences and Engineering Division. Her specific role is the Separation Science group leader within Heavy Element Chemistry and Separation Science (HESS), directing basic research focused on low-energy methods for isolating lanthanide and actinide elements from complex mixtures. She has made fundamental contributions to understanding f-block chemistry and characterizing f-block elements. Soderholm became a Fellow of the American Association for the Advancement of Science (AAAS) in 2013, and is also an Argonne Distinguished Fellow. == Early life and education == Soderholm was awarded her PhD in 1982 by McMaster University under the direction of Prof John Greedan. Her dissertation focused on characterizing the structural and magnetic properties of a series of ternary f-ion oxides. After graduating, she was awarded a NATO postdoctoral fellow at the Centre national de la recherche scientifique in France from 1982 until 1985. After a short postdoctoral appointment as an Argonne postdoctoral fellow she was promoted to staff scientist the same year. Over several years, she moved up the ranks, becoming a senior chemist in 2001. She was also an adjunct professor at the University of Notre Dame from 2003 until 2007. In 2021, Soderholm was appointed interim Division Director for the Chemical Sciences and Engineering Division. == Career and research == === Uncovering structure of Yttrium-123 Superconductor === Early in her career, Soderholm focused on the characterizing the magnetic and electronic behavior of compounds containing f-ions (lanthanides and actinides) with a focus on high-Tc materials, compounds that are superconducting under usually high temperatures. She was part of the research group that first determined the structure of YBa2Cu3O7. Their discovery formed the foundation for the further developments in the broad field of superconductivity. === Understanding f-ion speciation in solution === Continuing her interest in the f-elements, Soderholm shifted her focus from solid-state materials to nanoparticles and solutions, taking advantage of advances in X-ray structural probes made available by synchrotron facilities. Building on her earlier work using neutron scattering, her team became the first to discover that plutonium exists in solution as tiny, well-defined nanoparticles. This work solved a longstanding problem in understanding transport of plutonium in the environment and resulted in the development of a new, patented approach to separating plutonium during nuclear reprocessing. === Using machine learning to evaluate molecular structures === Soderholm's more recent projects use machine learning to understand the influence of complex molecular structuring in solutions, in connection with low-energy processes for separation of f-block elements from complex mixtures. == Awards and honors == University of Chicago Board of Governors' Distinguished Performance Award, 2009. Fellow of the American Association for the Advancement of Science, 2013. Argonne Distinguished Fellow, 2016 DOE materials sciences research competition for Outstanding Scientific Accomplishments in Solid State Physics, 1987. == Select publications == Beno, M. A.; Soderholm, L.; Capone, D. W., II; Hinks, D. G.; Jorgensen, J. D.; Grace, J. D.; Schuller, I. K.; Segre, C. U.; Zhang, K., Structure of the single-phase high-temperature superconductor yttrium barium copper oxide (YBa2Cu3O7−δ). Appl. Phys. Lett. 1987, 51 (1), 57–9. Soderholm, L.; Zhang, K.; Hinks, D. G.; Beno, M. A.; Jorgensen, J. D.; Segre, C. U.; Schuller, I. K., Incorporation of praseodymium in YBa2Cu3O7−δ: electronic effects on superconductivity. Nature (London) 1987, 328 (6131), 604–5. Antonio, M. R.; Williams, C. W.; Soderholm, L., Berkelium redox speciation. Radiochim. Acta 2002, 90 (12), 851–856. Soderholm, L.; Skanthakumar, S.; Neuefeind, J., Determination of actinide speciation in solution using high-energy X-ray scattering. Anal. Bioanal. Chem. 2005, 383 (1), 48–55. Forbes, T. Z.; Burns, P. C.; Skanthakumar, S.; Soderholm, L., Synthesis, structure, and magnetism of Np2O5. J. Am. Chem. Soc. 2007, 129 (10), 2760–2761. Soderholm, L.; Almond, P. M.; Skanthakumar, S.; Wilson, R. E.; Burns, P. C., The structure of the plutonium oxide nanocluster [Pu38O56Cl54(H2O)8]14-. Angew. Chem., Int. Ed. 2008, 47 (2), 298–302. Jensen, M. P.; Gorman-Lewis, D.; Aryal, B.; Paunesku, T.; Vogt, S.; Rickert, P. G.; Seifert, S.; Lai, B.; Woloschak, G. E.; Soderholm, L., An iron-dependent and transferrin-mediated cellular uptake pathway for plutonium. Nat. Chem. Biol. 2011, 7 (8), 560–565. Wilson, R. E.; Skanthakumar, S.; Soderholm, L., Separation of Plutonium Oxide Nanoparticles and Colloids. Angew. Chem., Int. Ed. 2011, 50 (47), 11234–11237. Knope, K. E.; Soderholm, L., Solution and solid-state structural chemistry of actinide hydrates and their hydrolysis and condensation products. Chem. Rev. 2013, 113 (2), 944–994. Luo, G.; Bu, W.; Mihaylov, M.; Kuzmenko, I.; Schlossman, M. L.; Soderholm, L., X-ray reflectivity reveals a nonmonotonic ion-density profile perpendicular to the surface of ErCl3 aqueous solutions. J. Phys. Chem. C 2013, 117 (37), 19082–19090. Jin, G. B.; Lin, J.; Estes, S. L.; Skanthakumar, S.; Soderholm, L., Influence of countercation hydration enthalpies on the formation of molecular complexes: A thorium-nitrate example. J. Am. Chem. Soc. 2017, 139 (49), 18003–18008. == Patents == Solvent extraction system for plutonium colloids and other oxide nano-particles, (2016).
Affordable affluence
Affordable affluence refers to a cultural phenomenon where consumers use accessible luxury goods and lifestyles to project status and align themselves with a higher social class, without requiring substantial wealth. This concept is embodied by brands such as Aritzia and Erewhon, which position themselves as offering high-end, trendy, or health-conscious products that are relatively accessible to the average consumer. A related concept is quiet luxury, where the ultra-wealthy signal wealth through subtle means. Quiet luxury emphasizes the widening gap between the ultra-wealthy and the general public, whereas accessible affluence provides a way for the general public to indulge in the lifestyle of the ultra-wealthy. == Origin of the term == An early use of the phrase in this context in a 2023 article in The Cut called "Meet the People Working 3 Jobs to Afford Erewhon." One of the interviewees used Erewhon as an archetype of affordable affluence. It was described as “a way for regular people to position themselves adjacent to the upper class.” == Background and description == The phenomenon arises due to an individual's desire to showcase status. For years, companies have strategized how to target the average consumers by providing a product that signals an elevated social status. For instance, Aritzia partnered with celebrities and micro-influencers to make it an aspirational brand at an affordable cost. Erewhon similarly has allowed middle class consumers to subtly signal a higher degree of perceived wealth by purchasing higher priced, but still attainable items. It has allowed middle-class individuals to feel as though they are part of an exclusive culture. This phenomenon has been seen particularly with Gen Z and Millennials in the setting of financial hardships in the 2020s. Affordable affluence is an example of the lipstick effect. Because traditional status symbols such as expensive cars became relatively more unattainable, posting clips on social media that showcase affordable affluence become an alternative status symbol. Particularly with food, the perception has evolved from a necessity to a luxury. A McKinsey & Company report demonstrated that these generations place a higher importance on groceries than restaurants, travel, and beauty/fashion.
DiscoVision
DiscoVision is the name of several things related to the video LaserDisc format. It was the original name of the "Reflective Optical Videodisc System" format later known as "LaserVision" or LaserDisc. == Description == MCA DiscoVision, Inc. was a division of entertainment giant MCA (Music Corporation of America), established in 1969 to develop and sell an optical videodisc system. MCA released discs pressed in Carson and Costa Mesa, California on the DiscoVision label from the format's Atlanta, Georgia launch in 1978 to 1982 and the release of the film The Four Seasons. DiscoVision titles included films from Universal Pictures, Paramount Pictures, Warner Bros. Pictures, and Disney content. Agreements were made with Columbia Pictures and United Artists, though no discs were released on the DiscoVision label from either studio. Most of these companies later established their own labels for the format, the first being Paramount with a dozen movies released on the Paramount Home Video label in the summer of 1981. The successor to MCA DiscoVision, DiscoVision Associates (DVA), was the result of a partnership between IBM and MCA. It was hoped that the merger would provide the basis for improvement of the quality of DiscoVision pressings, but no appreciable improvement ever took hold. In 1981, responsibility for the laser videodisc was sold to Pioneer Electronic Corporation, after MCA Discovision had previously started a partnership in 1977 with Pioneer, Universal Pioneer, to produce the Pioneer PR-7820 player (the first industrial model of DiscoVision player from 1978), as well as establishing disc pressing plants in Japan. As part of the partnership, Pioneer, in association with MCA, had a disc replication facility in Kofu, Japan that produced discs. Some of the last DiscoVision label discs were manufactured by Pioneer in Japan. In the same year, MCA discontinued their DiscoVision branding, due to the sale of the technology to Pioneer (who then rebranded the format as LaserDisc) and in turn rebranded their laserdisc releases, now fabricated by Pioneer, under the MCA Videodisc banner; this was changed to the "MCA Home Video" name for both its VHS and videodisc releases. Some of DiscoVision's technical staff went on to form MCA Video Games, in an effort to produce video game cartridges. DiscoVision Associates later evolved into a patent holding company which manages and licenses intellectual property related to LaserDisc, Compact Disc, and optical disc technologies, as well as other non-disc related fields. In 1989, Pioneer acquired DiscoVision Associates where it continues to license its technologies independently. As the portfolio of patent expired, the presence of DiscoVision became less visible. However, it established the success of a patent holding company, which other companies are stimulated to generate royalty income from their own patent portfolio.
Elonis v. United States
Elonis v. United States, 575 U.S. 723 (2015), was a United States Supreme Court case concerning whether conviction of threatening another person over interstate lines (under 18 U.S.C. § 875(c)) requires proof of subjective intent to threaten or whether it is enough to show that a "reasonable person" would regard the statement as threatening. In controversy were the purported threats of violent rap lyrics written by Anthony Douglas Elonis and posted to Facebook under a pseudonym. The ACLU filed an amicus brief in support of the petitioner. It was the first time the Court has heard a case considering true threats and the limits of speech on social media. == Background == In May 2010, Elonis was in the process of divorce and made a number of public Facebook posts. Prior to his postings, he had lost his job at an amusement park. He "posted the script of a sketch" by The Whitest Kids U' Know, which originally referenced saying "I want to kill the President of the United States" and replaced the president with his wife: Elonis ended the post with this statement: "Art is about pushing limits. I'm willing to go to jail for my constitutional rights. Are you?" A week later, Elonis posted about local law enforcement and a kindergarten class, which caught the attention of the Federal Bureau of Investigation. Then, he wrote a post on Facebook about one of the agents who visited him: He concluded: == Arrest and Conviction == These actions led to Elonis's arrest on December 8, 2010. He was indicted by a grand jury on five counts of threats to his estranged ex-wife, park employees and visitors, local law enforcement, an FBI agent, and a kindergarten class that had been relayed through interstate communication. At the district court, Elonis moved to dismiss the indictment for failing to allege that he had intended to threaten anyone, claiming his Facebook post was not were not intended as a threat. He argued that, as an aspiring rap artist, his posts were intended to be a form of artistic expression to help him cope with his recent loses. According to him, he did not mean anything said in his posts in a literal sense. His motion was denied. He requested a jury instruction that "the government must prove that he intended to communicate a true threat", which was also denied. He was convicted on the last four of the five counts, and was sentenced to 44 months in prison and three years on supervised release. He appealed unsuccessfully to the Third Circuit, renewing his challenge to the jury instructions. He then appealed to the U.S. Supreme Court based on lack of any attempt to show intent to threaten and on First Amendment rights. == Decision == On June 1, 2015, the U.S. Supreme Court reversed Elonis's conviction in an 8–1 decision. Chief Justice John Roberts wrote for a seven-justice majority, Samuel Alito authored an opinion concurring in part and dissenting in part, and Clarence Thomas authored a dissenting opinion. The finding of the circuit court was reversed and the matter remanded. === Majority opinion === The majority opinion, written by Roberts, did not rule on First Amendment matters or on the question of whether recklessness was sufficient mens rea to show intent. It ruled that mens rea was required to prove the commission of a crime under §875(c). Importantly, the mens rea issue had been preserved for review, since Elonis had raised that objection at every stage of the previous proceedings. The government contended that the presence of the words "intent to extort" in §875(b) and §875(d) implied that the absence in §875(c) was constructive. The court disagreed, holding that the absence of the language in §875(c) was because the section was intended to have a broader scope than threats relating to extortion. The opinion drew on many Supreme Court cases holding that in criminal law, mens rea was required though it had not been mentioned explicitly in statute. Consequently, the Supreme Court ruled in favor of Elonis. === Alito's concurrence === Justice Samuel Alito, concurring in part and dissenting in part, opined that while agreeing that mens rea was required and specifically that showing negligence was not sufficient, the court should have ruled on the question of recklessness. He further opined that recklessness was sufficient to show a crime under that provision on the basis that going further would amount to amending the statute, rather than interpreting it. Since Elonis explicitly argued that recklessness was not sufficient, Alito said: I would therefore remand for the Third Circuit to determine if Elonis’s failure (indeed, refusal) to argue for recklessness prevents reversal of his conviction. The Third Circuit should also have the opportunity to consider whether the conviction could be upheld on harmless error grounds. Alito also addressed the First Amendment question, elided by the majority opinion. He held that "lyrics in songs that are performed for an audience or sold in recorded form are unlikely to be interpreted as a real threat to a real person. ... Statements on social media that are pointedly directed at their victims, by contrast, are much more likely to be taken seriously." === Thomas's dissent === Justice Clarence Thomas, dissenting, wrote against discarding the "general intent" standard without replacing it with a clearer standard. Thomas argued that "there is no historical practice requiring more than general intent when a statute regulates speech." Thomas cited Rosen v. United States, arguing that general intent was sufficient in this case. However, the majority opinion offers refutation in that Rosen turned on ignorance of the law: knowledge as to whether material was legally obscene, not on whether it was intended to be obscene. Thomas also supported the government's claim that the presence of "intent to extort" language in the adjacent §875(b) and did not address the majority's reasoning on that language. Thomas used precedent, notably from the states and 18th-century England based on other but similar and, arguably, influencing legislation to support his "general intent" claim. Thomas also drew a parallel with general intent in tort. While he sought to address the First Amendment issues, he never strayed far from "general intent". == Aftermath == On remand, the Third Circuit reaffirmed the conviction "concluding beyond a reasonable doubt that Elonis would have been convicted if the jury had been properly instructed" and therefore was harmless error. In 2022, Elonis was once again arrested and indicted on three counts of cyberstalking involving three people. It was discovered that between 2018 and 2021, Elonis had sent numerous threatening messages over email, text, voice mail, and social media platforms like Twitter to a former prosecutor of the Eastern District of Pennsylvania, his ex-girlfriend, and ex-wife. On August 5, after a five-day trial, Elonis was found guilty on all three counts, and on March 23, 2023, he was sentenced by U.S. District Court Judge Edward G. Smith of Easton, Pennsylvania to twelve years and seven months in prison.
Arabic Ontology
Arabic Ontology is a website offering linguistic ontology services for the Arabic language which can be used like the online site WordNet. Users can use Arabic Ontology to classify or clarify the concepts and meanings of Arabic terms. == Ontology Structure == The ontology structure (i.e., data model) is similar to WordNet's structure. Each concept in the database is given a unique concept identifier (URI), informally described by a gloss, and lexicalized by one or more synonymous lemma terms. Each term-concept pair is called a sense, and is given a SenseID. A set of senses is called synset. Concepts and senses are described by further attributes such as era and area — to specify example usage and ontological analysis. Semantic relations are defined between concepts. Some important entities are included in the ontology, such as individual countries and bodies of water. These individuals are given separate IndividualIDs and linked with their concepts through the InstanceOf relation. == Mappings to other resources == Concepts in the Arabic Ontology are mapped to synsets in WordNet, as well as to BFO and DOLCE. Terms used in the Arabic Ontology are mapped to lemmas in the LDC's SAMA database. == Applications == Arabic Ontology can be used in many application domains, such as: Information retrieval, to enrich queries (e.g., in search engines) and improve the quality of the results, i.e. meaningful search rather than string-matching search; Machine translation and word-sense disambiguation, by finding the exact mapping of concepts across languages, especially that the Arabic ontology is also mapped to the WordNet; Data Integration and interoperability in which the Arabic ontology can be used as a semantic reference to link databases and information systems; Semantic Web and Web 3.0, by using the Arabic ontology as a semantic reference to disambiguate the meanings used in websites; among many other applications. == URLs Design == The URLs in the Arabic Ontology are designed according to the W3C's Best Practices for Publishing Linked Data, as described in the following URL schemes. This allows one to also explore the whole database like exploring a graph: Ontology Concept: Each concept in the Arabic Ontology has a ConceptID and can be accessed using: https://{domain}/concept/{ConceptID | Term}. In case of a term, the set of concepts that this term lexicalizes are all retrieved. In case of a ConceptID, the concept and its direct subtypes are retrieved, e.g. https://ontology.birzeit.edu/concept/293198 Semantic relations: Relationships between concepts can be accessed using these schemes: (i) the URL: https:// {domain}/concept/{RelationName}/{ConceptID} allows retrieval of relationships among ontology concepts. (ii) the URL: https://{domain}/lexicalconcept/{RelationName}/{lexicalConceptID} allows retrieval of relations between lexical concepts. For example, https://ontology.birzeit.edu/concept/instances/293121 retrieves the instances of the concept 293121. The relations that are currently used in our database are: {subtypes, type, instances, parts, related, similar, equivalent}.
MADI
Multichannel Audio Digital Interface (MADI) standardized as AES10 by the Audio Engineering Society (AES) defines the data format and electrical characteristics of an interface that carries multiple channels of digital audio. The AES first documented the MADI standard in AES10-1991 and updated it in AES10-2003 and AES10-2008. The MADI standard includes a bit-level description and has features in common with the two-channel AES3 interface. MADI supports serial digital transmission over coaxial cable or fibre-optic lines of 28, 56, 32, or 64 channels; and sampling rates to 96 kHz and beyond with an audio bit depth of up to 24 bits per channel. Like AES3 and ADAT Lightpipe, it is a unidirectional interface from one sender to one receiver. == Development and applications == MADI was developed by AMS Neve, Solid State Logic, Sony and Mitsubishi and is widely used in the audio industry, especially in the professional audio sector. It provides advantages over other audio digital interface protocols and standards such as AES3, ADAT Lightpipe, TDIF (Tascam Digital Interface), and S/PDIF (Sony/Philips Digital Interface). These advantages include: Support for a greater number of channels per line Use of coaxial and optical fiber media that support transmission of audio signals over 100 meters, up to 3000 meters over multi-mode and 40,000 meters over single-mode optical fiber The original specification (AES10-1991) defined the MADI link as a 56-channel transport for linking large-format mixing consoles to digital multitrack recording devices. Large broadcast studios also adopted it for routing multi-channel audio throughout their facilities. The 2003 revision (AES10-2003) adds a 64-channel capability by removing varispeed operation and supports 96 kHz sampling frequency with reduced channel capacity. The latest AES10-2008 standard includes minor clarifications and updates to correspond to the current AES3 standard. Audio over Ethernet of various types is the primary alternative to MADI for transport of many channels of professional digital audio. == Transmission format == MADI links use a transmission format similar to Fiber Distributed Data Interface (FDDI) networking. Since MADI is most often transmitted on copper links via 75-ohm coaxial cables, it more closely compares to the FDDI specification for copper-based links, called CDDI. AES10-2003 recommends using BNC connectors with coaxial cables and SC connectors with optic fibers. MADI over fibre can support a range of up to 2 km. The basic data rate is 100 Mbit/s of data using 4B5B encoding to produce a 125 MHz physical baud rate. Unlike AES3, this clock is not synchronized to the audio sample rate, and the audio data payload is padded using JK sync symbols. Sync symbols may be inserted at any subframe boundary, and must occur at least once per frame. Though the standard disassociates the transmission clock from the audio sample rate, and thus requires a separate word clock connection to maintain synchronization, some vendors do give the option of locking to parts of the transmission timing information for purposes of deriving a word clock. The audio data is almost identical to the AES3 payload, though with more channels. Rather than letters, MADI assigns channel numbers from 0–63. Frame synchronization is provided by sync symbols outside the data itself, rather than an embedded preamble sequence, and the first four time slots of each sub-channel are encoded as normal data, used for sub-channel identification: Bit 0: Set to 1 to mark channel 0, the first channel in each frame Bit 1: Set to 1 to indicate that this channel is active (contains interesting data) Bit 2: notA/B channel marker, used to mark left (0) and right (1) channels. Generally, even channels are A and odd channels are B. Bit 3: Set to 1 to mark the beginning of a 192-sample data block == Sampling frequency == The original AES10-1991 specification allowed 56 channels at sample rates from 32 to 48 kHz with an additional vari-speed range of ± 12.5%. This leads to a total range of 28 to 54 kHz. At the highest frequency, this produces a total of 56 × 32 × 54 = 96768 kbit/s, leaving 3.232% of the channel for synchronization marks and transmit clock error. The 2003 revision specifies different relations between sampling frequency and number of channels. 32 kHz to 48 kHz ± 12.5%, 56 channels; 32 kHz to 48 kHz nominal, 64 channels; 64 kHz to 96 kHz ± 12.5%, 28 channels. With a 48 kHz sampling frequency, 64 channels take 64 × 32 × 48000 = 98.304 Mbit/s. Adding the minimum 8 × 58 kbit/s of framing produces 98688 bit/s, leaving 1.312% free for timing variation and other overhead. Both versions of the standard accommodate higher sampling frequencies (for example, 96 kHz or 192 kHz) by using two or more channels per audio sample on the link.