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22,400 | The book's main content is the depiction, explanation, and solution of over 100 of these Sangaku puzzles, ranked by their difficulty, selected from over 1800 catalogued Sangaku and over 800 surviving examples. The solutions given use modern mathematical techniques where appropriate rather than attempting to model how t... | Sacred Mathematics | 0.809436 |
22,401 | The book begins with an introduction to Japanese culture and how this culture led to the production of Sangaku tablets, depicting geometry problems, their presentation as votive offerings at temples, and their display at the temples. It also includes a chapter on the Chinese origins of Japanese mathematics, and a chapt... | Sacred Mathematics | 0.809436 |
22,402 | This is the third English-language book on Japanese mathematics from Fukagawa; the first two were Japanese Temple Geometry Problems (with Daniel Pedoe, 1989) and Traditional Japanese Mathematics Problems from the 18th and 19th Centuries (with John Rigby, 2002). Sacred Mathematics expands on a 1998 article on Sangaku by... | Sacred Mathematics | 0.809436 |
22,403 | Sacred Mathematics: Japanese Temple Geometry is a book on Sangaku, geometry problems presented on wooden tablets as temple offerings in the Edo period of Japan. It was written by Fukagawa Hidetoshi and Tony Rothman, and published in 2008 by the Princeton University Press. It won the PROSE Award of the Association of Am... | Sacred Mathematics | 0.809436 |
22,404 | Sacred Geometry can be read by historians of mathematics, professional mathematicians, "people who are simply interested in geometry", and "anyone who likes mathematics", and the puzzles it presents also span a wide range of expertise. Readers are not expected to already have a background in Japanese culture and histor... | Sacred Mathematics | 0.809436 |
22,405 | As a natural vibrator, the string will oscillate with specific modes (the standing waves of a string in harmonic resonance), dependent on the length of the string. In classical physics, a radiator of energy will act as a natural vibrator. Additionally, since each mode will have the same energy, most of the energy in a ... | UV catastrophe | 0.809431 |
22,406 | This formula is obtained from the equipartition theorem of classical statistical mechanics which states that all harmonic oscillator modes (degrees of freedom) of a system at equilibrium have an average energy of k B T {\displaystyle k_{\rm {B}}T} . The "ultraviolet catastrophe" is the expression of the fact that the f... | UV catastrophe | 0.809431 |
22,407 | There are several types of constructions for bent functions. Combinatorial constructions: iterative constructions, Maiorana–McFarland construction, partial spreads, Dillon's and Dobbertin's bent functions, minterm bent functions, bent iterative functions Algebraic constructions: monomial bent functions with exponents o... | Bent function | 0.809429 |
22,408 | As early as 1982 it was discovered that maximum length sequences based on bent functions have cross-correlation and autocorrelation properties rivalling those of the Gold codes and Kasami codes for use in CDMA. These sequences have several applications in spread spectrum techniques. The properties of bent functions are... | Bent function | 0.809429 |
22,409 | In addition, detecting a change in the output of the function yields no information about what change occurred in the inputs, making the function immune to differential cryptanalysis. Bent functions were defined and named in the 1960s by Oscar Rothaus in research not published until 1976. They have been extensively stu... | Bent function | 0.809429 |
22,410 | In this case, g ^ ( a ) = 2 n / 2 ( − 1 ) f ( a ) {\displaystyle {\hat {g}}(a)=2^{n/2}(-1)^{f(a)}} , so f and g are considered dual functions.Every bent function has a Hamming weight (number of times it takes the value 1) of 2n−1 ± 2n/2−1, and in fact agrees with any affine function at one of those two numbers of point... | Bent function | 0.809429 |
22,411 | Rothaus defined a bent function as a Boolean function f: Z 2 n → Z 2 {\displaystyle f:\mathbb {Z} _{2}^{n}\to \mathbb {Z} _{2}} whose Walsh transform has constant absolute value. Bent functions are in a sense equidistant from all the affine functions, so they are equally hard to approximate with any affine function. Th... | Bent function | 0.809429 |
22,412 | More than 25 different generalizations of bent functions are described in Tokareva's 2015 monograph. There are algebraic generalizations (q-valued bent functions, p-ary bent functions, bent functions over a finite field, generalized Boolean bent functions of Schmidt, bent functions from a finite Abelian group into the ... | Bent function | 0.809429 |
22,413 | In molecular biology, the term double helix refers to the structure formed by double-stranded molecules of nucleic acids such as DNA. The double helical structure of a nucleic acid complex arises as a consequence of its secondary structure, and is a fundamental component in determining its tertiary structure. The term ... | Watson-Crick model | 0.809425 |
22,414 | The CAS database is the most comprehensive repository for data on organic compounds. The search tool SciFinder is offered. The Beilstein database contains information on 9.8 million substances, covers the scientific literature from 1771 to the present, and is today accessible via Reaxys. Structures and a large diversit... | Organic chemical | 0.809424 |
22,415 | This quickly became the de facto standard model, both in the industry as well as the astronomy field. Shortly after the publication of Report #3, NASA began posting elements for a variety of visible and other well known objects in their periodic NASA Prediction Bulletins, which consisted of the transmission format data... | Two-line elements | 0.809424 |
22,416 | TGen was established in July 2002 by Jeffrey Trent in Phoenix, Arizona, with an initial investment of US$100 million from Arizona public and private-sector investors.TGen conducts research on various human disorders, including Alzheimer's disease, autism, Parkinson's, diabetes, cancer, and other complex diseases. The i... | Translational Genomics Research Institute | 0.809422 |
22,417 | Packages can be built from source on any platform, or if additional optimizations or options are desired. The pkgsrc collection contains over 19,000 packages, of which nearly 800 are in scientific categories, and over 60 are biology-related. DebianThere are more than a hundred bioinformatics packages provided as part o... | BioLinux | 0.809422 |
22,418 | The build-from-source option also allows the ports system to automate installation of software with a license that does not permit redistribution. The ports collection contains over 31,000 ports, of which over 2,200 are in scientific categories, and over 240 are biology-related. New ports and updates are listed on the ... | BioLinux | 0.809422 |
22,419 | Its ports are analogous Gentoo's ebuilds. However, the project continuously builds pre-compiled binary packages for Tier-1 platforms such as x86 and ARM. Users can also choose to build and install any port from source in order to enable non-portable optimizations or other build options. | BioLinux | 0.809422 |
22,420 | In general, Linux distributions have a wide range of official packages available, but this does not usually include much in the way of scientific support. There are exceptions, such as those detailed below. Gentoo LinuxGentoo Linux provides over 156 bioinformatics applications (see Gentoo sci-biology herd in the main t... | BioLinux | 0.809422 |
22,421 | BioLinux is a term used in a variety of projects involved in making access to bioinformatics software on a Linux platform easier using one or more of the following methods: Provision of complete systems Provision of bioinformatics software repositories Addition of bioinformatics packages to standard distributions Live ... | BioLinux | 0.809422 |
22,422 | Fedora Core is a community supported derivative of Red Hat and is popular amongst those who like Red Hat's system but don't require commercial support. Many users of bioinformatics applications have produced RPMs (Red Hat's package format) designed to work with Fedora, which you can potentially also install on Red Hat ... | BioLinux | 0.809422 |
22,423 | Package repositories are generally specific to the distribution of Linux the bioinformatician is using. A number of Linux variants are prevalent in bioinformatics work. Fedora is a freely-distributed version of the commercial Red Hat system. Red Hat is widely used in the corporate world as they offer commercial support... | BioLinux | 0.809422 |
22,424 | Live DVDs or CDs are not an ideal way to provide bioinformatics computing, as they run from a CD/DVD drive. This means they are slower than a traditional hard disk installation and have limited ability to be configured. However, they can be suitable for providing ad hoc solutions where no other Linux access is availabl... | BioLinux | 0.809422 |
22,425 | Slackware is one of the less used Linux distributions. It is popular with those who have better knowledge of the Linux operating system and who prefer the command line over the various GUIs available. Packages are in the tgz or tgx format. The most widely known live distribution based on Slackware is Slax and it has be... | BioLinux | 0.809422 |
22,426 | Many Linux packages are compatible with Mac OS X and there are several projects which attempt to make it easy to install selected Linux packages (including bioinformatics software) on a computer running Mac OS X. (source?) | BioLinux | 0.809422 |
22,427 | Statistical shape analysis is an analysis of the geometrical properties of some given set of shapes by statistical methods. For instance, it could be used to quantify differences between male and female gorilla skull shapes, normal and pathological bone shapes, leaf outlines with and without herbivory by insects, etc. ... | Shape statistics | 0.80942 |
22,428 | Register pressure measures the availability of free registers at any point in time during the program execution. Register pressure is high when a large number of the available registers are in use; thus, the higher the register pressure, the more often the register contents must be spilled into memory. Increasing the n... | Register pressure | 0.809417 |
22,429 | A metamaterial is any material engineered to have a property that is not found in naturally occurring materials, usually by combining several materials to form a composite and / or tuning the shape, geometry, size, orientation and arrangement to achieve the desired property.In foams and textiles, the chemical structure... | Material | 0.809411 |
22,430 | Material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geological origin or biological function. Materials science is the study of materials... | Material | 0.809411 |
22,431 | He speculated on hydrocarbons,: 11 hydrofluoric acid, and ammonia as possible alternatives to water. Some of the properties of water that are important for life processes include: A complexity which leads to a large number of permutations of possible reaction paths including acid–base chemistry, H+ cations, OH− anions,... | Silicon-based life form | 0.809402 |
22,432 | Perhaps the least unusual alternative biochemistry would be one with differing chirality of its biomolecules. In known Earth-based life, amino acids are almost universally of the L form and sugars are of the D form. Molecules using D amino acids or L sugars may be possible; molecules of such a chirality, however, would... | Silicon-based life form | 0.809402 |
22,433 | In ten-dimensional geometry, a rectified 10-simplex is a convex uniform 10-polytope, being a rectification of the regular 10-simplex. These polytopes are part of a family of 527 uniform 10-polytopes with A10 symmetry. There are unique 5 degrees of rectifications including the zeroth, the 10-simplex itself. Vertices of ... | Rectified 10-simplex | 0.809398 |
22,434 | Environmental Science: Processes & Impacts is a monthly peer-reviewed scientific journal covering all aspects of environmental science. It is published by the Royal Society of Chemistry and Kris McNeill is the editor-in-chief. The journal was established in 1999 as the Journal of Environmental Monitoring and obtained i... | Environmental Science: Processes & Impacts | 0.809397 |
22,435 | The Royal Society of Chemistry publishes 2 other journals in the Environmental Science portfolio: Environmental Science: Nano was established in 2014 and Environmental Science: Water Research & Technology in 2015. | Environmental Science: Processes & Impacts | 0.809397 |
22,436 | These algorithms require a constant-rate assumption and produce trees in which the distances from the root to every branch tip are equal. When DNA, RNA and protein data are analyzed, the ultrametricity assumption is called the molecular clock. Models of intermittency in three dimensional turbulence of fluids make use o... | Ultrametric inequality | 0.809397 |
22,437 | In condensed matter physics, the self-averaging overlap between spins in the SK Model of spin glasses exhibits an ultrametric structure, with the solution given by the full replica symmetry breaking procedure first outlined by Giorgio Parisi and coworkers. Ultrametricity also appears in the theory of aperiodic solids. ... | Ultrametric inequality | 0.809397 |
22,438 | A contraction mapping may then be thought of as a way of approximating the final result of a computation (which can be guaranteed to exist by the Banach fixed-point theorem). Similar ideas can be found in domain theory. p-adic analysis makes heavy use of the ultrametric nature of the p-adic metric. | Ultrametric inequality | 0.809397 |
22,439 | The idea of "a set of good practices" including "some obligatory metadata" was first proposed by Nicolas Le Novère in October 2004 as part of a discussion to develop a common database of models in systems biology (which led to the creation of BioModels Database). These initial ideas were further refined at a meeting in... | Minimum information required in the annotation of models | 0.809397 |
22,440 | STP-H9-SWELL (Space Wireless Energy Laser Link), A test payload for Laser Communications a follow on to OPALS,Electric Propulsion Electrostatic Analyzer, A test device that will demonstrate re-boost using Ion Propulsion, Neutron Radiation Detection Instrument from NRL, Variable Voltage Ion Protection Experiment from NR... | Japanese Experiment Module | 0.809394 |
22,441 | MAXI – X-ray astronomy from 0.5 to 30 keV. Exposed Facility Slot 1. STP Houston 8 Payload-COWVR and TEMPEST Launched on SpaceX CRS-24 in 2021. Exposed Facility Slot 2 port originally held ICS-EF and CREAM which was moved to Slot 13 on the roof and stowed in hibernation. | Japanese Experiment Module | 0.809394 |
22,442 | Japanese: RYUTAI Rack 流体 (りゅうたい, ryūtai, fluid) – Fluid Physics Experiment Facility (FPEF), Solution Crystallization Observation Facility (SCOF), Protein Crystallization Research Facility (PCRF), Image Processing Unit (IPU) SAIBO Rack 細胞 (さいぼう, saibō, cell) – Cell Biology Experiment Facility (CBEF), Clean Bench (CB) KO... | Japanese Experiment Module | 0.809394 |
22,443 | The International System of Quantities (ISQ) consists of the quantities used in physics and in modern science in general, starting with basic quantities such as length and mass, and the relationships between those quantities. This system underlies the International System of Units (SI) but does not itself determine the... | Base quantity | 0.809392 |
22,444 | The other one is an isosceles triangle that has 2 angles measuring 45 degrees (45–45–90 triangle). Right triangles are fundamental in trigonometry, as they can be used to define trigonometric functions through trigonometric ratios. Triangles that do not have an angle measuring 90° are called oblique triangles. | Triangle (geometry) | 0.809392 |
22,445 | Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse. Special right triangles are right triangles with additional propertie... | Triangle (geometry) | 0.809392 |
22,446 | This fact is equivalent to Euclid's parallel postulate. This allows determination of the measure of the third angle of any triangle, given the measure of two angles. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a tr... | Triangle (geometry) | 0.809392 |
22,447 | The inverse trigonometric functions can be used to calculate the internal angles for a right angled triangle with the length of any two sides. Arcsin can be used to calculate an angle from the length of the opposite side and the length of the hypotenuse. θ = arcsin ( opposite side hypotenuse ) {\displaystyle \theta =... | Triangle (geometry) | 0.809392 |
22,448 | If the legs of a right triangle have the same length, then the angles opposite those legs have the same measure. Since these angles are complementary, it follows that each measures 45 degrees. By the Pythagorean theorem, the length of the hypotenuse is the length of a leg times √2. | Triangle (geometry) | 0.809392 |
22,449 | A central theorem is the Pythagorean theorem, which states in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. If the hypotenuse has length c, and the legs have lengths a and b, then the theorem states that a 2 + b 2 = c 2 . {\displaysty... | Triangle (geometry) | 0.809392 |
22,450 | Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle. | Triangle (geometry) | 0.809392 |
22,451 | Knut Schmidt-Nielsen (1915–2007) was a major figure in vertebrate comparative physiology, serving on the faculty at Duke University for many years and training a large number of students (obituary). He also authored several books, including an influential text, all known for their accessible writing style. Grover C. St... | Comparative physiology | 0.809391 |
22,452 | This is essentially physiological ecology or ecological physiology.4. To identify "model systems" for studying particular physiological functions. Examples of this include using squid giant axons to understand general principles of nerve transmission, using rattlesnake tail shaker muscles for measurement of in vivo cha... | Comparative physiology | 0.809391 |
22,453 | American Journal of Physiology - Regulatory, Integrative and Comparative Physiology Annual Review of Physiology Comparative Biochemistry and Physiology Integrative and Comparative Biology Journal of Comparative Physiology Journal of Experimental Biology Physiological and Biochemical Zoology | Comparative physiology | 0.809391 |
22,454 | A number of scientific societies feature sections on comparative physiology, including: American Physiological Society Australian & New Zealand Society for Comparative Physiology & Biochemistry Canadian Society of Zoologists Japanese Society for Comparative Physiology and Biochemistry Society for Integrative and Compar... | Comparative physiology | 0.809391 |
22,455 | In 1961, Bar Hillel first discussed the need and significance of practical knowledge for natural language processing in the context of machine translation. Some ambiguities are resolved by using simple and easy to acquire rules. Others require a broad acknowledgement of the surrounding world, thus they require more com... | Commonsense reasoning | 0.809391 |
22,456 | In artificial intelligence (AI), commonsense reasoning is a human-like ability to make presumptions about the type and essence of ordinary situations humans encounter every day. These assumptions include judgments about the nature of physical objects, taxonomic properties, and peoples' intentions. A device that exhibit... | Commonsense reasoning | 0.809391 |
22,457 | Compared with humans, existing AI lacks several features of human commonsense reasoning; most notably, humans have powerful mechanisms for reasoning about "naïve physics" such as space, time, and physical interactions. This enables even young children to easily make inferences like "If I roll this pen off a table, it w... | Commonsense reasoning | 0.809391 |
22,458 | COMET (2019), which uses both the OpenAI GPT language model architecture and existing commonsense knowledge bases such as ConceptNet, claims to generate commonsense inferences at a level approaching human benchmarks. Like many other current efforts, COMET over-relies on surface language patterns and is judged to lack d... | Commonsense reasoning | 0.809391 |
22,459 | Commonsense's reasoning study is divided into knowledge-based approaches and approaches that are based on machine learning over and using a large data corpora with limited interactions between these two types of approaches. There are also crowdsourcing approaches, attempting to construct a knowledge basis by linking th... | Commonsense reasoning | 0.809391 |
22,460 | The commonsense knowledge problem is a current project in the sphere of artificial intelligence to create a database that contains the general knowledge most individuals are expected to have, represented in an accessible way to artificial intelligence programs that use natural language. Due to the broad scope of the co... | Commonsense reasoning | 0.809391 |
22,461 | Qualitative reasoning is the form of commonsense reasoning analyzed with certain success. It is concerned with the direction of change in interrelated quantities. For instance, if the price of a stock goes up, the amount of stocks that are going to be sold will go down. If some ecosystem contains wolves and lambs and t... | Commonsense reasoning | 0.809391 |
22,462 | Issues of this kind arise in computer vision. For instance when looking at a photograph of a bathroom some items that are small and only partly seen, such as facecloths and bottles, are recognizable due to the surrounding objects (toilet, wash basin, bathtub), which suggest the purpose of the room. In an isolated image... | Commonsense reasoning | 0.809391 |
22,463 | The outer automorphism group is important in the topology of surfaces because there is a connection provided by the Dehn–Nielsen theorem: the extended mapping class group of the surface is the outer automorphism group of its fundamental group. | Outer automorphism | 0.809391 |
22,464 | Let G now be a connected reductive group over an algebraically closed field. Then any two Borel subgroups are conjugate by an inner automorphism, so to study outer automorphisms it suffices to consider automorphisms that fix a given Borel subgroup. Associated to the Borel subgroup is a set of simple roots, and the oute... | Outer automorphism | 0.809391 |
22,465 | Spherical bearings are used in car suspensions, engines, driveshafts, heavy machinery, sewing machines, robotics and many other applications: wherever rotational motion must be allowed to change the alignment of its rotation axis. An example, although this is rarely used in practice, is the drive axle bearings of a veh... | Spherical bearing | 0.809391 |
22,466 | A spherical bearing is a bearing that permits rotation about a central point in two orthogonal directions (usually within a specified angular limit based on the bearing geometry). Typically these bearings support a rotating shaft in the bore of the inner ring that must move not only rotationally, but also at an angle. ... | Spherical bearing | 0.809391 |
22,467 | Finding Aid for the American Association of Physics Teachers, South Atlantic Coast Section Records at the University of North Carolina at Greensboro | American Association of Physics Teachers | 0.809391 |
22,468 | American Association of Physics Teachers Richard M. Sutton records, 1934-1949 American Association of Physics Teachers miscellaneous publications, 1934-2013 American Association of Physics Teachers records of David Locke Webster, 1930-1958 American Journal of Physics editor's reports, 1967-2001 AAPT Chesapeake Section ... | American Association of Physics Teachers | 0.809391 |
22,469 | The American Association of Physics Teachers was founded on December 31, 1930, when forty-five physicists held a meeting during the joint APS-AAAS meeting in Cleveland specifically for that purpose. The AAPT became a founding member of the American Institute of Physics after the other founding members were convinced of... | American Association of Physics Teachers | 0.809391 |
22,470 | The association has two annual National Meetings (winter and summer) and has regional sections with their own meetings and organization. The association also offers grants and awards for physics educators, including the Richtmyer Memorial Award and programs and contests for physics educators and students. It is headqua... | American Association of Physics Teachers | 0.809391 |
22,471 | The American Association of Physics Teachers (AAPT) was founded in 1930 for the purpose of "dissemination of knowledge of physics, particularly by way of teaching." There are more than 10,000 members in over 30 countries. AAPT publications include two peer-reviewed journals, the American Journal of Physics and The Phys... | American Association of Physics Teachers | 0.809391 |
22,472 | The AAPT sponsors a number of competitions. The Physics Bowl, Six Flags' roller coaster contest, and the US Physics Team are just a few. The US physics team is determined by two preliminary exams and a week and a half long "boot camp." Each year, five members are selected to compete against dozens of countries in the I... | American Association of Physics Teachers | 0.809391 |
22,473 | When using just one-cell cloned embryos, the experiment has a 65% chance to fail in the process of making morula or blastocyst. The biochemistry also has to be extremely precise, as most late term cloned fetus deaths are the result of inadequate placentation. However, by 2014, researchers were reporting success rates o... | Therapeutic cloning | 0.809384 |
22,474 | Another reason why there is such high mortality rate with the cloned offspring is due to the fetus being larger than even other large offspring, resulting in death soon after birth. The biochemistry involved in reprogramming the differentiated somatic cell nucleus and activating the recipient egg was also far from unde... | Therapeutic cloning | 0.809384 |
22,475 | In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsa... | Resolution inference | 0.809384 |
22,476 | Most developed countries usually have a specific national body overseeing national science (including technology and innovation) policy. Many developing countries follow the same fashion. Many governments of developed countries provide considerable funds (primarily to universities) for scientific research (in fields su... | Science policy | 0.80938 |
22,477 | Public policy can directly affect the funding of capital equipment, intellectual infrastructure for industrial research, by providing tax incentives to those organizations who fund research. Vannevar Bush, director of the office of scientific research and development for the U.S. government in July 1945, wrote "Science... | Science policy | 0.809379 |
22,478 | Research funding by the Government of India comes from a number of sources. For basic science and technology research, these include the Council for Scientific and Industrial Research (CSIR), Department of Science and Technology (DST), and University Grants Commission (UGC). For medical research, these include the Indi... | Science policy | 0.809379 |
22,479 | In the United Kingdom, the Haldane principle, that decisions about what to spend research funds on should be made by researchers rather than politicians, is still influential in research policy. There are several university departments with a focus on science policy, such as the Science Policy Research Unit. There are ... | Science policy | 0.809379 |
22,480 | Most observers explain the project as over constrained: the cost goals too aggressive, the technology and mission too underpowered and undefined. The Japanese fifth generation computer systems project met every technological goal, but failed to produce commercially important artificial intelligence. Many observers beli... | Science policy | 0.809379 |
22,481 | The latter starts with an equilateral triangle and shows that a triangle may be built around it which will be similar to any selected triangle. Morley's theorem does not hold in spherical and hyperbolic geometry. One proof uses the trigonometric identity which, by using of the sum of two angles identity, can be shown t... | Morley's trisector theorem | 0.809376 |
22,482 | There are many proofs of Morley's theorem, some of which are very technical. Several early proofs were based on delicate trigonometric calculations. Recent proofs include an algebraic proof by Alain Connes (1998, 2004) extending the theorem to general fields other than characteristic three, and John Conway's elementary... | Morley's trisector theorem | 0.809376 |
22,483 | Morley's theorem entails 18 equilateral triangles. The triangle described in the trisector theorem above, called the first Morley triangle, has vertices given in trilinear coordinates relative to a triangle ABC as follows: Another of Morley's equilateral triangles that is also a central triangle is called the second Mo... | Morley's trisector theorem | 0.809376 |
22,484 | In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley. It h... | Morley's trisector theorem | 0.809376 |
22,485 | A cautionary note on prediction of absolute stereochemistry based on liquid chromatographic elution order of diastereomeric derivatives. showed that the mevalonate and homomevalonate produced by these enzymes has the same 3S optical isomer configuration as the vertebrate enzymes showed that isopentenyl diphosphate, and... | Juvenile hormone | 0.809368 |
22,486 | This yields an optimization problem of the form. min | | v w − v d | | 2 s . t . | Flux balance analysis | 0.809366 |
22,487 | A good description of the basic concepts of FBA can be found in the freely available supplementary material to Edwards et al. 2001 which can be found at the Nature website. Further sources include the book "Systems Biology" by B. Palsson dedicated to the subject and a useful tutorial and paper by J. Orth. Many other so... | Flux balance analysis | 0.809366 |
22,488 | The material balance model for this process becomes: I n p u t = O u t p u t + A c c u m u l a t i o n {\displaystyle \mathrm {Input} =\mathrm {Output} +\mathrm {Accumulation} } If we consider the system of microbial cells to be at steady state then we may set the accumulation term to zero and reduce the material balan... | Flux balance analysis | 0.809366 |
22,489 | In contrast to the traditionally followed approach of metabolic modeling using coupled ordinary differential equations, flux balance analysis requires very little information in terms of the enzyme kinetic parameters and concentration of metabolites in the system. It achieves this by making two assumptions, steady stat... | Flux balance analysis | 0.809366 |
22,490 | Accurately representing the biological limits of the system and returning the flux distribution closest to the natural fluxes within the target system/organism. Certain biological principles can help overcome the mathematical difficulties. While the stoichiometric matrix is almost always under-determined initially (mea... | Flux balance analysis | 0.809366 |
22,491 | The analysis of the null space of matrices is implemented in software packages specialized for matrix operations such as Matlab and Octave. Determination of the null space of S {\displaystyle \scriptstyle \mathbf {S} } tells us all the possible collections of flux vectors (or linear combinations thereof) that balance f... | Flux balance analysis | 0.809366 |
22,492 | Linear programming can be used to find a single optimal solution. The most common biological optimization goal for a whole-organism metabolic network would be to choose the flux vector v → {\displaystyle {\vec {v}}} that maximises the flux through a biomass function composed of the constituent metabolites of the organi... | Flux balance analysis | 0.809366 |
22,493 | In 2000, the association and the then editorial board started a new journal under the name Theory and Practice of Logic Programming, published by Cambridge University Press. Elsevier continued the journal with a new editorial board under the title Journal of Logic and Algebraic Programming. According to the Journal Cit... | Journal of Logical and Algebraic Methods in Programming | 0.809363 |
22,494 | The Journal of Logical and Algebraic Methods in Programming is a peer-reviewed scientific journal established in 1984. It was originally titled The Journal of Logic Programming; in 2001 it was renamed The Journal of Logic and Algebraic Programming, and in 2014 it obtained its current title. The founding editor-in-chief... | Journal of Logical and Algebraic Methods in Programming | 0.809363 |
22,495 | Building from the tradition of McCulloch and Pitts, the computational theory of cognition (CTC) states that neural computations explain cognition. The computational theory of mind asserts that not only cognition, but also phenomenal consciousness or qualia, are computational. That is to say, CTM entails CTC. While phen... | Computational theory of mind | 0.809362 |
22,496 | Computation is commonly understood in terms of Turing machines which manipulate symbols according to a rule, in combination with the internal state of the machine. The critical aspect of such a computational model is that we can abstract away from particular physical details of the machine that is implementing the comp... | Computational theory of mind | 0.809362 |
22,497 | In mathematics, in particular in homological algebra, a differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. | DG Algebra | 0.809362 |
22,498 | A Lipschitz structure on a topological manifold is defined using an atlas of charts whose transition maps are bilipschitz; this is possible because bilipschitz maps form a pseudogroup. Such a structure allows one to define locally Lipschitz maps between such manifolds, similarly to how one defines smooth maps between s... | Lipschitz constant | 0.809362 |
22,499 | In projective geometry, the circular points at infinity (also called cyclic points or isotropic points) are two special points at infinity in the complex projective plane that are contained in the complexification of every real circle. | Cyclic points | 0.809362 |
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