M-DISC (Millennial Disc) is a write-once optical disc technology introduced in 2009 by Millenniata, Inc. and available as DVD and Blu-ray discs. == Overview == M-DISC's design is intended to provide archival media longevity. M-Disc claims that properly stored M-DISC DVD recordings will last up to 1000 years. The M-DISC DVD looks like a standard disc, except it is almost transparent with later DVD and BD-R M-Disks having standard and inkjet printable labels. The patents protecting the M-DISC technology assert that the data layer is a glassy carbon material that is substantially inert to oxidation and has a melting point of 200–1000 °C (392–1832 °F). M-Discs are readable by most regular DVD players made after 2005 and Blu-Ray and BDXL disc drives and writable by most made after 2011. Available recording capacities conform to standard DVD/Blu-ray sizes: 4.7 GB DVD+R to 25 GB BD-R, 50 GB BD-R and 100 GB BDXL. == History == M-DISC developer Millenniata, Inc. was co-founded by Brigham Young University professors Barry Lunt, Matthew Linford, CEO Henry O'Connell and CTO Doug Hansen. The company was incorporated on May 13, 2010, in American Fork, Utah. Millenniata, Inc. officially went bankrupt in December 2016. Under the direction of CEO Paul Brockbank, Millenniata had issued convertible debt. When the obligation for conversion was not satisfied, the company defaulted on the debt payment and the debt holders took possession of all of the company's assets. The debt holders subsequently started a new company, Yours.co, to sell M-DISCs and related services. As of the 2020s, there are only 2 licensed manufacturers of M-Discs: Ritek, sold under the Ritek and RiDATA brands, and Verbatim with co-branded discs, marketed as the "Verbatim M-DISC". 128 GB BDXL never made it to market due to the 2016 bankruptcy. Early in 2022, Verbatim changed the formulation of their M-DISC branded Blu-rays. These new discs could be written at a faster rate than the previous ones – 6× speed instead of 4×. The new discs also had different colouration and markings compared with older version. Later in the year customers accused Verbatim of selling an inferior product and deceptive marketing. Verbatim responded that the new discs were a further development of the older discs and should have the same longevity, and that the technical changes therein were responsible for the altered appearance and higher write speeds. The updated M-DISC currently sold on the market uses the same metal ablative layer (MABL) metal oxide inorganic recording layer used in many of Verbatim's regular Blu-ray products. == Durability claims == The original M-DISC DVD+R was tested according to ISO/IEC 10995:2011 and ECMA-379 with a projected rated lifespan of several hundred years in archival use. The glassy carbon layers, in theory if preserved correctly in an environment like a salt mine, could store the data for over 10,000 years before going outside of readable specifications. However, the polycarbonate plastics, which are commonly used by almost all optical media and heavily in CBRN and ballistic protective equipment due to their optical, physical impact and chemical resistant properties, have a lifespan rating of only around 1000 years before degradation. Verbatim Japan claims that M-DISCs now use a titanium layer to prevent moisture ingression and to provide environmental stability. M-DISCs sold in Japan are advertised to have a projected lifespan of 100 years or more based on internal ISO/IEC 16963 testing, while other regional Verbatim websites claim that M-DISCs have a projected lifespan of "several hundred years" based on ISO/IEC 16963 testing. == Durability testing == In 2009, testing was done by the US Department of Defense (DoD) producing the China Lake Report testing Millenniata's M-Disk DVD to current market offerings from Delkin, MAM-A, Mitsubishi, Taiyo Yuden and Verbatim with all brands using organic dyes failing to pass the series of accelerated aging tests. From 2010 to 2012, the French National Laboratory of Metrology and Testing (LNE) used high-temperature accelerated aging testing, at 90 °C (194 °F) and 85% relative humidity inside a CLIMATS Excal 5423-U, for 250 to 1000 hours with a mix of inorganic DVD+R discs from MPO, Verbatim, Maxell, Syylex and DataTresor. The summary of the tests states that Syylex Glass Master Disc was rated for 1000+ hours, DataTresor Disc 250 hours+ and M-Disk under 250 hours. The Syylex disc was a custom-ordered product that could not be burned in a consumer player when they were still purchaseable from Syylex before their bankruptcy, so it was not truly in the same category as the others. In 2016, a consumer Mol Smith did real world stress testing on the 25 GB BD-R M-Disc alongside TDK's standard BD-R 25 GB disc using a copied movie, which demonstrated the reliability of M-Disc's molding compared to standard discs; after 60 days of outdoor direct exposure the M-Disk was played without error, while the TDK disc was physically destroyed. In 2022, the NIST Interagency Report NIST IR 8387 listed the M-Disc as an acceptable archival format rated for 100+ years, citing the aforementioned 2009 and 2012 tests by the US Department of Defense and French National Laboratory of Metrology and Testing as sources. == Commercial support == While recorded discs are readable in conventional DVD and BD drives, M-disc DVDs can only be burned by drives with firmware that supports the slightly higher power mode that M-Disk requires for burning its inorganic layers, as such writing speed is typically 2× speed. Blu-ray M-discs can be both written and read in most standard Blu-ray drives and are certified by the Blu-ray Disc Association to meet all current standard specifications as of 2019. Typically, the M-Discs cost 1.5–3× the price of standard Blu-Ray discs with DVD M-Discs now having sparse availability. With the first-generation DVD M-DISCs, it was difficult to determine which was the writable side of the disc due to being near fully translucent, until coloring and later labels similar to that on standard DVD discs was added to discs to help distinguish the sides preventing user error. Asus, LG Electronics, Lite-On, Pioneer, Buffalo Technology, and Hitachi-LG produce drives that can record M-DISC media while Verbatim and Ritek produce M-DISC discs. == Adoption == The regional government of the U.S. state of Utah has used M-Disc since 2011. Some consumers and avid datahoarders have adopted the format for cold digital data storage. == Alternative technologies == === Optical === Syylex Glass Master Disc: these discs use etched glass and are only typically degradable by physical or chemical damage, but not by normal ageing inside an archival environment. Current BD 25 GB, BD-R DL 50 GB & BDXL 100 GB (three layer) and Sony's BDXL 128 GB (four layer) discs are rated for up to 50 years (Standard inorganic HTL discs). Sony's Optical Disc Archive, is an optical competitor to the LTO tape-based data storage system, currently with up to 5.5 TB cartridges of dual-sided 120mm discs, with desktop readers and automated rackmount standard archival systems allowing for large scale archival and data retrieval rated for an estimated 100+ years. Pioneer DM for Archive is a disc media and drive combination developed by Pioneer to meet the requirements laid out by the Japanese government for preservation of financial data for a minimum of 100 years. The discs use a MABL type recording layer and are manufactured with tight tolerances. Although burnable in any BD Writer, when burned in Pioneers DM for Archive writers using the DM Archiver software the media and burn quality meet ISO/IEC 18630 which defines the testing methods needed for ensuring media and burn quality. === Magnetic === Linear Tape-Open (LTO) is rated for up to 30 years in a climate-controlled environment and is currently in use by most industries, including broadcast and corporate digital data systems. The latest generation released in 2026 is LTO-10, it defines two unique cartridge types which can hold 30 TB or 40 TB each Hard disk drives are currently available up to 30 TB (HDD) capacity in 3.5-inch format and 5 TB in 2.5-inch laptop format. However, unlike optical media, they are limited to 5–25 years of operation lifespan due to inevitable mechanical failure or magnetic instability. == Gallery ==
Singularity studies
Singularity studies is an interdisciplinary academic field which examines the idea of technological singularity — the hypothesised point at which artificial intelligence may surpass human intelligence, might be attained by artificial intelligence (AI), robotics, and other technologies and sciences, and its social impacts. In this academic field, the study and research are conducted across a broad array of terrains such as information science, robotics, social informatics, economics, philosophy, and ethics. The primary aim of singularity studies is to gain an integrative understanding of the transformation of social systems occurring in tandem with the explosive evolution of AI and also the changes to be effected by such transformation in the view of humans, ethics, and legal systems. == History == An academic work on technological singurality has appeared in computer science, philosophy, sociology, and law since the early 1990s. Early discussions of an intelligence explosion were popularised by science-fiction writer Vernor Vinge in 1993 and later systematised by futurist Ray Kurzweil. Since the 2010s, universities such as Oxford, Stanford, and Keio have established dedicated programmes, while peer-reviewed journals have begun to publish scenario analyses and policy studies. Ongoing debates question the predictive value of singularity scenarios and warn against a deterministic view of technology. == Characteristics of research == Singularity studies extends beyond mere future predictions and offer an intellectual foundation for proactively designing and creating a desirable future. Principal research themes in this realm include: Ethics of AI; Social implications of technologies; Possibility of harmonious coexistence of humans and AI; Communication with AI; and Redesign of social systems. == Technologists and academics == Vernor Vinge: Propounded the concept of singularity in 1993, making a massive impact on the academic and science-fiction spheres. Ray Kurzweil: Predicted the advent around 2045 of the technological singularity in his 2005 book The Singularity Is Near. Nick Bostrom: Offered philosophical reflections on superintelligence and the risks posed by AI. He is the founding director of the now-dissolved Future of Humanity Institute at the University of Oxford. === Japan === Kento Sasano: A social informatician, AI educator, and inventor. He is the president of the Japan Society of Singularity Studies. == Challenges and outlook == Singularity studies is still evolving as an academic field, and quite a few challenges remain unresolved in regard to the systematization of their theories, research methods, and educational curricula. That said, in this day and age of accelerating technological and societal shifts, interdisciplinary approaches have gained in importance and are drawing much attention in the arenas of scholarly research, intercorporate collaboration, and policy planning.
Lisp machine
Lisp machines are general-purpose computers designed to efficiently run Lisp as their main software and programming language, usually via hardware support. They are an example of a high-level language computer architecture. In a sense, they were the first commercial single-user workstations. Despite being modest in number (perhaps 7,000 units total as of 1988) Lisp machines commercially pioneered some now-commonplace technologies, including networking innovations such as Chaosnet, and effective garbage collection. Several firms built and sold Lisp machines in the 1980s: Symbolics (3600, 3640, XL1200, MacIvory, and other models), Lisp Machines Incorporated (LMI Lambda), Texas Instruments (Explorer, MicroExplorer), and Xerox (Interlisp-D workstations). The operating systems were written in Lisp Machine Lisp, Interlisp (Xerox), and later partly in Common Lisp. == History == === Historical context === Artificial intelligence (AI) computer programs of the 1960s and 1970s intrinsically required what was then considered a huge amount of computer power, as measured in processor time and memory space. The power requirements of AI research were exacerbated by the Lisp symbolic programming language, when commercial hardware was designed and optimized for assembly- and Fortran-like programming languages. At first, the cost of such computer hardware meant that it had to be shared among many users. As integrated circuit technology shrank the size and cost of computers in the 1960s and early 1970s, and the memory needs of AI programs began to exceed the address space of the most common research computer, the Digital Equipment Corporation (DEC) PDP-10, researchers considered a new approach: a computer designed specifically to develop and run large artificial intelligence programs, and tailored to the semantics of the Lisp language. To provide consistent performance for interactive programs, these machines would often not be shared, but would be dedicated to a single user at a time. === Initial development === In 1973, Richard Greenblatt and Thomas Knight, programmers at Massachusetts Institute of Technology (MIT) Artificial Intelligence Laboratory (AI Lab), began what would become the MIT Lisp Machine Project when they first began building a computer hardwired to run certain basic Lisp operations, rather than run them in software, in a 24-bit tagged architecture. The machine also did incremental (or Arena) garbage collection. More specifically, since Lisp variables are typed at runtime rather than compile time, a simple addition of two variables could take five times as long on conventional hardware, due to test and branch instructions. Lisp Machines ran the tests in parallel with the more conventional single instruction additions. If the simultaneous tests failed, then the result was discarded and recomputed; this meant in many cases a speed increase by several factors. This simultaneous checking approach was used as well in testing the bounds of arrays when referenced, and other memory management necessities (not merely garbage collection or arrays). Type checking was further improved and automated when the conventional byte word of 32 bits was lengthened to 36 bits for Symbolics 3600-model Lisp machines and eventually to 40 bits or more (usually, the excess bits not accounted for by the following were used for error-correcting codes). The first group of extra bits were used to hold type data, making the machine a tagged architecture, and the remaining bits were used to implement compressed data representation (CDR) coding (wherein the usual linked list elements are compressed to occupy roughly half the space), aiding garbage collection by reportedly an order of magnitude. A further improvement was two microcode instructions which specifically supported Lisp functions, reducing the cost of calling a function to as little as 20 clock cycles, in some Symbolics implementations. The first machine was called the CONS machine (named after the list construction operator cons in Lisp). Often it was affectionately referred to as the Knight machine, perhaps since Knight wrote his master's thesis on the subject; it was extremely well received. It was subsequently improved into a version called CADR (a pun; in Lisp, the cadr function, which returns the second item of a list, is pronounced /ˈkeɪ.dəɹ/ or /ˈkɑ.dəɹ/, as some pronounce the word "cadre") which was based on essentially the same architecture. About 25 of what were essentially prototype CADRs were sold within and without MIT for ~$50,000; it quickly became the favorite machine for hacking – many of the most favored software tools were quickly ported to it (e.g. Emacs was ported from ITS in 1975). It was so well received at an AI conference held at MIT in 1978 that Defense Advanced Research Projects Agency (DARPA) began funding its development. === Commercializing MIT Lisp machine technology === In 1979, Russell Noftsker, being convinced that Lisp machines had a bright commercial future due to the strength of the Lisp language and the enabling factor of hardware acceleration, proposed to Greenblatt that they commercialize the technology. In a counter-intuitive move for an AI Lab hacker, Greenblatt acquiesced, hoping perhaps that he could recreate the informal and productive atmosphere of the Lab in a real business. These ideas and goals were considerably different from those of Noftsker. The two negotiated at length, but neither would compromise. As the proposed firm could succeed only with the full and undivided assistance of the AI Lab hackers as a group, Noftsker and Greenblatt decided that the fate of the enterprise was up to them, and so the choice should be left to the hackers. The ensuing discussions of the choice divided the lab into two factions. In February 1979, matters came to a head. The hackers sided with Noftsker, believing that a commercial venture-fund-backed firm had a better chance of surviving and commercializing Lisp machines than Greenblatt's proposed self-sustaining start-up. Greenblatt lost the battle. It was at this juncture that Symbolics, Noftsker's enterprise, slowly came together. While Noftsker was paying his staff a salary, he had no building or any equipment for the hackers to work on. He bargained with Patrick Winston that, in exchange for allowing Symbolics' staff to keep working out of MIT, Symbolics would let MIT use internally and freely all the software Symbolics developed. A consultant from CDC, who was trying to put together a natural language computer application with a group of West-coast programmers, came to Greenblatt, seeking a Lisp machine for his group to work with, about eight months after the disastrous conference with Noftsker. Greenblatt had decided to start his own rival Lisp machine firm, but he had done nothing. The consultant, Alexander Jacobson, decided that the only way Greenblatt was going to start the firm and build the Lisp machines that Jacobson desperately needed was if Jacobson pushed and otherwise helped Greenblatt launch the firm. Jacobson pulled together business plans, a board, a partner for Greenblatt (one F. Stephen Wyle). The newfound firm was named LISP Machine, Inc. (LMI), and was funded by CDC orders, via Jacobson. Around this time Symbolics (Noftsker's firm) began operating. It had been hindered by Noftsker's promise to give Greenblatt a year's head start, and by severe delays in procuring venture capital. Symbolics still had the major advantage that while 3 or 4 of the AI Lab hackers had gone to work for Greenblatt, 14 other hackers had signed onto Symbolics. Two AI Lab people were not hired by either: Richard Stallman and Marvin Minsky. Stallman, however, blamed Symbolics for the decline of the hacker community that had centered around the AI lab. For two years, from 1982 to the end of 1983, Stallman worked by himself to clone the output of the Symbolics programmers, with the aim of preventing them from gaining a monopoly on the lab's computers. Regardless, after a series of internal battles, Symbolics did get off the ground in 1980/1981, selling the CADR as the LM-2, while Lisp Machines, Inc. sold it as the LMI-CADR. Symbolics did not intend to produce many LM-2s, since the 3600 family of Lisp machines was supposed to ship quickly, but the 3600s were repeatedly delayed, and Symbolics ended up producing ~100 LM-2s, each of which sold for $70,000. Both firms developed second-generation products based on the CADR: the Symbolics 3600 and the LMI-LAMBDA (of which LMI managed to sell ~200). The 3600, which shipped a year late, expanded on the CADR by widening the machine word to 36-bits, expanding the address space to 28-bits, and adding hardware to accelerate certain common functions that were implemented in microcode on the CADR. The LMI-LAMBDA, which came out a year after the 3600, in 1983, was compatible with the CADR (it could run CADR microcode), but hardware differences existed. Texas Instruments (TI) joined the fray whe
Eimear Kenny
Eimear E. Kenny is a researcher in population genetics and translation genomics, and is the Founding Director of the Institute for Genomic Health, and Endowed Chair and Professor of Genomic Health at the Icahn School of Medicine at Mount Sinai. She is known for novel approaches in computational genomics, advancing the study of human genetic variation and its connection to disease risk and diagnosis. Her research has laid the foundation for integrating artificial intelligence (AI) and genomics into precision medicine and routine clinical care. By combining genomics, computer science, and medicine, her work leverages genomic sequencing technologies and machine learning algorithms to uncover insights that improve patient care, accelerate genomic data analysis, and enable the future of AI-driven healthcare. She has led multiple genomics-based clinical trials, applying computational biology and AI in clinical settings to advance genomic medicine and precision healthcare. == Research == A recipient of the Early-Career Award from the American Society of Human Genetics (USA), Kenny, as of 2024, leads a team in genetics, computer science, and medicine, focusing on genetic ancestry, large-scale genomics, clinical trials, and genomic medicine at the Institute for Genomic Health. The lab works to advance understanding of genetic ancestry and its impact on health in order to inform better clinical medicine models. She is recognized for her work to leverage biobanks for translational genomics and her development of new genetic tests an strategies for health care management. In one study, she and her colleagues investigated genetic disorders that might be under-diagnosed due to insufficient data, and found a variant in a collagen gene associated with Steel syndrome. This syndrome caused short stature and bone and joint issues and was thought to be rare. However, the study revealed it is common in individuals with Puerto Rican ancestry. Three of Kenny's genomic medicine clinical trials assessed how to bring new technology, such as digital apps, or information, such as polygenic risk scores, into routine clinical care. In the 2010s, Kenny was instrumental in several large-scale sequencing studies, including the 1000 Genomes Project, the Exome Sequencing Project, the Genome Sequencing Project, and the Trans-Omics for Precision Medicine. In 2012, she led work that discovered the variant responsible for blond hair in Melanesia, work that was featured in the Smithsonian NHGRI Human Genome Exhibit in Washington, D.C. In 2017, her group was one of the first to demonstrate that polygenic risk scores derived in predominantly European populations have reduced accuracy when applied in populations now widely acknowledged as a major challenge in the field of genomic risk prediction. As of 2024, she is Principal Investigator in many NIH-funded international consortium focused on computational genomics and genomic medicine, including Electronic Medical Records and Genomics, Polygenic Risk Methods in Diverse Populations, and the Human Pangenome Reference Consortium. In 2023, Kenny played a key role in a groundbreaking advancement in genomics research by helping to map a diverse human pangenome—a major shift from reliance on a single reference genome. Unlike the earlier genetic map, based on one man of mixed European and African ancestry in Buffalo, this new pangenome project captures far greater human genetic diversity. As reported by The Washington Post, Kenny's work demonstrates how a more inclusive human genome can drive discoveries in rare genetic diseases, improve genomic medicine, and accelerate the future of precision healthcare. Kenny was co-developer and current license holder for Random Forest adMIXture (RFMix), a patented software for inferring continental and sub-continental ancestry at genomic loci. == Education and career == Kenny graduated from Trinity College Dublin with a BA in Biochemistry in 1999 and did a masters in Bioinformatics at Leeds University. She received her PhD in Computational Genomics at Rockefeller University, and did her post-doctoral work in the lab of Dr. Carlos D. Bustamante at Stanford University. === Academic appointments === As of 2024, at Mount Sinai, she serves as the Endowed Chair and Professor of Genomic Health, Professor at the Department of Medicine and Professor at the Department of Genetics and Genomic Sciences. Since 2018 she has served as the Founding Director of the Institute for Genomic Health, and since 2022, she also serves as the Founding Director of the Center for Translational Genomics. She is also the Director of Translational Research, Division for Genomic Medicine. Former appointments include Assistant Professor at the Department of Genetics and Genomic Sciences and Member at The Charles Bronfman Institute of Personalized Medicine, both at Mount Sinai. She was also Bioinformatics Programmer at the California Institute of Technology, and research assistant at the Massachusetts Institute of Technology. == Publications == As of 2024, Kenny is an advisor to Cell Genomics. Google Scholar reports 50,623 citations, an h-index of 66 and an i10-index of 130. The five most-cited articles she contributed to are: Auton, A; Brooks, LD; Durbin, RM; Garrison, EP; Kang, HM; Korbel, JO; Marchini, JL; McCarthy, S; McVean, GA; Abecasis, GR (2015). "A global reference for human genetic variation". Nature. 526 (7571): 68–74. Bibcode:2015Natur.526...68T. doi:10.1038/nature15393. PMC 4750478. PMID 26432245.. Cited by 14847 Abecasis, GR; Auton, A; Brooks, LD; DePristo, MA; Durbin, RM; Handsaker, RE; Kang, HM; Marth, GT; McVean, GA (2012). "An integrated map of genetic variation from 1,092 human genomes". Nature. 491 (7422): 56–65. Bibcode:2012Natur.491...56T. doi:10.1038/nature11632. PMC 3498066. PMID 23128226.. Cited by 8287 Jacob A. Tennessen et al. Evolution and Functional Impact of Rare Coding Variation from Deep Sequencing of Human Exomes.Science337,64–69(2012).DOI:10.1126/science.1219240 Cited by 1886 Taliun, D.; Harris, D.N.; Kessler, M.D.; et al. (2021). "Sequencing of 53,831 diverse genomes from the NHLBI TOPMed Program". Nature. 590 (7845): 290–299. Bibcode:2021Natur.590..290T. doi:10.1038/s41586-021-03205-y. PMC 7875770. PMID 33568819.. Cited by 1369 Vilhjálmsson, BJ; et al. (2015). "Modeling Linkage Disequilibrium Increases Accuracy of Polygenic Risk Scores". Am J Hum Genet. 97 (4): 576–92. doi:10.1016/j.ajhg.2015.09.001. PMC 4596916. PMID 26430803.. Cited by 1327
Sentential decision diagram
In artificial intelligence, a sentential decision diagram (SDD) is a type of knowledge representation used in knowledge compilation to represent Boolean functions. SDDs can be viewed as a generalization of the influential ordered binary decision diagram (OBDD) representation, by allowing decisions on multiple variables at once. Like OBDDs, SDDs allow for tractable Boolean operations, while being exponentially more succinct. For this reason, they have become an important representation in knowledge compilation. == Properties == SDDs are defined with respect to a generalization of variable ordering known as a variable tree (vtree). Provided that they satisfy additional properties known as compression and trimming (which are analogous to ROBDDs), SDDs are a canonical representation of Boolean functions; that is, they are unique given a vtree. Like OBDDs, they allow for operations such as conjunction, disjunction and negation to be computed directly on the representation in polynomial time, while being potentially more compact. They also allow for polynomial-time model counting. SDDs are known to be exponentially more succinct than OBDDs. == Applications == SDDs are used as a compilation target for probabilistic logic programs by the ProbLog 2 system since they support tractable (weighted) model counting as well as tractable negation, conjunction and disjunction while being more succinct than BDDs. SDDs have also been extended to model probability distributions, in which context they are known as probabilistic sentential decision diagrams (PSDD).
Kinematic chain
In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained motion that is the mathematical model for a mechanical system. As the word chain suggests, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator. Mathematical models of the connections, or joints, between two links are termed kinematic pairs. Kinematic pairs model the hinged and sliding joints fundamental to robotics, often called lower pairs and the surface contact joints critical to cams and gearing, called higher pairs. These joints are generally modeled as holonomic constraints. A kinematic diagram is a schematic of the mechanical system that shows the kinematic chain. The modern use of kinematic chains includes analysis of Linkages (mechanical), compliance that arises from flexure joints in precision mechanisms, link compliance in compliant mechanisms and micro-electro-mechanical systems, and cable compliance in cable robotic and tensegrity systems. == Mobility formula == The degrees of freedom, or mobility, of a kinematic chain is the number of parameters that define the configuration of the chain. A system of n rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame. This frame is included in the count of bodies, so that mobility does not depend on link that forms the fixed frame. This means the degree-of-freedom of this system is M = 6(N − 1), where N = n + 1 is the number of moving bodies plus the fixed body. Joints that connect bodies impose constraints. Specifically, hinges and sliders each impose five constraints and therefore remove five degrees of freedom. It is convenient to define the number of constraints c that a joint imposes in terms of the joint's freedom f, where c = 6 − f. In the case of a hinge or slider, which are one-degree-of-freedom joints, have f = 1 and therefore c = 6 − 1 = 5. The result in general where d {\displaystyle d} is the degrees of freedom for the mobility of a kinematic chain formed from n moving links and j joints each with freedom fi, i = 1, 2, …, j, is given by M = d n − ∑ i = 1 j ( d − f i ) = d ( N − 1 − j ) + ∑ i = 1 j f i {\displaystyle M=dn-\sum _{i=1}^{j}(d-f_{i})=d(N-1-j)+\sum _{i=1}^{j}f_{i}} Where N is the total number of links and includes the fixed link. Spacial linkages used d = 6 {\displaystyle d=6} and planar linkages use d = 3 {\displaystyle d=3} . This result is known as the Chebychev–Grübler–Kutzbach criterion. == Analysis of kinematic chains == The constraint equations of a kinematic chain couple the range of movement allowed at each joint to the dimensions of the links in the chain, and form algebraic equations that are solved to determine the configuration of the chain associated with specific values of input parameters, called degrees of freedom. The constraint equations for a kinematic chain are obtained using rigid transformations [Z] to characterize the relative movement allowed at each joint and separate rigid transformations [X] to define the dimensions of each link. In the case of a serial open chain, the result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link. A chain of n links connected in series has the kinematic equations, [ T ] = [ Z 1 ] [ X 1 ] [ Z 2 ] [ X 2 ] ⋯ [ X n − 1 ] [ Z n ] , {\displaystyle [T]=[Z_{1}][X_{1}][Z_{2}][X_{2}]\cdots [X_{n-1}][Z_{n}],\!} where [T] is the transformation locating the end-link—notice that the chain includes a "zeroth" link consisting of the ground frame to which it is attached. These equations are called the forward kinematics equations of the serial chain. Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called loop equations. The complexity (in terms of calculating the forward and inverse kinematics) of the chain is determined by the following factors: Its topology: a serial chain, a parallel manipulator, a tree structure, or a graph. Its geometrical form: how are neighbouring joints spatially connected to each other? Explanation Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system. == Synthesis of kinematic chains == The constraint equations of a kinematic chain can be used in reverse to determine the dimensions of the links from a specification of the desired movement of the system. This is termed kinematic synthesis. Perhaps the most developed formulation of kinematic synthesis is for four-bar linkages, which is known as Burmester theory. Ferdinand Freudenstein is often called the father of modern kinematics for his contributions to the kinematic synthesis of linkages beginning in the 1950s. His use of the newly developed computer to solve Freudenstein's equation became the prototype of computer-aided design systems. This work has been generalized to the synthesis of spherical and spatial mechanisms.
Leela Chess Zero
Leela Chess Zero (abbreviated as LCZero, lc0) is a free, open-source chess engine and volunteer computing project based on Google's AlphaZero engine. It was spearheaded by Gary Linscott, a developer for the Stockfish chess engine, and adapted from the Leela Zero Go engine. Like Leela Zero and AlphaGo Zero, early iterations of Leela Chess Zero started with no intrinsic chess-specific knowledge other than the basic rules of the game. It learned how to play chess through reinforcement learning from repeated self-play, using a distributed computing network coordinated at the Leela Chess Zero website. However, as of November 2024 most models used by the engine are trained through supervised learning on data generated by previous reinforcement learning runs. As of June 2025, Leela Chess Zero has played over 2.5 billion games against itself, playing around 1 million games every day, and is capable of play at a level that is comparable with Stockfish, the leading conventional chess program. == History == The Leela Chess Zero project was first announced on TalkChess.com on January 9, 2018, as an open-source, self-learning chess engine attempting to recreate the success of AlphaZero. Within the first few months of training, Leela Chess Zero had already reached the Grandmaster level, surpassing the strength of early releases of Rybka, Stockfish, and Komodo, despite evaluating orders of magnitude fewer positions due to the size of the deep neural network it uses as its evaluation function. In December 2018, the AlphaZero team published a paper in Science magazine revealing previously undisclosed details of the architecture and training parameters used for AlphaZero. These changes were soon incorporated into Leela Chess Zero and increased both its strength and training efficiency. Work on Leela Chess Zero has informed the AobaZero project for shogi. The engine has been rewritten and carefully iterated upon since its inception, and since 2019 has run on multiple backends, allowing it to run on both CPU and GPU. The engine can be configured to use different weights, including even different architectures. This same mechanism of substitutable weights can also be used for alternative chess rules, such as for the Fischer Random Chess variant, which was done in 2019. == Neural network == Like AlphaZero, Leela Chess Zero employs neural networks which output both a policy vector, a distribution over subsequent moves used to guide search, and a position evaluation. These neural networks are designed to run on GPU, unlike traditional engines. It originally used residual neural networks, but in 2022 switched to using a transformer-based architecture designed by Daniel Monroe and Philip Chalmers. These models represent a chessboard as a sequence of 64 tokens and apply a trunk consisting of a stack of Post-LN encoder layers, outputting a sequence of 64 encoded tokens which is used to generate a position evaluation and a distribution over subsequent moves. They use a custom domain-specific position encoding called smolgen to improve the self-attention layer. As of November 2024, the models used by the engine are significantly larger and more efficient than the residual network used by AlphaZero, reportedly achieving grandmaster-level strength at one position evaluation per move. These models are able to detect and exploit positional features like trapped pieces and fortresses to outmaneuver traditional engines, giving Leela a unique playstyle. There is also evidence that they are able to perform look-ahead. == Program and use == Like AlphaZero, Leela Chess Zero learns through reinforcement learning, continually training on data generated through self-play. However, unlike AlphaZero, Leela Chess Zero decentralizes its data generation through distributed computing, with volunteers generating self-play data on local hardware which is fed to the reinforcement algorithm. In order to contribute training games, volunteers must download the latest non-release candidate (non-rc) version of the engine and the client. The client connects to the Leela Chess Zero server and iteratively receives the latest neural network version and produces self-play games which are sent back to the server and use to train the network. In order to run the Leela Chess Zero engine, two components are needed: the engine binary used to perform search, and a network used to evaluate positions. The client, which is used to contribute training data to the project, is not needed for this purpose. Older networks can also be downloaded and used by placing those networks in the folder with the Lc0 binary. == Spinoffs == In season 15 of the Top Chess Engine Championship, the engine AllieStein competed alongside Leela. AllieStein is a combination of two different spinoffs from Leela: Allie, which uses the same neural network as Leela, but has a unique search algorithm for exploring different lines of play, and Stein, a network which was trained using supervised learning on existing game data from games between other engines. While neither of these projects were admitted to TCEC separately due to their similarity to Leela, the combination of Allie's search algorithm with the Stein network, called AllieStein, was deemed unique enough to warrant its inclusion in the competition. In early 2021, the LcZero blog announced Ceres, a transliteration of the engine to C# which introduced several algorithmic improvements. The engine has performed competitively in tournaments, achieving third place in the TCEC Swiss 7 and fourth place in the TCEC Cup 14. In 2024, the CeresTrain framework was announced to support training deep neural networks for chess in PyTorch. == Competition results == In April 2018, Leela Chess Zero became the first engine using a deep neural network to enter the Top Chess Engine Championship (TCEC), during Season 12 in the lowest division, Division 4. Out of 28 games, it won one, drew two, and lost the remainder; its sole victory came from a position in which its opponent, Scorpio 2.82, crashed in three moves. However, it improved quickly. In July 2018, Leela placed seventh out of eight competitors at the 2018 World Computer Chess Championship. In August 2018, it won division 4 of TCEC season 13 with a record of 14 wins, 12 draws, and 2 losses. In Division 3, Leela scored 16/28 points, finishing third behind Ethereal, which scored 22.5/28 points, and Arasan on tiebreak. By September 2018, Leela had become competitive with the strongest engines in the world. In the 2018 Chess.com Computer Chess Championship (CCCC), Leela placed fifth out of 24 entrants. The top eight engines advanced to round 2, where Leela placed fourth. Leela then won the 30-game match against Komodo to secure third place in the tournament. Leela participated in the "TCEC Cup", an event in which engines from different TCEC divisions can play matches against one another. Leela defeated higher-division engines Laser, Ethereal and Fire before finally being eliminated by Stockfish in the semi-finals. In December 2018, Leela participated in Season 14 of the Top Chess Engine Championship. Leela dominated divisions 3, 2, and 1, easily finishing first in all of them. In the premier division, Stockfish dominated while Houdini, Komodo and Leela competed for second place. It came down to a final-round game where Leela needed to hold Stockfish to a draw with black to finish second ahead of Komodo. Leela managed this and therefore met Stockfish in the superfinal. In a back and forth match, first Stockfish and then Leela took three game leads before Stockfish won by the narrow margin of 50.5–49.5. In February 2019, Leela scored its first major tournament win when it defeated Houdini in the final of the second TCEC cup. Leela did not lose a game the entire tournament. In April 2019, Leela won the Chess.com Computer Chess Championship 7: Blitz Bonanza, becoming the first neural-network project to take the title. In the season 15 of the Top Chess Engine Championship (May 2019), Leela defended its TCEC Cup title, this time defeating Stockfish with a score of 5.5–4.5 (+2 =7 −1) in the final after Stockfish blundered a seven-man tablebase draw. Leela also won the Superfinal for the first time, scoring 53.5–46.5 (+14 −7 =79) versus Stockfish, including winning as both white and black in the same predetermined opening in games 61 and 62. Season 16 of TCEC saw Leela finish in third place in premier division, missing qualification for the Superfinal to Stockfish and the new deep neural network engine AllieStein. Leela was the only engine not to suffer any losses in the Premier division, and defeated Stockfish in one of the six games they played. However, Leela only managed to score nine wins, while AllieStein and Stockfish both scored 14 wins. This inability to defeat weaker engines led to Leela finishing third, half a point behind AllieStein and a point behind Stockfish. In the fourth TCEC Cup, Leela was seeded first as the defending champion,