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The Singapore Satellite Positioning Reference Network ( SiReNT ), is an infrastructure network launched by the Survey Services section of the Singapore Land Authority in 2006. [ 1 ] Its purpose is to define Singapore's official spatial reference framework and to support the cadastral system in SVY21. It is a multi-purpose high precision positioning infrastructure which provides both Post Process Differential Global Positioning System (DGPS) DGPS services and Real Time DGPS services. The system supports all types of GPS positioning modes and formats.
SiReNT comprises five GPS reference stations connected to a data control centre at government data centre. [ 2 ] Four of the five reference stations are located at the extreme corners of the island of Singapore, with the fifth located in the centre of the island. The four external reference stations are located at Nanyang Technological University , Keppel Club , Loyang , and Senoko , with the designations SNTU, SKEP, SLOY, and SSEK, respectively. The central location is at Nanyang Polytechnic , designated by SNYP. [ 1 ] The entire set-up is made up of advanced GPS equipment and sophisticated computer hardware, software, communications and network.
SiReNT supports a great variety of applications. It provides data reliability, efficiency and productivity of survey work for land surveyors with the aid of GPS technology. It also offers a wide range of GPS data services with various accuracy levels ranging from metres to centimetres to suit different applications from positioning to tracking and monitoring.
These GPS reference stations receive satellite signals 24 hours a day and transmit GPS data continuously to the data control centre for storage and processing. Corrections processed from the data are then streamed to subscribed users.
SiReNT offers 4 types of services, namely Post Processing (PP) On-Demand, Post Processing (PP) Archive, Real Time Kinematic (RTK) and low accuracy Differential Global Positioning System (DGPS) to suit different applications. In 2010, SiReNT introduced support for telematics and structural monitoring solutions. | https://en.wikipedia.org/wiki/SiReNT |
Silicon disulfide is the inorganic compound with the formula Si S 2 . Like silicon dioxide , this material is polymeric , but it adopts a 1-dimensional structure quite different from the usual forms of SiO 2 .
The material is formed by heating silicon and sulfur or by the exchange reaction between SiO 2 and Al 2 S 3 . The material consists of chains of edge-shared tetrahedra , -Si(μ-S) 2 Si(μ-S) 2 -. [ 2 ]
Like other silicon sulfur-compounds (e.g., bis(trimethylsilyl)sulfide ) SiS 2 hydrolyzes readily to release H 2 S.
In liquid ammonia it is reported to form the imide Si(NH) 2 and NH 4 SH, [ 3 ] but a recent report has identified crystalline (NH 4 ) 2 [SiS 3 (NH 3 )]·2NH 3 as a product which contains the tetrahedral thiosilicate anion, SiS 3 (NH 3 ) 2- . [ 4 ]
Reaction with ethanol gives the alkoxide tetraethyl orthosilicate and H 2 S. [ 3 ] With bulky tert-butanol, alcoholysis gives tris(tert-butoxy)silanethiol : [ 5 ]
Reaction with sodium sulfide , magnesium sulfide and aluminum sulfide give thiosilicates . [ 3 ]
SiS 2 is claimed to occur in certain interstellar objects. [ 6 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/SiS2 |
Sialic acids are a class of alpha-keto acid sugars with a nine- carbon backbone . [ 1 ] The term "sialic acid" (from Greek σίαλον (síalon) ' saliva ' ) was first introduced by Swedish biochemist Gunnar Blix in 1952. The most common member of this group is N -acetylneuraminic acid (Neu5Ac or NANA) found in animals and some prokaryotes .
Sialic acids are found widely distributed in animal tissues and related forms are found to a lesser extent in other organisms like in some micro-algae , [ 2 ] bacteria and archaea . [ 3 ] [ 4 ] [ 5 ] [ 6 ] Sialic acids are commonly part of glycoproteins , glycolipids or gangliosides , where they decorate the end of sugar chains at the surface of cells or soluble proteins. [ 7 ] However, sialic acids have been also observed in Drosophila embryos and other insects. [ 8 ] Generally, plants seem not to contain or display sialic acids. [ 9 ]
In humans, the brain has the highest sialic acid content, where these acids play an important role in neural transmission and ganglioside structure in synaptogenesis . [ 7 ] More than 50 kinds of sialic acid are known, all of which can be obtained from a molecule of neuraminic acid by substituting its amino group or one of its hydroxyl groups. [ 1 ] In general, the amino group bears either an acetyl or a glycolyl group, but other modifications have been described. These modifications along with linkages have shown to be tissue specific and developmentally regulated expressions , so some of them are only found on certain types of glycoconjugates in specific cells. [ 8 ] The hydroxyl substituents may vary considerably; acetyl , lactyl , methyl , sulfate , and phosphate groups have been found. [ 10 ]
The sialic acid family includes many derivatives of the nine-carbon sugar neuraminic acid , but these acids rarely appear free in nature. Normally they can be found as components of oligosaccharide chains of mucins, glycoproteins and glycolipids occupying terminal, nonreducing positions of complex carbohydrates on both external and internal membrane areas where they are very exposed and develop important functions. [ 7 ]
The numbering of the carbon atoms starts at the carboxylate carbon and continues along the chain. The configuration that places the carboxylate in the axial position is the alpha-anomer.
The alpha-anomer is the form that is found when sialic acid is bound to glycans. However, in solution, it is mainly (over 90%) in the beta-anomeric form. A bacterial enzyme with sialic acid mutarotase activity, NanM, that is able to rapidly equilibrate solutions of sialic acid to the resting equilibrium position of around 90% beta/10% alpha has been discovered. [ 11 ]
In contrast to other animals, humans are genetically unable to produce the sialic acid variant N-glycolylneuraminic acid (Neu5Gc). Small amounts of Neu5Gc detected in human tissue however may be incorporated from exogenous (nutrient) sources. [ 12 ]
Sialic acid is synthesized by glucosamine 6 phosphate and acetyl-CoA through a transferase , resulting in N -acetylglucosamine-6-P. This becomes N -acetylmannosamine-6-P through epimerization , which reacts with phosphoenolpyruvate producing N -acetylneuraminic-9-P (sialic acid). For it to become active to enter in the oligosaccharide biosynthesis process of the cell, a monophosphate nucleoside is added, which comes from a cytidine triphosphate , turning sialic acid into cytidine monophosphate-sialic acid (CMP-sialic acid). This compound is synthesized in the nucleus of the animal cell. [ 13 ] [ 14 ]
In bacterial systems, sialic acids can be also biosynthesized by an aldolase . This enzyme uses for example a mannose derivative as a substrate, inserting three carbons from pyruvate into the resulting sialic acid structure. These enzymes can be used for chemoenzymatic synthesis of sialic acid derivatives. [ 15 ]
Sialic acid containing glycoproteins ( sialoglycoproteins ) bind selectin in humans and other organisms. Metastatic cancer cells often express a high density of sialic acid-rich glycoproteins. This overexpression of sialic acid on surfaces creates a negative charge on cell membranes. This creates repulsion between cells (cell opposition) [ 16 ] and helps these late-stage cancer cells enter the blood stream. Recent experiments have demonstrated the presence of sialic acid in the cancer-secreted extracellular matrix . [ 17 ]
Sialic acid-rich oligosaccharides on the glycoconjugates (glycolipids, glycoproteins, proteoglycans) found on surface membranes help keep water at the surface of cells [ citation needed ] . The sialic acid-rich regions contribute to creating a negative charge on the cells' surfaces. Since water is a polar molecule with partial positive charges on both hydrogen atoms, it is attracted to cell surfaces and membranes. This also contributes to cellular fluid uptake.
Sialic acid residues are present in the mucin glycoproteins of mucus. [ 18 ]
Sialic acid can "hide" mannose antigens on the surface of host cells or bacteria from mannose-binding lectin. [ citation needed ] This prevents activation of complement .
Sialic acid in the form of polysialic acid is an unusual posttranslational modification that occurs on the neural cell adhesion molecules (NCAMs). In the synapse , the strong negative charge of the polysialic acid prevents NCAM cross-linking of cells.
Administration of estrogen to castrated mice leads to a dose-dependent reduction of the sialic acid content of the vagina. Conversely, the sialic acid content of mouse vagina is a measure of the potency of the estrogen. Reference substances are estradiol for subcutaneous application and ethinylestradiol for oral administration. [ 19 ]
Sialic acids are found at all cell surfaces of vertebrates and some invertebrates, and also at certain bacteria that interact with vertebrates.
Many viruses such as the Ad26 [ 20 ] serotype of adenoviruses ( Adenoviridae ), rotaviruses ( Reoviridae ) and influenza viruses ( Orthomyxoviridae ) can use host-sialylated structures for binding to their target host cell. Sialic acids provide a good target for these viruses since they are highly conserved and are abundant in large numbers in virtually all cells. Unsurprisingly, sialic acids also play an important role in several human viral infections. The influenza viruses have hemagglutinin activity (HA) glycoproteins on their surfaces that bind to sialic acids found on the surface of human erythrocytes and on the cell membranes of the upper respiratory tract. This is the basis of hemagglutination when viruses are mixed with blood cells, and entry of the virus into cells of the upper respiratory tract. Widely used anti-influenza drugs ( oseltamivir and zanamivir ) are sialic acid analogs that interfere with release of newly generated viruses from infected cells by inhibiting the viral enzyme neuraminidase . [ 21 ]
Some bacteria also use host-sialylated structures for binding and recognition. For example, evidence indicates that free sialic acids can behave as a signal to some specific bacteria, like Pneumococcus . Free sialic acid possibly can help the bacterium to recognize that it has reached a vertebrate environment suitable for its colonization. Modifications of Sias, such as the N -glycolyl group at the 5 position or O -acetyl groups on the side chain, may reduce the action of bacterial sialidases. [ 21 ]
The synthesis and degradation of sialic acid are distributed in different compartments of the cell. The synthesis starts in the cytosol, where N -acetylmannosamine 6 phosphate and phosphoenolpyruvate give rise to sialic acid. Later on, Neu5Ac 9 phosphate is activated in the nucleus by a cytidine monophosphate (CMP) residue through CMP-Neu5Ac synthase. Although the linkage between sialic acid and other compounds tends to be a α binding, this specific one is the only one that is a β linkage. CMP-Neu5Ac is then transported to the endoplasmic reticulum or the Golgi apparatus, where it can be transferred to an oligosaccharide chain, becoming a new glycoconjugate. This bond can be modified by O- acetylation or O- methylation . When the glycoconjugate is mature it is transported to the cell surface.
The sialidase is one of the most important enzymes of the sialic acid catabolism. It can cause the removal of sialic acid residues from the cell surface or serum sialoglycoconjugates. Usually, in higher animals, the glycoconjugates that are prone to be degraded are captured by endocytosis. After the fusion of the late endosome with the lysosome, lysosomal sialidases remove sialic acid residues. The activity of these sialidases is based on the removal of O -acetyl groups. Free sialic acid molecules are transported to the cytosol through the membrane of the lysosome. There, they can be recycled and activated again to form another nascent glycoconjugate molecule in the Golgi apparatus. Sialic acids can also be degraded to acylmannosamine and pyruvate with the cytosolic enzyme acylneuraminate lyase.
Some severe diseases can depend on the presence or absence of some enzymes related to the sialic acid metabolism. Sialidosis and Sialic acid deficiency with mutations in the NANS gene (see below) would be examples of this type of disorder. [ 22 ]
Rat pups supplemented with sialic acid showed improved learning and memory as adults. [ 23 ] A relationship between dietary sialic acid supplementation and cognitive function was seen in piglets that had been fed high doses of sialic acid. [ 24 ]
Sialic acids are related to several different diseases observed in humans.
Biallelic recessive mutations in the sialic acid synthesis gene, N-acetyl-neuraminic acid synthase ( NANS ) in humans may result in a severe disease featuring intellectual disability and short stature, highlighting the importance of sialic acid in brain development. [ 25 ] A therapeutic trial with a short-term supplementation of sialic acid given orally has failed to show a significant beneficial effect on biochemical parameters [ 26 ]
Salla disease is an extremely rare illness which is considered the mildest form of the free sialic acid accumulation disorders [ 27 ] though its childhood form is considered an aggressive variant and people who suffer from it have mental retardation. [ 28 ] It is an autosomic recessive disorder caused by a mutation of the chromosome 6 . [ 29 ] It mainly affects the nervous system [ 27 ] and it is caused by a lysosomal storage irregularity which comes from a deficit of a specific sialic acid carrier located on the lysosomal membrane [ 30 ] Currently, there is no cure for this disease and the treatment is supportive, focusing on the control of symptoms. [ 27 ]
Subfractions of LDL cholesterol that are implicated in causing atherosclerosis have reduced levels of sialic acid. [ 31 ] These include small high density LDL particles and electronegative LDL. [ 31 ] Reduced levels of sialic acid in small high density LDL particles increases the affinity of those particles for the proteoglycans in arterial walls. [ 31 ]
All influenza A virus strains need sialic acid to connect with cells. There are different forms of sialic acids which have different affinity with influenza A virus variety. This diversity is an important fact that determines which species can be infected. [ 32 ] When a certain influenza A virus is recognized by a sialic acid receptor the cell tends to endocytose the virus so the cell becomes infected.
Sialic acids are highly abundant in vertebrate tissues where they are involved in many different biological processes. Originally discovered within the Deuterostome lineage of animals, sialic acids can be actually considered as a subset of a more ancient family of 9-carbon backbone monosaccharides called nonulosonic acids (NulOs), which more recently have been also found in Eubacteria and Archaea. [ 33 ] Many pathogenic bacteria incorporate sialic acid into cell surface features like their lipopolysaccharide or capsule polysaccharides, which helps them to evade the innate immune response of the host. [ 34 ] A recent genome level study examined a large set of sequenced microbial genomes, which indicated that biosynthetic pathways to produce nonulosonic acids (NulOs) are far more widely distributed across the phylogenetic tree of life, than previously realized. [ 35 ] This finding is moreover supported by recent lectin staining studies and a molecular level survey on prokaryotic nonulosonic acids, showing that also many non-pathogenic and purely environmental strains produce bacterial sialic acids (NulOs). [ 36 ] [ 37 ] Some ( anammox ) bacteria produce NulOs that in addition to the very acidic alpha-keto acid group also display (neutralizing) basic groups (free amines). [ 38 ] Comparable cell surface sialic acids have been produced by chemical remodelling to manipulate the cell surface charge by producing a free amine at C5, which neutralizes the negatively charged carboxyl group at C1. [ 39 ] | https://en.wikipedia.org/wiki/Sialic_acid |
The word, sialome, is a junction of the Greek word for saliva (sialos) and the suffix used in molecular biology to reference a totality of some sort, -ome. [ 1 ] [ 2 ] The name relating to its role in biochemistry.
In biochemistry , the term sialome may refer to two distinct concepts:
Thus, the sialome can refer to the totality of the salivary gland mRNA and proteins expressed by an organism, at a particular time and under specific cellular conditions.
Sialome can also refer to the total complement of sialic acid derivative modifications found at the terminal ends of glycan chains that cover the surfaces of proteins, organelles, and cells. These modifications can be found in vertebrates and more complex invertebrates , and consists of the anionic nine-carbon monosaccharide structure of sialic acid with various structural additions to the hydroxyl groups of the molecule resulting in various derivatives with varying chemical properties. The modifications are responsible for conferring proteins, organelles, and cells with physical and electrostatic properties to facilitate specific functions, like facilitating protein folding , cell transport, or mediate non specific interactions with other macromolecules or cells. [ 5 ]
Furthermore, the terminal saccharide in glycan chains can serve to function in specific ligand interactions with lectins (carbohydrate binding molecules), these lectins can originate from the host and can interact with the terminal saccharides of a glycan chain in a specific process or they can originate from pathogens and interact with terminal saccharides to aid in pathogen entry into cells. [ 5 ] | https://en.wikipedia.org/wiki/Sialome |
Siamesed cylinders are engine cylinders arranged in such a way that they have no channels between them to allow water or other coolant to circulate. [ 1 ] [ 2 ]
Cylinders are generally arranged in this manner when the engine block is of limited size or when stability of the cylinder bores is of concern, such as in racing engines. [ 3 ] The advantage is that the engine block will be reduced in size, or the bore can be increased in size. The disadvantage is a higher temperature between two cylinders, requiring a stronger engine block to avoid distortion of the metal, and better gasket sealing between the two bores. [ 1 ]
Engines with siamesed cylinders:
This article about an automotive part or component is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Siamesed_cylinders |
Sian Hayley " Leo " Proctor (March 28, 1970) is an American commercial astronaut , geology professor, artist, author, and science communicator. She became the first female commercial spaceship pilot and the first artist selected to go to be an astronaut on the all-civilian Inspiration4 orbital spaceflight , 15 September 2021. [ 2 ] [ 3 ] [ 4 ] [ 5 ] As pilot of the Inspiration4's SpaceX Crew Dragon space capsule , Proctor became the first African-American woman to pilot a spacecraft. [ 6 ] She was also the education outreach officer for the first Hawaii Space Exploration Analog and Simulation ( HI-SEAS ) Mission. [ 7 ] In 2024, Proctor was selected to be a U.S. Science Envoy for the United States Department of State . [ 8 ]
Since Inspiration4, Sian Proctor has become a noted Afrofuturist artist, poet and author. [ 9 ] [ 10 ] [ 11 ] Proctor is the first African American astronaut to paint in space. [ 12 ]
Proctor is a major in the Civil Air Patrol where she serves as the aerospace education officer for its Arizona Wing. [ 13 ]
Sian Proctor was born on 28 March 1970, in Hagåtña , Guam , to Edward Langley Proctor Jr. and Gloria Deloris. Her father was a Sperry Corporation UNIVAC engineer working for NASA at the Guam Remote Ground Terminal during the Apollo era. [ 14 ] She is the youngest of four children, with two brothers, Edward Langley Proctor III and Christopher Proctor, and sister Robyn Selent. After the moon landings, Proctor's family moved to Minnesota and later to various Northeastern states while her father changed jobs. Her family moved to Fairport, New York , when she was 14 where she later graduated from Fairport High School . [ 15 ] [ 16 ]
She studied at Arizona State University , where she received an undergraduate degree on environmental sciences and later a masters degree in Geology in 1998. In 2006 she obtained a PhD in Science education. [ 17 ] That same year, Proctor got her pilot's license. [ 18 ]
She is a member of the Association of Space Explorers . Furthermore in December 2022 she was selected as a member of the National Space Council ’s Users Advisory Group. [ 19 ] [ 20 ] As part of her training as pilot of the Inspiration4 flight, she trained in a Cessna CitationJet CJ3 [ 21 ] and (under the tutelage of veteran pilot Isaacman) a MiG-29. [ 22 ]
In 2022 she received the honorary degree of Doctor of Humane Letters from University of Massachusetts Lowell . [ 23 ]
In 2023 she participated in the space camp Space 2101 at King Abdullah University of Science and Technology . [ 24 ]
Proctor was a finalist for the 2009 NASA Astronaut Selection Process. She was one of 47 finalists competing against over 3,500 applicants. Nonetheless, during the final round, she was not one of the nine astronaut candidates selected for the 2009 NASA Astronaut Group. [ 15 ]
Proctor went to space as a commercial astronaut and pilot of the Crew Dragon orbital spaceflight mission Inspiration4 , which launched on 15 September 2021. The Prosperity seat, was obtained as she won an entrepreneur competition. During the flight training she received the call sign Leo . [ 25 ] [ 26 ] [ 27 ] [ 28 ]
She was joined by Jared Isaacman , Hayley Arceneaux , and Chris Sembroski , for the first all-civilian human spaceflight mission. In August 2021 she was featured on the cover of a Time magazine double issue with the rest of the crew of Inspiration4. [ 29 ] [ 30 ] [ 31 ]
As a scientist-astronaut, Proctor was selected to be a U.S. Science Envoy in 2024 to represent the United States Department of State 's global initiative to promote civil use of space in order "to build peer-to-peer connections with foreign researchers, promote space science education, and raise awareness of the importance of space science to society." [ 32 ] [ 33 ] The 2024 Cohort of U.S. Science Envoys is the first all-female cohort in the history of the U.S. Science Envoy Program. [ 34 ]
Proctor acted as education outreach officer for the NASA-funded Hawaii Space Exploration Analog and Simulation ( HI-SEAS ) mission. The purpose of the mission was to investigate food strategies for long duration spaceflight and missions to the Moon or Mars.
During the four-month simulation, Proctor was hired by Discover Magazine as the photographer for Kate Greene's article Simulating Mars on Earth . She also filmed the Meals for Mars YouTube series while in the Mars simulation. [ 35 ] [ 36 ] [ 37 ]
In 2014, she was selected as a PolarTREC teacher, which is a program funded by the National Science Foundation (NSF) that connects teachers with scientists conducting research in the arctic and Antarctic regions. As part of this program, she spent a month in Barrow, Alaska learning historical ecology for risk management and investigating the impact of climate change on the coastline and community. [ 38 ] [ 39 ]
In 2016, she was selected as a ACEAP Ambassador. A program from the National Science Foundation (NSF) that sends K–16 formal and informal astronomy educators to US astronomy facilities in Chile. During the summer of 2016, she joined eight other ambassadors as they visited Cerro Tololo Inter-American Observatory (CTIO) , Gemini South Observatory , and the Atacama Large Millimeter-submillimeter Array (ALMA) . [ 40 ]
Proctor returned to San Pedro, Chile in 2017 to engage in STEM education outreach activities with the local high school and surrounding community.
She participated in the National Oceanic and Atmospheric Administration (NOAA) Teacher at Sea program in 2017. The program was started in 1990 and provides teachers with research experience working at sea. In her case, during three weeks she conducted pollock research in the Bering Sea on the fisheries vessel Oscar Dyson and detailed her experience for the blog of NOAA. [ 41 ]
She is an international speaker, communicating about science education, leadership, spacial simulations, sustainable foods and diversity in science. Furthermore, she has given several TEDx Talks . [ 36 ] [ 42 ] [ 43 ] [ 44 ]
Proctor is a life-long artist, painter, and poet. She is a noted Afrofurist artist, working in digital, multi-media, and painting mediums. Proctor is known for her expressions of connection, source, and the divine that she calls AfroGaia . [ 45 ] Following her spaceflight, her work frequently makes reference to and is inspired by the space orbit phenomenon of sunlight reflecting off the Earth and back into space and onto spacecraft and astronauts in orbit known as Earthlight (astronomy) . [ 46 ] She is an artist-in-residence at Arizona State University . [ 47 ] While aboard the orbiting Crew Dragon spaceship, she became the first African-American to paint in space. [ 48 ]
Dr Proctor has made multiple appearances on television series and documentaries. [ 13 ] [ 49 ] [ 50 ] [ 51 ] | https://en.wikipedia.org/wiki/Sian_Proctor |
Sibelektroterm ( Russian : Сибэлектротерм ) is a manufacturing company in Kirovsky District of Novosibirsk , Russia . It was founded in 1945. [ 1 ] The enterprise is a developer and manufacturer of electrometallurgical equipment. [ 1 ]
The plant produces electric furnaces, gas distribution and mining equipment, agricultural equipment etc. [ 1 ]
The company collaborates with the Budker Institute of Nuclear Physics . In 2020, Sibelektroterm completed several complicated orders for the research work of this scientific organization. In addition, in November 2020, the company won a tender for the supply of magnetic cores for the Siberian Ring Photon Source (SKIF), which has been under construction in Koltsovo since August 2021. [ 2 ] [ 3 ]
According to an article published in Kontinent Sibir Online in 2021, 80% of the customers of Sibelektroterm's products were Kazakhstan plants. [ 2 ] | https://en.wikipedia.org/wiki/Sibelektroterm |
Animals, including siblings, compete for resources such as food, territory, and potential mating partners. In animal sibling rivalry , individuals compete for parental care or limited resources, which can sometimes result in siblicide , the killing of siblings. [ 1 ] Sibling rivalry occurs in many different forms. Siblings may compete for resources in a prenatal and/or post-birth environment. The degree of rivalry varies, ranging from a low level of violence in non-aggressive to the killing of kin in siblicide.
When there are multiple offspring in a single brood, the potential for sibling rivalry arises due to competition for food and parental attention. Natural selection may favor behaviors that allow an individual offspring to gain more resources, even if the behavior decreases a sibling's fitness. Competition for food and resources can be seen in many bird species. For example, blue-footed booby ( Sula nebouxii ) siblings often exhibit aggression towards each other, with older chicks pecking at younger chicks. This behavior increases when there are food shortages, indicating more intense competition. [ 2 ] In other bird species, siblings compete for food through manipulation of parental behavior rather than direct aggressive acts. Increased parental attention may mean more food for the offspring, favoring the development of begging behavior in nestlings. American robin ( Turdus migratorius ) chicks compete for food provided by their parents through louder and more prominent cheeps or other vocalizations, with the most food given to chicks exhibiting the most intense begging behavior. [ 3 ]
Sibling rivalry may not seem to align with the kin selection theory , which predicts that altruistic behaviors may evolve if inclusive fitness benefits (including those of relatives) from such behaviors outweigh the costs. [ 4 ] Theoretically, helping relatives would allow individuals to spread genes related to their own. However, some species may show sibling rivalry when the fitness costs outweigh the benefits of helping relatives. Sibling relatedness can influence degree of rivalry. Canary nestlings are more selfish and competitive if other nestlings are less related. [ 5 ] When offspring beg for more food from their parents, they also are “competing” with their future siblings by decreasing the fitness of parents, reducing their ability to invest in future offspring. This is known as interbrood rivalry, which can lead to parent–offspring conflict .
Siblicide is a consequence of sibling rivalry, and its occurrence may be due to a variety of factors, such as food shortages and limited parental care . Killing a sibling could be advantageous for an animal because it monopolizes more resources through the elimination of a competitor. Moreover, there are different types of siblicide. For example, obligate siblicide is the unconditional killing of a sibling. In species of birds that exhibit this behavior, the larger chick commits the act of siblicide. On the other hand, facultative siblicide refers to situations in which the death of a sibling does not always occur, but is usually motivated by environmental factors such as limited resources. [ 6 ] Facultative siblicide is exhibited by the previously discussed case of the blue-footed booby ( Sula nebouxii ). In this species, senior chicks may sometimes eliminate siblings when there are food shortages. During these shortages, chicks exhibit higher levels of pecking, but this aggression decreases when food levels are brought back to sufficient levels. [ 7 ] In some species, parents have evolved behaviors to take advantage of siblicide to increase their own fitness. For example, the laughing gull exhibits asynchronous hatching patterns in order to cut parental losses. In this species, birds that lay their eggs at different times produce, on average, a larger number of fledglings per nest in comparison to birds with synchronous hatches. [ 8 ] Staggered hatching creates chicks in different stages of growth. Older, and thus larger, chicks kill their younger siblings, reducing brood size and allowing the parent to concentrate efforts when food is scarce. Once the brood is reduced, sibling rivalry decreases because there are fewer competitors, benefitting the surviving offspring. This also benefits the parents by minimizing unproductive parental investment in offspring that are unlikely to be successful. This is especially advantageous during food shortages when parents are unable to adequately feed all offspring.
Siblicide has also been noted in mammalian species. For instance, spotted hyenas ( Crocuta crocuta ) have been known to exhibit facultative siblicidal behavior. Intense sibling aggression begins only a few minutes after birth and then continues for a few days. [ 9 ] The function of sibling aggression is to establish and maintain rank relationship between litter mates, but this aggression does not always lead to sibling death. [ 10 ] However, during periods of intense feeding competition, aggression can escalate to siblicide. [ 11 ] Spotted hyena aggression demonstrates how facultative siblicide can be triggered by environmental factors.
Intrauterine cannibalism (see also: cannibalism ) occurs when siblings eat each other in the embryonic phase. This can take the form of embryophagy when siblings eat embryos, and oophagy , when siblings eat eggs. [ 12 ] Intrauterine cannibalism can benefit embryos by providing increased nutrition. Fire salamander ( Salamandra salamandra ) populations exhibiting intrauterine cannibalism have embryos that develop more quickly into larvae due to nutritional supplementation from feeding on siblings. [ 13 ] Lamnoid shark embryos have adaptations to facilitate intrauterine cannibalism in the form of precocious teeth, which they use to feed on intrauterine eggs and siblings after their yolk supply is used up. [ 14 ] In sand tiger sharks ( Carcharias taurus ), the first embryo to reach a certain size, referred to as "the hatchling," will always consume the smaller, less-developed siblings in the womb. [ 15 ] Because the first embryo may have a different father from the eaten embryos, this form of siblicide early during development may be indirectly involved in male competition. This phenomenon of embryonic cannibalism may play a role in sexual selection , as males compete post-fertilization for paternity. [ 16 ] Thus, intrauterine cannibalism in sharks may reflect not only sibling rivalry, but also male competition for successful mating with females, which is an example of sexual selection .
Not all forms of sibling rivalry in animals involve direct aggression or death of a sibling. This is not an extremely aggressive form of rivalry; however, it still results in reduced sibling fitness.
Fetal programming (see also: Barker's Hypothesis ) refers to the persisting effects in adult life caused by the fetal environment. In sheep, competition for resources within the uterus may lead to impaired reproductive abilities and different body composition. Sheep that were born 600 grams lighter than their twins have an impaired reproductive ability - the lighter the sheep weighed in comparison to their twin, the more impaired. Although the sheep are not competing physically like in intrauterine cannibalism, the disparity in birth weight suggests an overall fitness difference. [ 17 ]
Is the teat that he fattens his flesh on. He fights for his teat with tenacity Against any sibling's audacity. The piglet, to arm for this mission, Is born with a warlike dentition Of eight tiny tusks, sharp as sabres, Which help in impressing the neighbors; But to render these weapons less harrowing, Most farmers remove them at farrowing. We studied pig sisters and brothers When some had their teeth, but not others. We found that when siblings aren't many, The weapons help little if any, But when there are many per litter, The teeth help their owners grow fitter. But how did selection begin To make weapons to use against kin? [ 18 ]
(Abstract from the paper “Armed Sibling Rivalry among Suckling Piglets” by Fraser and Thompson)
Domestic piglets ( Sus scrofa ) have been shown to exhibit different forms of non-lethal competition such as uterine competition. The relative development of the embryo in the uterus can affect their chance of survival. Pig embryos follow different developmental paths because during estrus, sows will ovulate the majority of their follicles during a short period of time and then a few during a longer period of time. [ 19 ] This pattern causes a difference in development, so the less developed embryos are less likely to survive. Competition also exists over space in the uterus of the sow. The central portion of the uterus is the most crowded and the site of the greatest competition. This competition prevents some embryos from fully growing, often resulting in a low birthweight that may put piglets at a disadvantage once out of the womb. [ 20 ] Neonatal competition also exists among piglets as they directly compete against their siblings for their mother's teats only hours after their birth. [ 21 ] Competition is responsible for 43% of piglet neonatal death due to starvation. Under normal conditions (i.e. stable environment, average litter size), larger piglets appear to have an advantage in survival partially due to their ability to win more fights against smaller piglets over access to teats. [ 22 ] It is believed that teeth in piglets evolved as a product of an evolutionary arms race caused by sibling competition, resulting in armed sibling rivalry. Teeth become more important when the litter size is larger than normal, causing increased competition. In these situations, the teeth can help the individual piglet compete against siblings. [ 23 ]
Sibling rivalry can be mediated and/or encouraged by parents, especially in bird species. Sibling rivalry can also have a negative impact on the parent and the fitness of future offspring due to interbrood conflict which may lead to parent–offspring conflict . This conflict may force parents to exert extra energy at the expense of future broods.
Parents may play a passive role in encouraging sibling rivalry. The most common case is in food distribution. When parent birds distribute food, they do not favor any individual offspring. Great tits ( Parus major ) preferentially distribute food from similar locations, so offspring compete for those prime spots closest to the feeding site where they will get more food, leading to unequal growth of offspring. This behavior exemplified in the young can be interpreted as an optimal foraging strategy driven by scramble competition . [ 24 ]
Alternatively, parents may take an active role in mediating the intensity of rivalry between siblings. Again, great tit parents can choose what location to distribute food to as a means of controlling competition between nestlings. When parents feed chicks at one or two feeding locations in the nest, the distance between the male and female parents influences the level of competition between nestlings. In other words, parents may decrease sibling competition by varying the locations within the nest that receive food.
Interbrood conflict occurs when the current brood demands more at the expense of future broods. This sibling rivalry can lead to parent–offspring conflict, in which there are different optimal levels of parental investments whether viewed from the parental or offspring perspective. Biological signalling theory suggests that young can communicate with parents to maximize the amount of food they can get. Therefore, young that need or want more food may solicit or beg at higher levels. Parents can respond to this by providing more food, but this is based on the assumption of honest begging , in which chicks beg only when they actually need more food. However, if all the young start soliciting at higher levels, this incurs a cost on the parents because they will need to expend more energy searching for food. The increased travel to and from the nest may attract predators as well. These factors reduce the energy and resources parents have for future offspring. This is an example of where nestling intrabrood competition can influence the parents' investment in future broods. [ 25 ] | https://en.wikipedia.org/wiki/Sibling_rivalry_(animals) |
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Siboglinidae is a family of polychaete annelid worms whose members made up the former phyla Pogonophora and Vestimentifera (the giant tube worms ). [ 1 ] [ 2 ] The family is composed of around 100 species of vermiform creatures which live in thin tubes buried in sediment (Pogonophora) or in tubes attached to hard substratum (Vestimentifera) at ocean depths ranging from 100 to 10,000 m (300 to 32,800 ft). They can also be found in association with hydrothermal vents , methane seeps , sunken plant material, and whale carcasses .
The first specimen was dredged from the waters of Indonesia in 1900. These specimens were given to French zoologist Maurice Caullery , who studied them for nearly 50 years.
Most siboglinids are less than 1 millimetre (0.04 in) in diameter, but 10–75 centimetres (3.9–29.5 in) in length. They inhabit tubular structures composed of chitin which are fixed to rocks or substrates. The tubes are often clustered together in large colonies. [ 3 ]
Their bodies are divided into four regions. The anterior end is called the cephalic lobe, which ranges from one to over 200 thin branchial ciliated tentacles , each with tiny side branches known as pinnules. Behind this is a glandular forepart, which helps to secrete the tube. The main part of the body is the trunk, which is greatly elongated and bears various annuli, papillae, and ciliary tracts. Posterior to the trunk is the short metamerically segmented opisthosoma , bearing external paired chaetae , which help to anchor the animal to the base of its tube. [ 3 ]
The body cavity has a separate compartment in each of the first three regions of the body and extends into the tentacles. The opisthosoma has a coelomic chamber in each of its 5 to 23 segments, separated by septa . The worms have a complex closed circulatory system and a well-developed nervous system , but as adults, siboglinids completely lack a mouth, gut, and anus. [ 4 ]
The family Siboglinidae has been difficult to place in an evolutionary context. [ 5 ] After examination of genetic differences between annelids, Siboglinidae were placed within the order Polychaeta by scientific consensus. [ 6 ] The fossil record along with molecular clocks suggest the family has Mesozoic (250 – 66 Mya) or Cenozoic (66 Mya – recent) origins. [ 5 ] However, some fossils of crystallized tubes are attributed to early Siboglinidae dating back to 500 Mya. [ 5 ] The oldest definitive specimens referred to the family came from Early Jurassic ( Pliensbachian - Toarcian ) Figueroa Sulfide deposits from San Rafael Mountains , found to be similar to modern Ridgeia . [ 7 ] This tubes, known as ‘Figueroa tubes’, along the ‘Troodos collared tubes’ ( Cyprus , Turonian ) were resolved among modern vestimentiferans. [ 8 ] Molecular work aligning five genes has identified four distinct clades within Siboglinidae. [ 9 ] [ 10 ] [ 11 ] The clades are Vestimentifera , Sclerolinum , Frenulata , and Osedax . [ 10 ] Vestimentiferans live in vent and seep habitats. [ 10 ] Separation of vestimentiferans into seep and deep-sea-dwelling clades is still debated due to some phylogenies based on sequencing data placing the genera along a continuum. [ 12 ] Sclerolinum is a monogeneric clade (which may be called Monilifera) living on organic-rich remains. [ 5 ] Frenulates live in organic-rich sediment habitats. [ 13 ] Osedax is a monogeneric clade specialized in living on whale bones, although recent evidence shows them living on fish bones as well. [ 14 ]
One probable relationship between the four clades is shown in the cladogram below. The position of Osedax is weakly supported. [ 5 ]
clade Frenulata
Osedax
Sclerolinum (clade Monilifera)
clade Vestimentifera
Like other tube worms, vestimentiferans are benthic marine creatures. Riftia pachyptila , a vestimentiferan, is known only from the hydrothermal vent systems. [ 5 ]
Vestimentiferan bodies are divided into four regions: the obturaculum, vestimentum, trunk, and opisthosome. The main trunk of the body bears wing-like extensions. Unlike other siboglinids that never have a digestive tract , they have one that they completely lose during metamorphosis .
The obturaculum is the first anterior body part. [ 15 ] It is possible that the obturaculum is actually an outgrowth of the vestimentum rather than a separate body segment which would distinguish it from other siboglinids.
The vestimentum, from which the group's name is derived, is a wing-like body part with glands that secrete the tube. In a ventroanterior position in the vestimentum is the brain which is postulated to be simpler than relatives that maintain a gut in the adult form. [ 15 ] The opisthosome is the anchoring rear body part.
Their primary nutrition is derived from the sulfide-rich fluids emanating from the hydrothermal vents where they live. The sulfides are metabolized by symbiotic hydrogen sulfide- or methane-oxidizing bacteria living in an internal organ, the trophosome . One gram of trophosome tissue can contain one billion bacteria. The origin of this symbiotic relationship is not currently known. The bacteria appear to colonize the host animal larvae after they have settled on a surface, entering them through their skin. [ 16 ] This method of entry, known as horizontal transmission, means that each organism may have different species of bacteria assisting in this symbiosis. However, these bacteria all play similar roles in sustaining the vestimentiferans. Endosymbionts have a wide variety of metabolic genes, which may allow them to switch between autotrophic and heterotrophic methods of nutrient acquisition. [ 17 ] When the host dies, the bacteria are released and return to the free-living population in the seawater. [ 18 ]
Discovery of the hydrothermal vents in the eastern Pacific Ocean was quickly followed by the discovery and description of new vestimentiferan tubeworm species. These tubeworms are one of the most dominant organisms associated with the hydrothermal vents in the Pacific Ocean. Tubeworms anchor themselves to the substratum of the hydrocarbon seep by roots located at the basal portion of their bodies. [ 19 ] Intact tubeworm roots have proven very difficult to obtain for study because they are extremely delicate, and often break off when a tubeworm is removed from hypothermal vent regions. How long the roots of the tube worms can grow is unknown, but roots have been recovered longer than 30 m. [ citation needed ]
A single aggregation of tubeworms can contain thousands of individuals, and the roots produced by each tubeworm can become tangled with the roots of neighbouring tubeworms. [ 20 ] These mats of roots are known as "ropes", and travel down the tubes of dead tubeworms, and run through holes in rocks. The diameter and wall thickness of the tubeworm roots do not appear to change with distance from the trunk portion of the tubeworm's body.
Like the trunk portion of the body, the roots of the vestimentiferan tubeworms are composed of chitin crystallites, which support and protect the tubeworm from predation and environmental stresses. Tubeworms build the external chitin structure themselves by secreting chitin from specialized glands located in their body walls. | https://en.wikipedia.org/wiki/Siboglinidae |
cis is a mathematical notation defined by cis x = cos x + i sin x , [ nb 1 ] where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number (angle between line to point and x-axis in polar form ). The notation is less commonly used in mathematics than Euler's formula , e ix , which offers an even shorter notation for cos x + i sin x , but cis(x) is widely used as a name for this function in software libraries .
The cis notation is a shorthand for the combination of functions on the right-hand side of Euler's formula :
where i 2 = −1 . So,
i.e. " cis " is an acronym for " Cos i Sin ".
It connects trigonometric functions with exponential functions in the complex plane via Euler's formula. While the domain of definition is usually x ∈ R {\displaystyle x\in \mathbb {R} } , complex values z ∈ C {\displaystyle z\in \mathbb {C} } are possible as well:
so the cis function can be used to extend Euler's formula to a more general complex version . [ 5 ]
The function is mostly used as a convenient shorthand notation to simplify some expressions, [ 6 ] [ 7 ] [ 8 ] for example in conjunction with Fourier and Hartley transforms , [ 9 ] [ 10 ] [ 11 ] or when exponential functions shouldn't be used for some reason in math education.
In information technology, the function sees dedicated support in various high-performance math libraries (such as Intel 's Math Kernel Library (MKL) [ 12 ] or MathCW [ 13 ] ), available for many compilers and programming languages (including C , C++ , [ 14 ] Common Lisp , [ 15 ] [ 16 ] D , [ 17 ] Haskell , [ 18 ] Julia , [ 19 ] and Rust [ 20 ] ). Depending on the platform, the fused operation is about twice as fast as calling the sine and cosine functions individually. [ 17 ] [ 3 ]
These follow directly from Euler's formula .
The identities above hold if x and y are any complex numbers. If x and y are real, then
The cis notation was first coined by William Rowan Hamilton in Elements of Quaternions (1866) [ 23 ] [ 24 ] and subsequently used by Irving Stringham (who also called it " sector of x ") in works such as Uniplanar Algebra (1893), [ 25 ] [ 26 ] James Harkness and Frank Morley in their Introduction to the Theory of Analytic Functions (1898), [ 26 ] [ 27 ] or by George Ashley Campbell (who also referred to it as "cisoidal oscillation") in his works on transmission lines (1901) and Fourier integrals (1928). [ 28 ] [ 29 ] [ 30 ]
In 1942, inspired by the cis notation, Ralph V. L. Hartley introduced the cas (for cosine-and-sine ) function for the real-valued Hartley kernel , a meanwhile established shortcut in conjunction with Hartley transforms : [ 31 ] [ 32 ]
The cis notation is sometimes used to emphasize one method of viewing and dealing with a problem over another. [ 33 ] The mathematics of trigonometry and exponentials are related but not exactly the same; exponential notation emphasizes the whole, whereas cis x and cos x + i sin x notations emphasize the parts. This can be rhetorically useful to mathematicians and engineers when discussing this function, and further serve as a mnemonic (for cos + i sin ). [ 30 ]
The cis notation is convenient for math students whose knowledge of trigonometry and complex numbers permit this notation, but whose conceptual understanding does not yet permit the notation e ix . The usual proof that cis x = e ix requires calculus , which the student may not have studied before encountering the expression cos x + i sin x .
This notation was more common when typewriters were used to convey mathematical expressions. [ citation needed ] | https://en.wikipedia.org/wiki/Sich_(mathematics) |
Sicherman dice / ˈ s ɪ k ər m ən / are a pair of 6-sided dice with non-standard numbers—one with the sides 1, 2, 2, 3, 3, 4 and the other with the sides 1, 3, 4, 5, 6, 8. They are notable as the only pair of 6-sided dice that are not normal dice , bear only positive integers , and have the same probability distribution for the sum as normal dice. They were invented in 1978 by George Sicherman of Buffalo, New York.
A standard exercise in elementary combinatorics is to calculate the number of ways of rolling any given value with a pair of fair six-sided dice (by taking the sum of the two rolls). The table shows the number of such ways of rolling a given value n {\displaystyle n} :
Crazy dice is a mathematical exercise in elementary combinatorics , involving a re-labeling of the faces of a pair of six-sided dice to reproduce the same frequency of sums as the standard labeling. The Sicherman dice are crazy dice that are re-labeled with only positive integers . (If the integers need not be positive, to get the same probability distribution, the number on each face of one die can be decreased by k and that of the other die increased by k , for any natural number k , giving infinitely many solutions.)
The table below lists all possible totals of dice rolls with standard dice and Sicherman dice. One Sicherman die is colored for clarity: 1 – 2 – 2 – 3 – 3 – 4 , and the other is all black, 1–3–4–5–6–8.
The Sicherman dice were discovered by George Sicherman of Buffalo, New York and were originally reported by Martin Gardner in a 1978 article in Scientific American .
The numbers can be arranged so that all pairs of numbers on opposing sides sum to equal numbers, 5 for the first and 9 for the second.
Later, in a letter to Sicherman, Gardner mentioned that a magician he knew had anticipated Sicherman's discovery. For generalizations of the Sicherman dice to more than two dice and noncubical dice, see Broline (1979), Gallian and Rusin (1979), Brunson and Swift (1997/1998), and Fowler and Swift (1999).
Let a canonical n -sided die be an n -hedron whose faces are marked with the integers [1,n] such that the probability of throwing each number is 1/ n . Consider the canonical cubical (six-sided) die. The generating function for the throws of such a die is x + x 2 + x 3 + x 4 + x 5 + x 6 {\displaystyle x+x^{2}+x^{3}+x^{4}+x^{5}+x^{6}} . The product of this polynomial with itself yields the generating function for the throws of a pair of dice: x 2 + 2 x 3 + 3 x 4 + 4 x 5 + 5 x 6 + 6 x 7 + 5 x 8 + 4 x 9 + 3 x 10 + 2 x 11 + x 12 {\displaystyle x^{2}+2x^{3}+3x^{4}+4x^{5}+5x^{6}+6x^{7}+5x^{8}+4x^{9}+3x^{10}+2x^{11}+x^{12}} . From the theory of cyclotomic polynomials , we know that
where d ranges over the divisors of n and Φ d ( x ) {\displaystyle \Phi _{d}(x)} is the d -th cyclotomic polynomial, and
We therefore derive the generating function of a single n -sided canonical die as being
Φ 1 ( x ) = x − 1 {\displaystyle \Phi _{1}(x)=x-1} and is canceled. Thus the factorization of the generating function of a six-sided canonical die is
The generating function for the throws of two dice is the product of two copies of each of these factors. How can we partition them to form two legal dice whose spots are not arranged traditionally? Here legal means that the coefficients are non-negative and sum to six, so that each die has six sides and every face has at least one spot. (That is, the generating function of each die must be a polynomial p(x) with positive coefficients, and with p(0) = 0 and p(1) = 6.)
Only one such partition exists:
and
This gives us the distribution of spots on the faces of a pair of Sicherman dice as being {1,2,2,3,3,4} and {1,3,4,5,6,8}, as above.
This technique can be extended for dice with an arbitrary number of sides.
This article incorporates material from Crazy dice on PlanetMath , which is licensed under the Creative Commons Attribution/Share-Alike License . | https://en.wikipedia.org/wiki/Sicherman_dice |
Sickness behavior is a coordinated set of adaptive behavioral changes that develop in ill individuals during the course of an infection . [ 1 ] They usually, but not always, [ 2 ] accompany fever and aid survival.
Such illness responses include lethargy , depression , anxiety , malaise , loss of appetite , [ 3 ] [ 4 ] sleepiness , [ 5 ] hyperalgesia , [ 6 ] reduction in grooming [ 1 ] [ 7 ] and failure to concentrate . [ 8 ] Sickness behavior is a motivational state that reorganizes the organism's priorities to cope with infectious pathogens . [ 8 ] [ 9 ] It has been suggested as relevant to understanding depression , [ 10 ] and some aspects of the suffering that occurs in cancer .
Sick animals have long been recognized by farmers as having different behavior. Initially it was thought that this was due to physical weakness that resulted from diverting energy to the body processes needed to fight infection. However, in the 1960s, it was shown that animals produced a blood-carried factor X that acted upon the brain to cause sickness behavior. [ 11 ] [ 12 ] In 1987, Benjamin L. Hart brought together a variety of research findings that argued for them being survival adaptations that if prevented would disadvantage an animal's ability to fight infection. In the 1980s, the blood-borne factor was shown to be proinflammatory cytokines produced by activated leukocytes in the immune system in response to lipopolysaccharides (a cell wall component of Gram-negative bacteria ). These cytokines acted by various humoral and nerve routes upon the hypothalamus and other areas of the brain. Further research showed that the brain can also learn to control the various components of sickness behavior independently of immune activation. [ citation needed ]
In 2015, Shakhar and Shakhar [ 13 ] suggested instead that sickness behavior developed primarily because it protected the kin of infected animals from transmissible diseases. According to this theory, termed the Eyam hypothesis, after the English Parish of Eyam , sickness behavior protects the social group of infected individuals by limiting their direct contacts, preventing them from contaminating the environment, and broadcasting their health status. Kin selection would help promote such behaviors through evolution. In a highly prosocial species like humans, however, sickness behavior may act as a signal to motivate others to help and care for the sick individual. [ 14 ]
Sickness behavior in its different aspects causes an animal to limit its movement; the metabolic energy not expended in activity is diverted to the fever responses, which involves raising body temperature. [ 1 ] This also limits an animal's exposure to predators while it is cognitively and physically impaired. [ 1 ]
The individual components of sickness behavior have specific individual advantages. Anorexia limits food ingestion and therefore reduces the availability of iron in the gut (and from gut absorption). Iron may aid bacterial reproduction, so its reduction is useful during sickness. [ 15 ] Plasma concentrations of iron are lowered for this anti-bacterial reason in fever. [ 16 ] Lowered threshold for pain ensures that an animal is attentive that it does not place pressure on injured and inflamed tissues that might disrupt their healing. [ 1 ] Reduced grooming is adaptive since it reduces water loss. [ 1 ]
According to the ' Eyam hypothesis', [ 13 ] sickness behavior, by promoting immobility and social disinterest, limits the direct contacts of individuals with their relatives. By reducing eating and drinking, it limits diarrhea and defecation, reducing environmental contamination. By reducing self-grooming and changing stance, gait and vocalization, it also signals poor health to kin. All in all, sickness behavior reduces the rate of further infection, a trait that is likely propagated by kin selection . [ citation needed ]
Humans helped each other in case of sickness or injury throughout their hunter-gatherer past and afterwards. Convincing others of being badly in need of relief, assistance, and care heightened the chance of survival of the sick individual. High direct costs, such as energy spent on fever and potential harm caused by high body temperatures, and high opportunity costs, as caused by inactivity, social disinterest, and lack of appetite, make sickness behavior a highly costly and therefore credible signal of need. [ 14 ]
Lipopolysaccharides trigger the immune system to produce proinflammatory cytokines IL-1 , IL-6 , and tumor necrosis factor (TNF). [ 17 ] These peripherally released cytokines act on the brain via a fast transmission pathway involving primary input through the vagus nerves , [ 18 ] [ 19 ] and a slow transmission pathway involving cytokines originating from the choroid plexus and circumventricular organs and diffusing into the brain parenchyma by volume transmission . [ 20 ] Peripheral cytokines are capable of entering the brain directly [ 21 ] [ 22 ] but are large lipophilic polypeptide proteins that generally do not easily passively diffuse across the blood-brain barrier. They may also induce the expression of other cytokines in the brain that cause sickness behavior. [ 23 ] [ 24 ] Acute psycho social stress enhances the ability of an immune response to trigger both inflammation and behavioral sickness. [ 25 ]
The components of sickness behavior can be learned by conditional association . For example, if a saccharin solution is given with a chemical that triggers a particular aspect of sickness behavior, on later occasions the saccharin solution will trigger it by itself. [ 26 ] [ 27 ]
It has been proposed that major depressive disorder is nearly identical with sickness behavior, raising the possibility that it is a maladaptive manifestation of sickness behavior due to abnormalities in circulating cytokines. [ 28 ] [ 29 ] [ 30 ] Moreover, chronic, but not acute, treatment with antidepressant drugs was found to attenuate sickness behavior symptoms in rodents. [ 31 ] The mood effects caused by interleukin-6 following an immune response have been linked to increased activity within the subgenual anterior cingulate cortex , [ 32 ] an area involved in the etiology of depression. [ 33 ] Inflammation-associated mood change can also produce a reduction in the functional connectivity of this part of the brain to the amygdala , medial prefrontal cortex , nucleus accumbens , and superior temporal sulcus . [ 32 ]
In cancer, both the disease and the chemotherapy treatment can cause proinflammatory cytokine release which can cause sickness behavior as a side effect . [ 34 ] [ 35 ] | https://en.wikipedia.org/wiki/Sickness_behavior |
SICONOS is an open source scientific software primarily targeted at
modeling and simulating non-smooth dynamical systems (NSDS): [ 1 ]
Other applications are found in Systems and Control (hybrid systems, differential inclusions, optimal control with state constraints), Optimization ( Complementarity problem and Variational inequality ) Biology Gene regulatory network , Fluid Mechanics and Computer graphics , etc.
The software is based on 3 main components [ 2 ]
According to peer reviewed studies published by its developers, Siconos was approximately five times faster than Ngspice or ELDO (a commercial SPICE by Mentor Graphics ) and 250 times faster than PLECS when solving a buck converter . [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/Siconos |
Siddhānta Śiromaṇi ( Sanskrit : सिद्धान्त शिरोमणि [siddʱɑn̪t̪ᵊ ɕɪɾoməɳiː] for "Crown of treatises") [ 1 ] is the major treatise of Indian mathematician Bhāskara II . [ 2 ] He wrote the Siddhānta Śiromaṇi in 1150 when he was 36 years old. The work is composed in Sanskrit Language in 1450 verses. [ 3 ]
The name of the book comes from his daughter, Līlāvatī. It is the first volume of the Siddhānta Śiromaṇi . The book contains thirteen chapters, 278 verses, mainly arithmetic and measurement .
It is the second volume of Siddhānta Śiromaṇi . It is divided into six parts, contains 213 verses and is devoted to algebra .
Gaṇitādhyāya and Golādhyāya of Siddhānta Śiromaṇi are devoted to astronomy. All put together there are about 900 verses. [ 4 ] ( Gaṇitādhyāya has 451 and Golādhyāya has 501 verses).
In 1797, Safdar Ali Khan of Hyderabad translated the Siddhanta Shiromani into Persian as Zij-i Sarumani . The translation is now a lost work , and is known only from a mention in Khan's other work - Zij-i Safdari . [ 5 ] [ 6 ]
This article about the history of mathematics is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Siddhānta_Shiromani |
In geometric topology, the side-approximation theorem was proved by Bing (1963) . It implies that a 2-sphere in R 3 can be approximated by polyhedral 2-spheres.
This topology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Side-approximation_theorem |
A side-stick or sidestick controller is an aircraft control stick that is located on the side console of the pilot , usually on the righthand side, or outboard on a two-seat flightdeck . Typically this is found in aircraft that are equipped with fly-by-wire control systems. [ 1 ]
The throttle controls are typically located to the left of a single pilot or centrally on a two-seat flightdeck. Only one hand is required to operate them; two handed operation is neither possible nor necessary.
The side-stick is used in many modern military fighter aircraft , such as the F-16 Fighting Falcon , Mitsubishi F-2 , Dassault Rafale , and F-22 Raptor , F-35 Lightning 2 , Chengdu J-20 , AIDC F-CK 1 Ching-Kuo and also on civil aircraft, such as the Sukhoi Superjet 100 , Airbus A320 and all subsequent Airbus aircraft, [ 2 ] including the largest passenger jet in service, the Airbus A380 .
It is also used in new helicopter models such as the Bell 525 .
A side-stick arrangement contrasts with the more conventional design where the stick is located in the centre of the cockpit between the pilot's legs, called a " centre stick ". A side-stick arrangement allows HOTAS and increases ejection seat safety for the pilot as there is less interference amongst flight controls. [ citation needed ]
In Airbus' implementation, input values of both side-sticks are normally added up, [ 3 ] except when the "priority takeover button" is held down. In such a scenario, any inputs on the other side-stick will be ignored. [ 4 ] Holding this button down for a minimum of 40 seconds will result in the other side-stick being disabled. This can reversed by pressing the button on either side-stick again. A green light will activate on the side of the pilot currently on control. In contrast, on the side of the other pilot, a red light will turn on to indicate that their side-stick's inputs are being ignored. [ 5 ]
While the inputs are added up, the sum is clamped to the value of the maximum possible deflection a single side-stick; [ 6 ] but this still means that when both side-stick are deflected 50% in the same direction, the resulting effective input will be that of a fully deflected side-stick, despite neither one being deflected over 50%. In addition, because the inputs are added up, any deflection of the other side-stick in the opposite direction will in effect be subtracted, resulting in the inputs partially cancelling each other out. In fact, if two inputs have opposite directions but equal magnitudes, the sum will be zero, and thus the flight control surfaces would remain in their current positions.
In addition to visual indications, [ 7 ] detection of more than a single side-stick deflection greater than 2° [ 8 ] from neutral without the priority takeover button being held down results in an aural "DUAL INPUT" warning being played every five seconds. [ 9 ] Due to this aural warning having the lowest priority, it will not be played if there are warnings with a higher priority, such as those from the EGPWS , as those will take precedence, [ 10 ] posing a potential risk for pilots.
Examples of this occurring include the 2009 crash of Air France Flight 447 (an Airbus A330 flying from Rio de Janeiro to Paris ), the 2010 crash of Afriqiyah Airways Flight 771 an Airbus A330 from flying Johannesburg to Tripoli [ 11 ] [ 12 ] and the 2014 crash of Indonesia AirAsia Flight 8501 (an Airbus A320 flying from Surabaya to Singapore ). [ 13 ] [ 14 ] .
In the centre stick design, like traditional airplane yokes , both the pilot flying, PF's, and pilot not flying, PNF's, controls are mechanically connected together so each pilot has a sense of the control inputs of the other.
In aircraft with passive side-sticks, on the other hand, they and move independently from each other, and do not offer any haptic feedback on what the other pilot is inputting. This can lead to "dual input" situations, which should be avoided. To see how dual input situations are handled, see § Handling of dual input situations
However a later, significant, development is the 'active' side-stick, [ 15 ] which is in the new Gulfstream G500/G600 series business jet aircraft. In this system, movements in one side-stick produce the same actions in the other side-stick and therefore provides valuable feedback to the other pilot. This addresses the earlier criticisms of the 'passive' side-stick. The 'active' side-stick also provides tactile feedback [ 16 ] to the pilot during manual flight. In fact the three largest avionics manufacturers, Honeywell, Rockwell Collins and Thales, [ 17 ] believe it will become the standard for all new fly-by-wire aircraft. In 2015 Ratier-Figeac as a subsidiary of UTC Aerospace Systems , and supplier of ‘passive’ side-sticks to Airbus since the 1980s [ 18 ] became the supplier of ‘active’ side-sticks for the Irkut MC-21 . [ 19 ] This is the first airliner to use them.
Such an active side-stick can also be used to increase adherence to a safe flight envelope by applying a force feedback when the pilot makes a control input that would bring the aircraft closer to (or beyond) the borders of the safe flight envelope. This reduces the risk of pilots entering dangerous states of flights outside the operational borders while maintaining the pilots' final authority and increasing their situation awareness . [ 20 ] | https://en.wikipedia.org/wiki/Side-stick |
Branch Side-chain Pendant chain An oligomeric or polymeric offshoot from a macromolecular chain.
Notes
In organic chemistry and biochemistry , a side chain is a chemical group that is attached to a core part of the molecule called the "main chain" or backbone . The side chain is a hydrocarbon branching element of a molecule that is attached to a larger hydrocarbon backbone. It is one factor in determining a molecule's properties and reactivity. [ 2 ] A side chain is also known as a pendant chain , but a pendant group (side group) has a different definition.
The placeholder R is often used as a generic placeholder for alkyl (saturated hydrocarbon) group side chains in structural formulae . To indicate other non-carbon groups in structure diagrams, X , Y , or Z are often used.
The R symbol was introduced by 19th-century French chemist Charles Frédéric Gerhardt , who advocated its adoption on the grounds that it would be widely recognizable and intelligible given its correspondence in multiple European languages to the initial letter of "root" or "residue": French racine ("root") and résidu ("residue"), these terms' respective English translations along with radical (itself derived from Latin radix below), Latin radix ("root") and residuum ("residue"), and German Rest ("remnant" and, in the context of chemistry, both "residue" and "radical"). [ 3 ]
In polymer science , the side chain of an oligomeric or polymeric offshoot extends from the backbone chain of a polymer. Side chains have noteworthy influence on a polymer's properties, mainly its crystallinity and density . An oligomeric branch may be termed a short-chain branch, and a polymeric branch may be termed a long-chain branch. Side groups are different from side chains; they are neither oligomeric nor polymeric. [ 4 ]
In proteins , which are composed of amino acid residues, the side chains are attached to the alpha-carbon atoms of the amide backbone. The side chain connected to the alpha-carbon is specific for each amino acid and is responsible for determining charge and polarity of the amino acid. The amino acid side chains are also responsible for many of the interactions that lead to proper protein folding and function. [ 5 ] Amino acids with similar polarity are usually attracted to each other, while nonpolar and polar side chains usually repel each other. Nonpolar/polar interactions can still play an important part in stabilizing the secondary structure due to the relatively large amount of them occurring throughout the protein. [ 6 ] Spatial positions of side-chain atoms can be predicted based on protein backbone geometry using computational tools for side-chain reconstruction. [ 7 ] | https://en.wikipedia.org/wiki/Side_chain |
The side effects of penicillin are bodily responses to penicillin and closely related antibiotics that do not relate directly to its effect on bacteria. A side effect is an effect that is not intended with normal dosing. [ 1 ] Some of these reactions are visible and some occur in the body's organs or blood. Penicillins are a widely used group of medications that are effective for the treatment of a wide variety of bacterial infections in human adults and children as well as other species. Some side effects are predictable, of which some are common but not serious, some are uncommon and serious and others are rare. [ 2 ] The route of administration of penicillin can have an effect on the development of side effects. An example of this is irritation and inflammation that develops at a peripheral infusion site when penicillin is administered intravenously. In addition, penicillin is available in different forms. There are different penicillin medications ( penicillin G benzathine , penicillin G potassium , Penicillin G sodium , penicillin G procaine , and penicillin V ) [ 3 ] as well as a number of β-lactam antibiotics derived from penicillin (e.g. amoxicillin ).
Side effects may only last for a short time and then go away. Side effects can be relieved in some cases with non pharmacological treatment. [ 4 ] Some side effects require treatment to correct potentially serious and sometimes fatal reactions to penicillin. Penicillin has not been found to cause birth defects. [ 5 ]
Many people have indicated that they have a side effect related to an allergic reaction to penicillin. It has been proposed that as many as 90% of those claiming to have an allergy to penicillin are able to take it and do not have a true allergy. Research has suggested that having penicillin allergy incorrectly noted in the medical records can have negative consequences. [ 6 ] [ 7 ]
Identifying an allergy to penicillin requires a hypersensitivity skin test, which diagnoses IgE-mediated immune responses caused by penicillin. This test is typically performed by an allergist who uses a skin-prick and intradermal injection of penicilloyl-polylysine, a negative control (normal saline), and a positive control ( histamine ). [ 8 ]
A small proportion of people who are allergic to penicillins also have similar cross sensitivities to other antibiotics such as cephalosporins . If someone has developed side effects when taking penicillin, these side effects may develop with a new medication even though the person has not taken the new medication before. Those medications that may cause a cross sensitivity reaction are: carbapenems , ampicillin , cefazolin , cephalosporins and cloxacillin . [ 9 ] [ 8 ] [ 10 ]
Of patients with documented penicillin allergy, approximately 95% will return a negative penicillin skin-prick test [ 11 ] but patients carrying a penicillin allergy label are significantly more likely to experience worse outcomes. [ 12 ] As such, it is important for clinicians to verify the nature of reported penicillin allergy at admission and de-label when appropriate.
For this purpose, clinical risk assessment tools have been developed such as "PEN-FAST":
Patients scoring 4 or greater have a high (50%) probability of testing positive for penicillin allergy. [ 13 ]
Common adverse drug reactions (≥ 1% of people) associated with use of the penicillins include diarrhea , hypersensitivity , nausea , rash, neurotoxicity , urticaria (hives), and superinfection (including candidiasis ). Infrequent adverse effects (0.1–1% of people) include fever, vomiting , erythema , dermatitis , angioedema , seizures (especially in people with epilepsy ), and pseudomembranous colitis . [ 14 ] [ needs update ]
When penicillin is used at high doses hypokalemia , metabolic acidosis , and hyperkalemia can occur. [ 17 ] Developing hypernatremia after administering high doses of penicillin can be a serious side effect. [ 10 ]
The side effects of penicillin can be altered by taking other medications at the same time. Taking oral contraceptives along with penicillin may lower the effects of the contraceptive. When probenecid is used concurrently with penicillin, kidney excretion of probenecid is decreased resulting in higher blood levels of penicillin in the circulation. In some instances, this would be an intended therapeutic effect. In other instances, this is an unintended side effect. Neomycin can lower the absorption of penicillin from the gastrointestinal tract resulting in lower than expected levels of penicillin in the circulation. This side effect may result in an ineffective therapeutic effect of penicillin. When methotrexate is administered with penicillin, toxicity may occur related to methotrexate. [ 10 ]
Animals are often treated with antibiotics for infections they have developed. There are side effects of penicillin when it is used in animals. MRSA may develop in pets as a consequence of treatment. [ 18 ] [ 19 ] Nutritional deficiencies can develop in pets as a side effect. [ 20 ] Destruction of the normal protective flora of beneficial bacteria can occur in dogs and horses. [ 21 ] [ 22 ] Dogs may have side effects that include: joint pain, loss of appetite, vomiting, flatulence (intestinal gas), fungal infections and digestive problems. [ 23 ] Like humans, dogs can have a similar side effect related to developing a serious allergy. A serious and possibly fatal anaphylactic can occur. Side effects that are concurrent with anaphylaxis include: breathing problems and shock . [ citation needed ]
Cats and dogs have had adverse reactions to intravenous penicillin that include: hypothermia , pruritus, hypotension, tremors, seizures, blindness, vocalization, agitation, cardiac arrest and transient loss of vision. [ 24 ]
Penicillin is known to become less effective as strains of bacteria become resistant. [ 25 ] | https://en.wikipedia.org/wiki/Side_effects_of_penicillin |
A side population (SP) in flow cytometry is a sub-population of cells that is distinct from the main population on the basis of the markers employed. By definition, cells in a side population have distinguishing biological characteristics (for example, they may exhibit stem cell -like characteristics), but the exact nature of this distinction depends on the markers used in identifying the side population. [ 1 ]
Side populations were first identified in hematopoietic stem cells by Dr. Margaret Goodell . [ 2 ] SPs have been identified in hepatocellular carcinomas and may be the cells that efflux chemotherapy drugs, accounting for the resistance of cancer to chemotherapy. [ 3 ]
Recent studies on testicular stem cells indicate that more than 40% of the SP (defined in this case as cells that show higher efflux of DNA-binding dye Hoechst 33342) was undifferentiated spermatogonia , while other differentiated fractions were represented by only 0.2%. SP cells can rapidly efflux lipophilic fluorescent dyes to produce a characteristic profile based on fluorescence-activated flow cytometric analysis. Previous studies have demonstrated SP cells in bone marrow obtained from patients with acute myeloid leukemia, suggesting that these cells might be candidate leukemic stem cells, and recent studies have found a SP of tumor progenitor cells in human solid tumors. These new data indicate that the ability of malignant SP cells to expel anticancer drugs may directly improve their survival and sustain their clonogenicity during exposure to cytostatic drugs, allowing disease recurrence when therapy is withdrawn. Identification of a tumor progenitor population with intrinsic mechanisms for cytostatic drug resistance might also provide clues for improved therapeutic intervention. [ 4 ] The molecules involved in effluxing Hoechst 33342 are members of the ATP-binding cassette family, such as MDR1 (P-glycoprotein) and ABCG2.
This cell biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Side_population |
A side reaction is a chemical reaction that occurs at the same time as the actual main reaction, but to a lesser extent. It leads to the formation of by-product , so that the yield of main product is reduced: [ 1 ]
P 1 is the main product if k 1 > k 2 . The by-product P 2 is generally undesirable and must be separated from the actual main product (usually in a costly process ).
B and C from the above equations usually represent different compounds . However, they could also just be different positions in the same molecule .
A side reaction is also referred to as competing reaction [ 2 ] [ 3 ] when different compounds (B, C) compete for another reactant (A). If the side reaction occurs about as often as the main reaction, it is spoken of parallel reactions [ 4 ] (especially in the kinetics, see below).
Also there may be more complicated relationships: Compound A could reversibly but quickly react to substance B (with speed k 1 ) or irreversible but slow (k 1 > k −1 >> k 2 ) to substance C:
Assuming that the reaction to substance C is irreversible, as it is thermodynamically very stable. In this case, B is the kinetic and C is the thermodynamic product of the reaction (see also here ). [ 5 ] [ 6 ] [ 7 ] If the reaction is carried out at low temperatures and stopped after a short time, it is spoken of kinetic control, primarily the kinetic product B would be formed. When the reaction is carried out at high temperatures and for long time (in which case the necessary activation energy for the reaction to C is available, which is progressively formed over time), it is spoken of thermodynamic control; the thermodynamic product C is primarily formed.
In organic synthesis , elevated temperatures usually lead to more side products. Side products are usually undesirable, therefore low temperatures are preferred ("mild conditions"). The ratio between competing reactions may be influenced by a change in temperature because their activation energies are different in most cases. Reactions with high activation energy can be more strongly accelerated by an increase in temperature than those with low activation energy. Also, the state of equilibrium depends on temperature. [ 8 ]
Detection reactions can be distorted by side reactions.
Side reactions are also described in the reaction kinetics , a branch of physical chemistry . Side reactions are understood as complex reaction , since the overall reaction (main reaction + side reaction) is composed of several (at least two) elementary reactions . [ 9 ] Other complex reactions are competing reactions, parallel reactions, consecutive reactions, chain reactions, reversible reactions, etc. [ 10 ] : 280–291
If one reaction occurs much faster than the other one (k 1 > k 2 ), it (k 1 ) will be called the main reaction, the other one (k 2 ) side reaction. If both reactions roughly of same speed (k 1 ≅ k 2 ) is spoken of parallel reactions. [ 4 ]
If the reactions A + B → k 1 P 1 {\displaystyle {\ce {{A}+B->[{k_{1}}]P1}}} and A + C → k 2 P 2 {\displaystyle {\ce {{A}+C->[{k_{2}}]P2}}} are irreversibly (without reverse reaction), then the ratio of P 1 and P 2 corresponds to the relative reactivity of B and C compared with A: | https://en.wikipedia.org/wiki/Side_reaction |
Side valleys and tributary valleys are valleys whose brooks or rivers flow into greater ones. [ 1 ]
Upstream, the valleys can be classified in an increasing order which is equivalent to the usual orographic order : the tributaries are ordered from those nearest to the source of the river to those nearest to the mouth of the river . A confluence is where two or more tributaries or rivers flow together.
In the orographic classification (order of rivers) the tributary river has order n+1 , if n describes the primary (or main) river. A river which flows directly into the ocean (e.g. the English rivers Thames or Humber ) has the orographic order n=1, the River Ouse n=2, the Wharfe n=3 and so on.
The term "side valley" is used for higher order valleys near mountains (example above: the Pennines ), as opposed to lower valleys that do not have a strong relief. This is because the " main stem river " (into which the secondary river flows) passes much more water than its tributaries and therefore
The higher the order of a valley, the steeper the hillsides . Looking upstream, the steepest slopes are normally near the source of a brook (with the exception of very hard rocks in downstream direction).
The estuary of broad rivers lies in flat regions (river flats) rather than in regions with higher elevation. Therefore, the stream gradient of the tributary near its mouth is small (e.g. 1 m per km), but much more at waters of higher order (in the Alps up to 100 m per km). This is one reason for the large number of hanging valleys in some mountain ranges (e.g. Salzburg or Graubünden ).
Glaciologic or geologic reasons:
These stages of valley genesis can be seen in higher mountain ranges - e.g. in the "young" Rocky Mountains , in the "old" ranges and fjords of Scandinavia , or in the Eastern Alps ( Salzach or Inn valley).
Sandbanks often occur at reaches with slow current, especially near river banks . Studying the various gravel rock types is an excellent and cheap survey for a summarized geology of the rivers watershed (catchment area).
Generally the main river and tributary are easily identified, as one stream is both longer and carries more water than the other. Occasionally one stream is longer, but the other carries more water. This case offers no fixed rules, but the longer valley is usually chosen as the main valley. In Switzerland the long Alpine Rhine is chosen as the main stream, although the Aar carries more water. The Mississippi River carries more water while the Missouri River is much longer, but is still rated the tributary.
Whereas the valleys near river flats don't have special forms, the shape of alpine valleys depends much more from the former glaciology and of the rock type .
Side- or secondary valleys can be V-shaped or U-shaped. Valley floors vary - from just a few meters up to some 100 m (e.g. Bad Gastein or St. Moritz , where small towns have been developed instead of 1000 or 1500 m altitude).
Some valleys are stepped in longitudinal direction (German "Talstufe") which means that these zones show a quicker current than average. The brook digs its own canal and the eroded sediments are deposed at the end of each clammy, forming a series of local plains . They are an excellent sites for alpine agriculture or pastures . | https://en.wikipedia.org/wiki/Side_valley |
Sidera Lodoicea / ˈ s ɪ d ər ə ˌ l oʊ d oʊ ˈ ɪ s iː ə / is the name given by the astronomer Giovanni Domenico Cassini to the four moons of Saturn discovered by him in the years 1671, 1672, and 1684 and published in his Découverte de deux nouvelles planètes autour de Saturne in 1673 and in the Journal des sçavans in 1686. These satellites are today known by the following names, given in 1847:
The name Sidera Lodoicea means "Louisian Stars", from Latin sidus "star" and Lodoiceus , a nonce adjective coined from Lodoicus , one of several Latin forms of the French name Louis (reflecting an older form, Lodhuwig ). Cassini intended the name to honor King Louis XIV of France, who reigned from 1643 to 1715, and who was Cassini's benefactor as patron of the Paris Observatory , of which Cassini was the director.
The name was modelled on Sidera Medicea , "Medicean stars", the Latin name used by Galileo to name the four Galilean satellites of Jupiter , in honor of the Florentine house of Medici .
The following contemporary (1686) notice records Cassini's choice of name, and explains his rationale for the same:
In the Conclusion, the Discoverer considers that the Antient Astronomers, having translated the Names of their Heroes among the Starrs, those Names have continued down to us unchanged, notwithstanding the endeavour of following Ages to alter them; and that Galileo , after their Example, had honoured the House of the Medici with the discovery of the Satellites of Jupiter , made by him under the Protection of Cosmus II ; which Starrs will be always known by the Name of Sidera Medicea . Wherefore he concludes that the Satellites of Saturn , being much more exalted and more difficult to discover, are not unworthy to bear the Name of Louis le Grand , under whose Reign and in whose Observatory the same have been detected, which therefore he calls Sidera Lodoicea , not doubting but to have perpetuated the Name of that King, by a Monument much more lasting than those of Brass and Marble, which shall be erected to his Memory. [ 1 ] | https://en.wikipedia.org/wiki/Sidera_Lodoicea |
Sidereal time ("sidereal" pronounced / s aɪ ˈ d ɪər i əl , s ə -/ sy- DEER -ee-əl, sə- ) is a system of timekeeping used especially by astronomers . Using sidereal time and the celestial coordinate system , it is easy to locate the positions of celestial objects in the night sky . Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars ". [ 1 ] A sidereal day (also known as the sidereal rotation period ) represents the time for one rotation about the planet axis relative to the stars. [ 2 ]
Viewed from the same location , a star seen at one position in the sky will be seen at the same position on another night at the same time of day (or night), if the day is defined as a sidereal day. This is similar to how the time kept by a sundial ( Solar time ) can be used to find the location of the Sun . Just as the Sun and Moon appear to rise in the east and set in the west due to the rotation of Earth, so do the stars. Both solar time and sidereal time make use of the regularity of Earth's rotation about its polar axis: solar time is reckoned according to the position of the Sun in the sky while sidereal time is based approximately on the position of the fixed stars on the theoretical celestial sphere.
More exactly, sidereal time is the angle, measured along the celestial equator , from the observer's meridian to the great circle that passes through the March equinox (the northern hemisphere's vernal equinox) and both celestial poles , and is usually expressed in hours, minutes, and seconds. (In the context of sidereal time, "March equinox" or "equinox" or "first point of Aries" is currently a direction, from the center of the Earth along the line formed by the intersection of the Earth's equator and the Earth's orbit around the Sun, toward the constellation Pisces; during ancient times it was toward the constellation Aries.) [ 3 ] Common time on a typical clock (using mean Solar time ) measures a slightly longer cycle, affected not only by Earth's axial rotation but also by Earth's orbit around the Sun.
The March equinox itself precesses slowly westward relative to the fixed stars, completing one revolution in about 25,800 years, so the misnamed "sidereal" day ("sidereal" is derived from the Latin sidus meaning "star") is 0.0084 seconds shorter than the stellar day , Earth's actual period of rotation relative to the fixed stars. [ 4 ] The slightly longer stellar period is measured as the Earth rotation angle (ERA), formerly the stellar angle. [ 5 ] An increase of 360° in the ERA is a full rotation of the Earth.
A sidereal day on Earth is approximately 86164.0905 seconds (23 h 56 min 4.0905 s or 23.9344696 h).
(Seconds are defined as per International System of Units and are not to be confused with ephemeris seconds .)
Each day, the sidereal time at any given place and time will be about four minutes shorter than local civil time (which is based on solar time), so that for a complete year the number of sidereal "days" is one more than the number of solar days.
Solar time is measured by the apparent diurnal motion of the Sun. Local noon in apparent solar time is the moment when the Sun is exactly due south or north (depending on the observer's latitude and the season). A mean solar day (what we normally measure as a "day") is the average time between local solar noons ("average" since this varies slightly over a year).
Earth makes one rotation around its axis each sidereal day; during that time it moves a short distance (about 1°) along its orbit around the Sun. So after a sidereal day has passed, Earth still needs to rotate slightly more before the Sun reaches local noon according to solar time. A mean solar day is, therefore, nearly 4 minutes longer than a sidereal day.
The stars are so far away that Earth's movement along its orbit makes nearly no difference to their apparent direction (except for the nearest stars if measured with extreme accuracy; see parallax ), and so they return to their highest point at the same time each sidereal day.
Another way to understand this difference is to notice that, relative to the stars, as viewed from Earth, the position of the Sun at the same time each day appears to move around Earth once per year. A year has about 36 5 .24 solar days but 36 6 .24 sidereal days. Therefore, there is one fewer solar day per year than there are sidereal days, similar to an observation of the coin rotation paradox . [ 6 ] This makes a sidereal day approximately 365.24 / 366.24 times the length of the 24-hour solar day.
Earth's rotation is not a simple rotation around an axis that remains always parallel to itself. Earth's rotational axis itself rotates about a second axis, orthogonal to the plane of Earth's orbit, taking about 25,800 years to perform a complete rotation. This phenomenon is termed the precession of the equinoxes . Because of this precession, the stars appear to move around Earth in a manner more complicated than a simple constant rotation.
For this reason, to simplify the description of Earth's orientation in astronomy and geodesy , it was conventional to chart the positions of the stars in the sky according to right ascension and declination , which are based on a frame of reference that follows Earth's precession, and to keep track of Earth's rotation, through sidereal time, relative to this frame as well. (The conventional reference frame, for purposes of star catalogues, was replaced in 1998 with the International Celestial Reference Frame , which is fixed with respect to extra-galactic radio sources. Because of the great distances, these sources have no appreciable proper motion . [ 7 ] ) In this frame of reference, Earth's rotation is close to constant, but the stars appear to rotate slowly with a period of about 25,800 years. It is also in this frame of reference that the tropical year (or solar year), the year related to Earth's seasons, represents one orbit of Earth around the Sun. The precise definition of a sidereal day is the time taken for one rotation of Earth in this precessing frame of reference.
During the past, time was measured by observing stars with instruments such as photographic zenith tubes and Danjon astrolabes, and the passage of stars across defined lines would be timed with the observatory clock. Then, using the right ascension of the stars from a star catalog, the time when the star should have passed through the meridian of the observatory was computed, and a correction to the time kept by the observatory clock was computed. Sidereal time was defined such that the March equinox would transit the meridian of the observatory at 0 hours local sidereal time. [ 8 ]
Beginning during the 1970s, the radio astronomy methods very-long-baseline interferometry (VLBI) and pulsar timing overtook optical instruments for the most precise astrometry . This resulted in the determination of UT1 (mean solar time at 0° longitude) using VLBI, a new measure of the Earth Rotation Angle, and new definitions of sidereal time. These changes became effective 1 January 2003. [ 9 ]
The Earth rotation angle ( ERA ) measures the rotation of the Earth from an origin on the celestial equator, the Celestial Intermediate Origin , also termed the Celestial Ephemeris Origin , [ 10 ] that has no instantaneous motion along the equator; it was originally referred to as the non-rotating origin . This point is very close to the equinox of J2000. [ 11 ]
ERA, measured in radians , is related to UT1 by a simple linear relation: [ 4 ] θ ( t U ) = 2 π ( 0.779 057 273 2640 + 1.002 737 811 911 354 48 ⋅ t U ) {\displaystyle \theta (t_{U})=2\pi (0.779\,057\,273\,2640+1.002\,737\,811\,911\,354\,48\cdot t_{U})} where t U is the Julian UT1 date (JD) minus 2451545.0.
The linear coefficient represents the Earth's rotation speed around its own axis.
ERA replaces Greenwich Apparent Sidereal Time (GAST). The origin on the celestial equator for GAST, termed the true equinox , does move, due to the movement of the equator and the ecliptic. The lack of motion of the origin of ERA is considered a significant advantage. [ 12 ]
The ERA may be converted to other units; for example, the Astronomical Almanac for the Year 2017 tabulated it in degrees, minutes, and seconds. [ 13 ]
As an example, the Astronomical Almanac for the Year 2017 gave the ERA at 0 h 1 January 2017 UT1 as 100° 37′ 12.4365″. [ 14 ] Since Coordinated Universal Time (UTC) is within a second or two of UT1, this can be used as an anchor to give the ERA approximately for a given civil time and date.
Although ERA is intended to replace sidereal time, there is a need to maintain definitions for sidereal time during the transition, and when working with older data and documents.
Similarly to mean solar time, every location on Earth has its own local sidereal time (LST), depending on the longitude of the point. Since it is not feasible to publish tables for every longitude, astronomical tables use Greenwich sidereal time (GST), which is sidereal time on the IERS Reference Meridian , less precisely termed the Greenwich, or Prime meridian . There are two varieties, mean sidereal time if the mean equator and equinox of date are used, and apparent sidereal time if the apparent equator and equinox of date are used. The former ignores the effect of astronomical nutation while the latter includes it. When the choice of location is combined with the choice of including astronomical nutation or not, the acronyms GMST, LMST, GAST, and LAST result.
The following relationships are true: [ 15 ]
The new definitions of Greenwich mean and apparent sidereal time (since 2003, see above) are: G M S T ( t U , t ) = θ ( t U ) − E P R E C ( t ) {\displaystyle \mathrm {GMST} (t_{U},t)=\theta (t_{U})-E_{\mathrm {PREC} }(t)} G A S T ( t U , t ) = θ ( t U ) − E 0 ( t ) {\displaystyle \mathrm {GAST} (t_{U},t)=\theta (t_{U})-E_{0}(t)}
such that θ is the Earth Rotation Angle, E PREC is the accumulated precession, and E 0 is equation of the origins, which represents accumulated precession and nutation. [ 16 ] The calculation of precession and nutation was described in Chapter 6 of Urban & Seidelmann.
As an example, the Astronomical Almanac for the Year 2017 gave the ERA at 0 h 1 January 2017 UT1 as 100° 37′ 12.4365″ (6 h 42 m 28.8291 s). The GAST was 6 h 43 m 20.7109 s. For GMST the hour and minute were the same but the second was 21.1060. [ 14 ]
If a certain interval I is measured in both mean solar time (UT1) and sidereal time, the numerical value will be greater in sidereal time than in UT1, because sidereal days are shorter than UT1 days. The ratio is: I m e a n s i d e r e a l I U T 1 = r ′ = 1.002 737 379 093 507 95 + 5.9006 × 10 − 11 t − 5.9 × 10 − 15 t 2 {\displaystyle {\frac {I_{\mathrm {mean\,sidereal} }}{I_{\mathrm {UT1} }}}=r'=1.002\,737\,379\,093\,507\,95+5.9006\times 10^{-11}t-5.9\times 10^{-15}t^{2}}
such that t represents the number of Julian centuries elapsed since noon 1 January 2000 Terrestrial Time . [ 17 ]
Six of the eight solar planets have prograde rotation—that is, they rotate more than once per year in the same direction as they orbit the Sun, so the Sun rises in the east. [ 18 ] Venus and Uranus , however, have retrograde rotation. For prograde rotation, the formula relating the lengths of the sidereal and solar days is:
or, equivalently:
When calculating the formula for a retrograde rotation, the operator of the denominator will be a plus sign (put another way, in the original formula the length of the sidereal day must be treated as negative). This is due to the solar day being shorter than the sidereal day for retrograde rotation, as the rotation of the planet would be against the direction of orbital motion.
If a planet rotates prograde, and the sidereal day exactly equals the orbital period, then the formula above gives an infinitely long solar day ( division by zero ). This is the case for a planet in synchronous rotation ; in the case of zero eccentricity, one hemisphere experiences eternal day, the other eternal night, with a "twilight belt" separating them.
All the solar planets more distant from the Sun than Earth are similar to Earth in that, since they experience many rotations per revolution around the Sun, there is only a small difference between the length of the sidereal day and that of the solar day – the ratio of the former to the latter never being less than Earth's ratio of 0.997. But the situation is quite different for Mercury and Venus. Mercury's sidereal day is about two-thirds of its orbital period, so by the prograde formula its solar day lasts for two revolutions around the Sun – three times as long as its sidereal day. Venus rotates retrograde with a sidereal day lasting about 243.0 Earth days, or about 1.08 times its orbital period of 224.7 Earth days; hence by the retrograde formula its solar day is about 116.8 Earth days, and it has about 1.9 solar days per orbital period.
By convention, rotation periods of planets are given in sidereal terms unless otherwise specified. | https://en.wikipedia.org/wiki/Sidereal_time |
A sidereal year ( / s aɪ ˈ d ɪər i . əl / , US also / s ɪ -/ ; from Latin sidus ' asterism, star ' ), also called a sidereal orbital period , is the time that Earth or another planetary body takes to orbit the Sun once with respect to the fixed stars .
Hence, for Earth, it is also the time taken for the Sun to return to the same position relative to Earth with respect to the fixed stars after apparently travelling once around the ecliptic .
It equals 365.256 363 004 ephemeris days for the J2000.0 epoch. [ 1 ] The sidereal year differs from the solar year , "the period of time required for the ecliptic longitude of the Sun to increase 360 degrees", [ 2 ] due to the precession of the equinoxes .
The sidereal year is 20 min 24.5 s longer than the mean tropical year at J2000.0 (365.242 190 402 ephemeris days) . [ 1 ]
At present, the rate of axial precession corresponds to a period of 25,772 years, [ 3 ] so sidereal year is longer than tropical year by 1,224.5 seconds (20 min 24.5 s, ~365.24219*86400/25772).
Before the discovery of the precession of the equinoxes by Hipparchus in the Hellenistic period , the difference between sidereal and tropical year was unknown to the Greeks. [ 4 ] For naked-eye observation, the shift of the constellations relative to the equinoxes only becomes apparent over centuries or " ages ", and pre-modern calendars such as Hesiod 's Works and Days would give the times of the year for sowing, harvest, and so on by reference to the first visibility of stars, effectively using the sidereal year. [ citation needed ] The Indian national calendar , based on the works of Maga Brahmins , as are the calendars of neighbouring countries, is traditionally reckoned by the Sun's entry into the sign of Aries and is also supposed to align with the spring equinox and have relevance to the harvesting and planting season and thus the tropical year. [ citation needed ] However, as the entry into the constellation occurs 25 days later, according to the astronomical calculation of the sidereal year, this date marks the South and Southeast Asian solar New Year in other countries and cultures [ citation needed ] | https://en.wikipedia.org/wiki/Sidereal_year |
Siderophilic bacteria are bacteria that require or are facilitated by free iron . They may include Vibrio vulnificus , Listeria monocytogenes , Yersinia enterocolica , Salmonella enterica (serotype Typhimurium), Klebsiella pneumoniae and Escherichia coli . One possible symptom of haemochromatosis is susceptibility to infections from these species. [ 1 ] Certain non-bacterial microorganisms such as Rhizopus arrhizus and Mucor may also be siderophilic.
This bacteria -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Siderophilic_bacteria |
Siderophores (Greek: "iron carrier") are small, high-affinity iron - chelating compounds that are secreted by microorganisms such as bacteria and fungi. They help the organism accumulate iron. [ 2 ] [ 3 ] [ 4 ] [ 5 ] Although a widening range of siderophore functions is now being appreciated, [ 6 ] siderophores are among the strongest (highest affinity) Fe 3+ binding agents known. Phytosiderophores are siderophores produced by plants.
Despite being one of the most abundant elements in the Earth's crust, iron is not readily bioavailable. In most aerobic environments, such as the soil or sea, iron exists in the ferric (Fe 3+ ) state, which tends to form insoluble rust-like solids. To be effective, nutrients must not only be available, they must be soluble. [ 7 ] Microbes release siderophores to scavenge iron from these mineral phases by formation of soluble Fe 3+ complexes that can be taken up by active transport mechanisms. Many siderophores are nonribosomal peptides , [ 3 ] [ 8 ] although several are biosynthesised independently. [ 9 ]
Siderophores are also important for some pathogenic bacteria for their acquisition of iron. [ 3 ] [ 4 ] [ 10 ] In mammalian hosts, iron is tightly bound to proteins such as hemoglobin , transferrin , lactoferrin and ferritin . The strict homeostasis of iron leads to a free concentration of about 10 −24 mol L −1 , [ 11 ] hence there are great evolutionary pressures put on pathogenic bacteria to obtain this metal. For example, the anthrax pathogen Bacillus anthracis releases two siderophores, bacillibactin and petrobactin , to scavenge ferric ion from iron containing proteins. While bacillibactin has been shown to bind to the immune system protein siderocalin , [ 12 ] petrobactin is assumed to evade the immune system and has been shown to be important for virulence in mice. [ 13 ]
Siderophores are amongst the strongest binders to Fe 3+ known, with enterobactin being one of the strongest of these. [ 11 ] Because of this property, they have attracted interest from medical science in metal chelation therapy , with the siderophore desferrioxamine B gaining widespread use in treatments for iron poisoning and thalassemia . [ 14 ]
Besides siderophores, some pathogenic bacteria produce hemophores ( heme binding scavenging proteins) or have receptors that bind directly to iron/heme proteins. [ 15 ] In eukaryotes, other strategies to enhance iron solubility and uptake are the acidification of the surroundings (e.g. used by plant roots) or the extracellular reduction of Fe 3+ into the more soluble Fe 2+ ions.
Siderophores usually form a stable, hexadentate , octahedral complex preferentially with Fe 3+ compared to other naturally occurring abundant metal ions, although if there are fewer than six donor atoms water can also coordinate. The most effective siderophores are those that have three bidentate ligands per molecule, forming a hexadentate complex and causing a smaller entropic change than that caused by chelating a single ferric ion with separate ligands. [ 16 ] Fe 3+ is a strong Lewis acid , preferring strong Lewis bases such as anionic or neutral oxygen atoms to coordinate with. Microbes usually release the iron from the siderophore by reduction to Fe 2+ which has little affinity to these ligands. [ 8 ] [ 2 ]
Siderophores are usually classified by the ligands used to chelate the ferric iron. The major groups of siderophores include the catecholates (phenolates), hydroxamates and carboxylates (e.g. derivatives of citric acid ). [ 3 ] Citric acid can also act as a siderophore. [ 17 ] The wide variety of siderophores may be due to evolutionary pressures placed on microbes to produce structurally different siderophores which cannot be transported by other microbes' specific active transport systems, or in the case of pathogens deactivated by the host organism. [ 3 ] [ 10 ]
Examples of siderophores produced by various bacteria and fungi :
Hydroxamate siderophores [ 18 ]
( deferoxamine )
Streptomyces coelicolor
Catecholate siderophores
enteric bacteria
Bacillus anthracis
Mixed ligands
Amino carboxylate ligands
A comprehensive list of siderophore structures (over 250) is presented in Appendix 1 in reference. [ 3 ]
In response to iron limitation in their environment, genes involved in microbe siderophore production and uptake are derepressed , leading to manufacture of siderophores and the appropriate uptake proteins. In bacteria, Fe 2+ -dependent repressors bind to DNA upstream to genes involved in siderophore production at high intracellular iron concentrations. At low concentrations, Fe 2+ dissociates from the repressor, which in turn dissociates from the DNA, leading to transcription of the genes. In gram-negative and AT-rich gram-positive bacteria, this is usually regulated by the Fur (ferric uptake regulator) repressor, whilst in GC-rich gram-positive bacteria (e.g. Actinomycetota ) it is DtxR (diphtheria toxin repressor), so-called as the production of the dangerous diphtheria toxin by Corynebacterium diphtheriae is also regulated by this system. [ 8 ]
This is followed by excretion of the siderophore into the extracellular environment, where the siderophore acts to sequester and solubilize the iron. [ 3 ] [ 20 ] [ 21 ] [ 22 ] Siderophores are then recognized by cell specific receptors on the outer membrane of the cell. [ 2 ] [ 3 ] [ 23 ] In fungi and other eukaryotes, the Fe-siderophore complex may be extracellularly reduced to Fe 2+ , while in many cases the whole Fe-siderophore complex is actively transported across the cell membrane. In gram-negative bacteria, these are transported into the periplasm via TonB-dependent receptors , and are transferred into the cytoplasm by ABC transporters . [ 3 ] [ 8 ] [ 16 ] [ 24 ]
Once in the cytoplasm of the cell, the Fe 3+ -siderophore complex is usually reduced to Fe 2+ to release the iron, especially in the case of "weaker" siderophore ligands such as hydroxamates and carboxylates. Siderophore decomposition or other biological mechanisms can also release iron, [ 16 ] especially in the case of catecholates such as ferric-enterobactin, whose reduction potential is too low for reducing agents such as flavin adenine dinucleotide , hence enzymatic degradation is needed to release the iron. [ 11 ]
Although there is sufficient iron in most soils for plant growth, plant iron deficiency is a problem in calcareous soil , due to the low solubility of iron(III) hydroxide . Calcareous soil accounts for 30% of the world's farmland. Under such conditions graminaceous plants (grasses, cereals and rice) secrete phytosiderophores into the soil, [ 25 ] a typical example being deoxymugineic acid . Phytosiderophores have a different structure to those of fungal and bacterial siderophores having two α-aminocarboxylate binding centres, together with a single α-hydroxycarboxylate unit. This latter bidentate function provides phytosiderophores with a high selectivity for iron(III). When grown in an iron -deficient soil, roots of graminaceous plants secrete siderophores into the rhizosphere. On scavenging iron(III) the iron–phytosiderophore complex is transported across the cytoplasmic membrane using a proton symport mechanism. [ 26 ] The iron(III) complex is then reduced to iron(II) and the iron is transferred to nicotianamine , which although very similar to the phytosiderophores is selective for iron(II) and is not secreted by the roots. [ 27 ] Nicotianamine translocates iron in phloem to all plant parts.
Iron is an important nutrient for the bacterium Pseudomonas aeruginosa , however, iron is not easily accessible in the environment. To overcome this problem, P. aeruginosa produces siderophores to bind and transport iron. [ 28 ] But the bacterium that produced the siderophores does not necessarily receive the direct benefit of iron intake. Rather all members of the cellular population are equally likely to access the iron-siderophore complexes. The production of siderophores also requires the bacterium to expend energy. Thus, siderophore production can be looked at as an altruistic trait because it is beneficial for the local group but costly for the individual. This altruistic dynamic requires every member of the cellular population to equally contribute to siderophore production. But at times mutations can occur that result in some bacteria producing lower amounts of siderophore. These mutations give an evolutionary advantage because the bacterium can benefit from siderophore production without suffering the energy cost. Thus, more energy can be allocated to growth. Members of the cellular population that can efficiently produce these siderophores are commonly referred to as cooperators; members that produce little to no siderophores are often referred to as cheaters. [ 29 ] Research has shown when cooperators and cheaters are grown together, cooperators have a decrease in fitness while cheaters have an increase in fitness. It is observed that the magnitude of change in fitness increases with increasing iron-limitation. [ 30 ] With an increase in fitness, the cheaters can outcompete the cooperators; this leads to an overall decrease in fitness of the group, due to lack of sufficient siderophore production.
In a recent study, [ 31 ] the production of pyoverdine (PVD), a type of siderophore, in the bacterium Pseudomonas aeruginosa has been explored. This study focused on the construction, modeling, and dynamic simulation of PVD biosynthesis, [ 32 ] a virulence factor, through a systemic approach. This approach considers that the metabolic pathway of PVD synthesis is regulated by the phenomenon of quorum-sensing (QS), a cellular communication system that allows bacteria to coordinate their behavior based on their population density.
The study showed that as bacterial growth increases, so does the extracellular concentration of QS signaling molecules , thus emulating the natural behavior of P. aeruginosa PAO1. To carry out this study, a metabolic network model of P. aeruginosa was built based on the iMO1056 model, the genomic annotation of the P. aeruginosa PAO1 strain, and the metabolic pathway of PVD synthesis. This model included the synthesis of PVD, transport reactions, exchange, and QS signaling molecules.
The resulting model, called CCBM1146, [ 33 ] showed that the QS phenomenon directly influences the metabolism of P. aeruginosa towards the biosynthesis of PVD as a function of the change in QS signal intensity. This work is the first in silico report of an integrative model that comprises the QS gene regulatory network and the metabolic network of P. aeruginosa, providing a detailed view of how the production of pyoverdine and siderophores in Pseudomonas aeruginosa are influenced by the quorum-sensing phenomenon
Furthermore, intratumor P. aeruginosa may scavenge iron by producing pyoverdine, which indirectly protect tumor cells from ferroptosis ('iron death'), emphasizing the need for ferroptosis inducers (thiostrepton) for cancer treatment. [ 34 ]
Siderophores become important in the ecological niche defined by low iron availability, iron being one of the critical growth limiting factors for virtually all aerobic microorganisms. There are four major ecological habitats: soil and surface water, marine water, plant tissue (pathogens) and animal tissue (pathogens).
The soil is a rich source of bacterial and fungal genera. Common Gram-positive species are those belonging to the Actinomycetales and species of the genera Bacillus , Arthrobacter and Nocardia . Many of these organisms produce and secrete ferrioxamines which lead to growth promotion of not only the producing organisms, but also other microbial populations that are able to utilize exogenous siderophores. Soil fungi include Aspergillus and Penicillium predominantly produce ferrichromes. This group of siderophores consist of cyclic hexapeptides and consequently are highly resistant to environmental degradation associated with the wide range of hydrolytic enzymes that are present in humic soil. [ 35 ] Soils containing decaying plant material possess pH values as low as 3–4. Under such conditions organisms that produce hydroxamate siderophores have an advantage due to the extreme acid stability of these molecules. The microbial population of fresh water is similar to that of soil, indeed many bacteria are washed out from the soil. In addition, fresh-water lakes contain large populations of Pseudomonas , Azomonas , Aeromonas and Alcaligenes species. [ 36 ] As siderophores are secreted into the surroundings, siderophores can be detected by bacterivorous predators, including Caenorhabditis elegans , resulting in the nematode migration to the bacterial prey. [ 37 ]
In contrast to most fresh-water sources, iron levels in surface sea-water are extremely low (1 nM to 1 μM in the upper 200 m) and much lower than those of V, Cr, Co, Ni, Cu and Zn. Virtually all this iron is in the iron(III) state and complexed to organic ligands. [ 38 ] These low levels of iron limit the primary production of phytoplankton and have led to the Iron Hypothesis [ 39 ] where it was proposed that an influx of iron would promote phytoplankton growth and thereby reduce atmospheric CO 2 . This hypothesis has been tested on more than 10 different occasions and in all cases, massive blooms resulted. However, the blooms persisted for variable periods of time. An interesting observation made in some of these studies was that the concentration of the organic ligands increased over a short time span in order to match the concentration of added iron, thus implying biological origin and in view of their affinity for iron possibly being of a siderophore or siderophore-like nature. [ 40 ] Significantly, heterotrophic bacteria were also found to markedly increase in number in the iron-induced blooms. Thus there is the element of synergism between phytoplankton and heterotrophic bacteria. Phytoplankton require iron (provided by bacterial siderophores), and heterotrophic bacteria require non-CO 2 carbon sources (provided by phytoplankton).
The dilute nature of the pelagic marine environment promotes large diffusive losses and renders the efficiency of the normal siderophore-based iron uptake strategies problematic. However, many heterotrophic marine bacteria do produce siderophores, albeit with properties different from those produced by terrestrial organisms. Many marine siderophores are surface-active and tend to form molecular aggregates, for example aquachelins . The presence of the fatty acyl chain renders the molecules with a high surface activity and an ability to form micelles . [ 41 ] Thus, when secreted, these molecules bind to surfaces and to each other, thereby slowing the rate of diffusion away from the secreting organism and maintaining a relatively high local siderophore concentration. Phytoplankton have high iron requirements and yet the majority (and possibly all) do not produce siderophores. Phytoplankton can, however, obtain iron from siderophore complexes by the aid of membrane-bound reductases [ 42 ] and certainly from iron(II) generated via photochemical decomposition of iron(III) siderophores. Thus a large proportion of iron (possibly all iron) absorbed by phytoplankton is dependent on bacterial siderophore production. [ 43 ]
Most plant pathogens invade the apoplasm by releasing pectolytic enzymes which facilitate the spread of the invading organism. Bacteria frequently infect plants by gaining entry to the tissue via the stomata . Having entered the plant they spread and multiply in the intercellular spaces. With bacterial vascular diseases, the infection is spread within the plants through the xylem .
Once within the plant, the bacteria need to be able to scavenge iron from the two main iron-transporting ligands, nicotianamine and citrate. [ 44 ] To do this they produce siderophores, thus the enterobacterial Erwinia chrysanthemi produces two siderophores, chrysobactin and achromobactin. [ 45 ] Xanthomonas group of plant pathogens produce xanthoferrin siderophores to scavenge the iron. [ 46 ]
Like in humans, plants also possess siderophore binding proteins involved in host defense, like the major birch pollen allergen, Bet v 1 , which are usually secreted and possess a lipocalin -like structure. [ 43 ]
Pathogenic bacteria and fungi have developed the means of survival in animal tissue. They may invade the gastro-intestinal tract ( Escherichia , Shigella and Salmonella ), the lung ( Pseudomonas , Bordetella , Streptococcus and Corynebacterium ), skin ( Staphylococcus ) or the urinary tract ( Escherichia and Pseudomonas ). Such bacteria may colonise wounds ( Vibrio and Staphylococcus ) and be responsible for septicaemia ( Yersinia and Bacillus ). Some bacteria survive for long periods of time in intracellular organelles, for instance Mycobacterium . (see table). Because of this continual risk of bacterial and fungal invasion, animals have developed a number of lines of defence based on immunological strategies, the complement system, the production of iron–siderophore binding proteins and the general "withdrawal" of iron. [ 47 ]
There are two major types of iron-binding proteins present in most animals that provide protection against microbial invasion – extracellular protection is achieved by the transferrin family of proteins and intracellular protection is achieved by ferritin. Transferrin is present in the serum at approximately 30 μM, and contains two iron-binding sites, each with an extremely high affinity for iron. Under normal conditions it is about 25–40% saturated, which means that any freely available iron in the serum will be immediately scavenged – thus preventing microbial growth. Most siderophores are unable to remove iron from transferrin. Mammals also produce lactoferrin, which is similar to serum transferrin but possesses an even higher affinity for iron. [ 48 ] Lactoferrin is present in secretory fluids, such as sweat, tears and milk, thereby minimising bacterial infection.
Ferritin is present in the cytoplasm of cells and limits the intracellular iron level to approximately 1 μM. Ferritin is a much larger protein than transferrin and is capable of binding several thousand iron atoms in a nontoxic form. Siderophores are unable to directly mobilise iron from ferritin.
In addition to these two classes of iron-binding proteins, a hormone, hepcidin, is involved in controlling the release of iron from absorptive enterocytes, iron-storing hepatocytes and macrophages. [ 49 ] Infection leads to inflammation and the release of interleukin-6 (IL-6 ) which stimulates hepcidin expression. In humans, IL-6 production results in low serum iron, making it difficult for invading pathogens to infect. Such iron depletion has been demonstrated to limit bacterial growth in both extracellular and intracellular locations. [ 47 ]
In addition to "iron withdrawal" tactics, mammals produce an iron –siderophore binding protein, siderochelin. Siderochelin is a member of the lipocalin family of proteins, which while diverse in sequence, displays a highly conserved structural fold, an 8-stranded antiparallel β-barrel that forms a binding site with several adjacent β-strands. Siderocalin (lipocalin 2) has 3 positively charged residues also located in the hydrophobic pocket, and these create a high affinity binding site for iron(III)–enterobactin. [ 11 ] Siderocalin is a potent bacteriostatic agent against E. coli . As a result of infection it is secreted by both macrophages and hepatocytes, enterobactin being scavenged from the extracellular space.
Siderophores have applications in medicine for iron and aluminum overload therapy and antibiotics for improved targeting. [ 10 ] [ 50 ] [ 3 ] Understanding the mechanistic pathways of siderophores has led to opportunities for designing small-molecule inhibitors that block siderophore biosynthesis and therefore bacterial growth and virulence in iron-limiting environments. [ 51 ] [ 52 ]
Siderophores are useful as drugs in facilitating iron mobilization in humans, especially in the treatment of iron diseases, due to their high affinity for iron. One potentially powerful application is to use the iron transport abilities of siderophores to carry drugs into cells by preparation of conjugates between siderophores and antimicrobial agents. Because microbes recognize and utilize only certain siderophores, such conjugates are anticipated to have selective antimicrobial activity. [ 10 ] [ 16 ] An example is the cephalosporin antibiotic cefiderocol . [ 53 ]
Microbial iron transport (siderophore)-mediated drug delivery makes use of the recognition of siderophores as iron delivery agents in order to have the microbe assimilate siderophore conjugates with attached drugs. These drugs are lethal to the microbe and cause the microbe to apoptosise when it assimilates the siderophore conjugate. [ 10 ] Through the addition of the iron-binding functional groups of siderophores into antibiotics, their potency has been greatly increased. This is due to the siderophore-mediated iron uptake system of the bacteria.
Poaceae (grasses) including agriculturally important species such as barley and wheat are able to efficiently sequester iron by releasing phytosiderophores via their root into the surrounding soil rhizosphere . [ 20 ] Chemical compounds produced by microorganisms in the rhizosphere can also increase the availability and uptake of iron. Plants such as oats are able to assimilate iron via these microbial siderophores. It has been demonstrated that plants are able to use the hydroxamate-type siderophores ferrichrome, rhodotorulic acid and ferrioxamine B; the catechol-type siderophores, agrobactin; and the mixed ligand catechol-hydroxamate-hydroxy acid siderophores biosynthesized by saprophytic root-colonizing bacteria. All of these compounds are produced by rhizospheric bacterial strains, which have simple nutritional requirements, and are found in nature in soils, foliage, fresh water, sediments, and seawater. [ 54 ]
Fluorescent pseudomonads have been recognized as biocontrol agents against certain soil-borne plant pathogens. They produce yellow-green pigments ( pyoverdines ) which fluoresce under UV light and function as siderophores. They deprive pathogens of the iron required for their growth and pathogenesis. [ 55 ]
Siderophores, natural or synthetic, can chelate metal ions other than iron ions. Examples include aluminium , [ 2 ] [ 23 ] [ 54 ] [ 56 ] gallium , [ 2 ] [ 23 ] [ 54 ] [ 56 ] chromium , [ 23 ] [ 54 ] copper , [ 23 ] [ 54 ] [ 56 ] zinc , [ 23 ] [ 56 ] lead , [ 23 ] manganese , [ 23 ] cadmium , [ 23 ] vanadium , [ 23 ] zirconium , [ 57 ] indium , [ 23 ] [ 56 ] plutonium , [ 58 ] berkelium , californium , [ 59 ] and uranium . [ 58 ]
Alternative means of assimilating iron are surface reduction, lowering of pH, utilization of heme, or extraction of protein-complexed metal. [ 2 ] Recent data suggest that iron-chelating molecules with similar properties to siderophores, were produced by marine bacteria under phosphate limiting growth condition. In nature phosphate binds to different type of iron minerals, and therefore it was hypothesized that bacteria can use siderophore-like molecules to dissolve such complex in order to access the phosphate. [ 60 ] | https://en.wikipedia.org/wiki/Siderophore |
In mathematics , LHS is informal shorthand for the left-hand side of an equation . Similarly, RHS is the right-hand side . The two sides have the same value, expressed differently, since equality is symmetric . [ 1 ]
More generally, these terms may apply to an inequation or inequality ; the right-hand side is everything on the right side of a test operator in an expression , with LHS defined similarly.
The expression on the right side of the "=" sign is the right side of the equation and the expression on the left of the "=" is the left side of the equation.
For example, in
x + 5 is the left-hand side (LHS) and y + 8 is the right-hand side (RHS).
In solving mathematical equations, particularly linear simultaneous equations , differential equations and integral equations , the terminology homogeneous is often used for equations with some linear operator L on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homogeneous , as exemplified by
with g a fixed function, which equation is to be solved for f . Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution.
For example in mathematical physics , the homogeneous equation may correspond to a physical theory formulated in empty space , while the inhomogeneous equation asks for more 'realistic' solutions with some matter, or charged particles.
More abstractly, when using infix notation
the term T stands as the left-hand side and U as the right-hand side of the operator *. This usage is less common, though. | https://en.wikipedia.org/wiki/Sides_of_an_equation |
Sidewalk cycling is the practice of riding bicycles on sidewalks or footpaths , where pedestrians usually have priority. It is controversial, [ 1 ] and is illegal in many countries (including well-known cycling countries such as the Netherlands [ 2 ] and Denmark [ 3 ] ), in some municipalities, [ 4 ] cities [ 5 ] or districts, [ 6 ] while in some places it is only permitted for children up to the age of 12 [ 7 ] or 14. [ 8 ] [ 9 ]
Cycling on sidewalks puts cyclists in direct conflict with pedestrians, [ 5 ] and undermines the principle of a reverse traffic pyramid . Some instead advocate vehicular cycling in places without dedicated cycling infrastructure , which is in line with the principle of an inverted traffic pyramid that prioritizes the convenience and safety of pedestrians, cyclists, and motorists, in that order.
Some argue that cars take up most of the traffic, while cyclists and pedestrians often come second in urban planning and traffic planning , and have to "fight for the crumbs". [ 10 ] In contrast, sidewalks are designed for walking speed, and often have curbs and other obstacles (benches, signs, lamp posts, garbage cans) that make them uncomfortable or risky to cycle on. [ 5 ] Cycling on sidewalks has been greatly reduced in places where streets have been redesigned with pedestrians and cyclists in mind. [ 10 ]
Most legislation assumes for cycling either on separate cycling infrastructure or together with cars. [ 11 ] In Norway, cycling on sidewalks was allowed for adults in 1978, [ 12 ] and continued in 1986. It has been argued that original intent of the law was for children and "weak" cyclists to use the sidewalk, while adults still were expected to use the roadway for cycling. [ 12 ] In a commentary on why Norwegian cycling culture in the 2010s has become so aggressive, it has been argued that it was a big mistake to allow cycling on sidewalks in the 1970s. [ 13 ] Some argue that allowing cycling on sidewalks even prevents development of dedicated cycling infrastructure. On the other hand, it has been argued that the development of dedicated cycling infrastructure also benefits motorists and pedestrians. [ 14 ]
Reasons why many cyclists choose to cycle on the sidewalk may be less perceived risk , although the actual risk is often higher compared to cycling on the road. [ 1 ] Some cyclists do so because it is perceived as a "faster" route. Some choose to cycle fast for exercise, or cycle on and off the sidewalk to avoid "losing speed". Sometimes cyclists prefer the sidewalk to cycling in narrow bike lanes (which lack protection from cars). [ 1 ]
Sidewalk cycling is associated with many types of serious accidents between cars and bicycles, [ 5 ] particularly at intersections and crosswalks , because drivers do not typically expect traffic coming from the sidewalk at high speeds, or may have difficulty seeing cyclists due to the design of intersections (regardless of who has the right of way ). [ 5 ]
The risk of collisions with cars increases significantly, and it has been claimed that adults experience 4-6 times more collisions when cycling on sidewalks than on roads. [ 16 ] Cyclists become less visible to motorists, [ 1 ] [ 17 ] and the degree of improvisation results in a greater risk that cyclists' maneuvers appear unexpected to motorists. [ 16 ] At intersections, motorists may perceive cyclists as "coming out of nowhere." When cycling on sidewalks, cyclists should also be particularly alert when crossing driveways and exits.
Some cyclists believe that cycling on the sidewalk is humiliating and that they have the right to cycle on the road. [ 18 ] Cycling on the sidewalk is also seen as "forbidden fruit" by some. [ 18 ] On the other hand, some believe that one must be fearless as a cyclist to dare to cycle with cars. [ 1 ]
Since cyclists travel at significantly higher speeds than pedestrians they can make pedestrians feel unsafe. [ 19 ] In particular there have been several examples of conflicts between dog owners and cyclists, for various reasons, since dogs can move unpredictably. [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ]
Some recommend to always get off and walk the bike on the sidewalk. [ 5 ] In cases where cycling on the sidewalk is permitted, there are rules and recommendations to ensure that pedestrians feel safe. For example, the Norwegian traffic regulations require that cyclists pass at walking speed, with a good distance, and in any case not faster than 6 km/h, [ 25 ] but in practice this has proven difficult for cyclists to comply with. [ 26 ]
If one must cycle on a sidewalk or footpath one should pay the utmost attention to pedestrians: | https://en.wikipedia.org/wiki/Sidewalk_cycling |
Siding or wall cladding is the protective material attached to the exterior side of a wall of a house or other building. Along with the roof, it forms the first line of defense against the elements, most importantly sun, rain/snow, heat and cold, thus creating a stable, more comfortable environment on the interior side. The siding material and style also can enhance or detract from the building's beauty. There is a wide and expanding variety of materials to side with, both natural and artificial, each with its own benefits and drawbacks. Masonry walls as such do not require siding, but any wall can be sided. Walls that are internally framed, whether with wood, or steel I-beams, however, must always be sided.
Most siding consists of pieces of weather-resistant material that are smaller than the wall they cover, to allow for expansion and contraction of the materials due to moisture and temperature changes. There are various styles of joining the pieces, from board and batton, where the butt joints between panels is covered with a thin strip (usually 25 to 50 mm wide) of wood, to a variety of clapboard, also called lap siding, in which planks are laid horizontally across the wall starting from the bottom, and building up, the board below overlapped by the board above it. These techniques of joinery are designed to prevent water from entering the walls. Siding that does not consist of pieces joined would include stucco, which is widely used in the Southwestern United States. It is a plaster-like siding and is applied over a lattice, just like plaster. However, because of the lack of joints, it eventually cracks and is susceptible to water damage. Rainscreen construction is used to improve siding's ability to keep walls dry.
Wood siding is very versatile in style and can be used on a wide variety of building structures. It can be painted or stained in any color palette desired.
Though installation and repair is relatively simple, wood siding requires more maintenance than other popular solutions, requiring treatment every four to nine years depending on the severity of the elements to which it is exposed. Ants and termites are a threat to many types of wood siding, such that extra treatment and maintenance that can significantly increase the cost in some pest-infested areas.
Wood is a moderately renewable resource and is biodegradable. However, most paints and stains used to treat wood are not environmentally friendly and can be toxic. Wood siding can provide some minor insulation and structural properties as compared to thinner cladding materials.
Wood shingles or irregular cedar " shake " siding was used in early New England construction, and was revived in Shingle Style and Queen Anne style architecture in the late 19th century.
Wood siding in overlapping horizontal rows or "courses" is called clapboard , weatherboard (British English), or bevel siding which is made with beveled boards, thin at the top edge and thick at the butt.
In colonial North America, Eastern white pine was the most common material. Wood siding can also be made of naturally rot-resistant woods such as redwood or cedar .
Jointed horizontal siding (also called "drop" siding or novelty siding) may be shiplapped or tongue and grooved (though less common). Drop siding comes in a wide variety of face finishes, including Dutch Lap (also called German or Cove Lap) and log siding (milled with curve).
Vertical siding may have a cover over the joint: board and batten , popular in American wooden Carpenter Gothic houses; or less commonly behind the joint called batten and board or reversed board and batten .
Plywood sheet siding is sometimes used on inexpensive buildings, sometimes with grooves to imitate vertical shiplap siding. One example of such grooved plywood siding is the type called Texture 1–11, T1-11 , or T111 ("tee-one-eleven"). There is also a product known as reverse board-and-batten RBB that looks similar but has deeper grooves. Some of these products may be thick enough and rated for structural applications if properly fastened to studs. Both T-11 and RBB sheets are quick and easy to install as long as they are installed with compatible flashing at butt joints.
Slate shingles may be simple in form but many buildings with slate siding are highly decorative.
Wood clapboard is often imitated using vinyl siding or uPVC weatherboarding . It is usually produced in units twice as high as clapboard. Plastic imitations of wood shingle and wood shakes also exist.
Since plastic siding is a manufactured product, it may come in unlimited color choices and styles. Historically vinyl sidings would fade, crack and buckle over time, requiring the siding to be replaced. However, newer vinyl options have improved and resist damage and wear better. Vinyl siding is sensitive to direct heat from grills, barbecues or other sources. Unlike wood, vinyl siding does not provide additional insulation for the building, unless an insulation material (e.g., foam) has been added to the product. It has also been criticized by some fire safety experts for its heat sensitivity. This sensitivity makes it easier for a house fire to jump to neighboring houses in comparison to materials such as brick, metal or masonry.
Vinyl siding has a potential environmental cost. While vinyl siding can be recycled, it cannot be burned (due to toxic dioxin gases that would be released). If dumped in a landfill, plastic siding does not break down quickly.
Vinyl siding is also considered one of the more unattractive siding choices by many. Although newer options and proper installation can eliminate this complaint, vinyl siding often has visible seam lines between panels and generally do not have the quality appearance of wood, brick, or masonry. The fading and cracking of older types of plastic siding compound this issue. In many areas of newer housing development, particularly in North America, entire neighbourhoods are often built with all houses clad in vinyl siding, given an unappealing uniformity. Some cities now campaign for house developers to incorporate varied types of siding during construction.
A predecessor to modern maintenance free sidings was asphalt brick siding. Asphalt impregnated panels (about 2 by 4 ft or 0.61 by 1.22 m) give the appearance of brick or even stone. Many buildings have this siding, especially old sheds and garages. If the panels are straight and level and not damaged, the only indication that they are not real brick may be seen at the corner caps. Trademarked names included Insulbrick, Insulstone, Insulwood. Commonly used names now are faux brick, lick-it-and-stick-it brick, and ghetto brick. Often such siding is now covered with newer metal or plastic siding. Today thin panels of real brick are manufactured for veneer or siding.
Insulated siding has emerged as a new siding category in recent years. Considered an improvement over vinyl siding , insulated siding is custom fit with expanded polystyrene foam (EPS) that is fused to the back of the siding, which fills the gap between the home and the siding.
Products provide environmental advantages by reducing energy use by up to 20 percent. On average, insulated siding products have an R-value of 3.96, triple that of other exterior cladding materials. Insulated siding products are typically Energy Star qualified, engineered in compliance with environmental standards set by the U.S. Department of Energy and the United States Environmental Protection Agency .
In addition to reducing energy consumption, insulated siding is a durable exterior product, designed to last more than 50 years, according to manufacturers. The foam provides rigidity for a more ding- and wind-resistant siding, maintaining a quality look for the life of the products. The foam backing also creates straighter lines when hung, providing a look more like that of wood siding, while remaining low maintenance.
Manufacturers report that insulated siding is permeable or "breathable", allowing water vapor to escape, which can protect against rot, mold and mildew, and help maintain healthy indoor air quality .
Metal siding comes in a variety of metals, styles, and colors. It is most often associated with modern, industrial, and retro buildings. Utilitarian buildings often use corrugated galvanized steel sheet siding or cladding, which often has a coloured vinyl finish. Corrugated aluminium cladding is also common where a more durable finish is required, while also being lightweight for easy shaping and installing making it a popular metal siding choice.
Formerly, imitation wood clapboard was made of aluminium (aluminium siding). That role is typically played by vinyl siding today. Aluminium siding is ideal for homes in coastal areas with much moisture and salt, since aluminium reacts with air to form aluminium oxide, an extremely hard coating that seals the aluminium surface from further degradation. In contrast, steel forms rust , which can weaken the structure of the material, and corrosion-resistant coatings for steel, such as zinc, sometimes fail around the edges as years pass. However, an advantage of steel siding can be its dent-resistance, which is excellent for regions with severe storms—especially if the area is prone to hail .
The first architectural application of aluminium was the mounting of a small grounding cap on the Washington Monument in 1884. Sheet-iron or steel clapboard siding units had been patented in 1903, and Sears, Roebuck & Company had been offering embossed steel siding in stone and brick patterns in their catalogues for several years by the 1930s. Alcoa began promoting the use of aluminium in architecture by the 1920s when it produced ornamental spandrel panels for the Cathedral of Learning and the Chrysler and Empire State Buildings in New York. The exterior of the A.O. Smith Corporation Building in Milwaukee was clad entirely in aluminium by 1930, and 3-foot-square (0.91 m) siding panels of Duralumin sheet from Alcoa sheathed an experimental exhibit house for the Architectural League of New York in 1931. Most architectural applications of aluminium in the 1930s were on a monumental scale, and it was another six years before it was put to use on residential construction.
In the first few years after World War II, manufacturers began developing and widely distributing aluminium siding. Among them Indiana businessman Frank Hoess was credited with the invention of the configuration seen on modern aluminium siding. His experiments began in 1937 with steel siding in imitation of wooden clapboards. Other types of sheet metal and steel siding on the market at the time presented problems with warping, creating openings through which water could enter, introducing rust. Hoess remedied this problem through the use of a locking joint, which was formed by small flap at the top of each panel that joined with a U-shaped flange on the lower edge of the previous panel thus forming a watertight horizontal seam. After he had received a patent for his siding in 1939, Hoess produced a small housing development of about forty-four houses covered in his clapboard-style steel siding for blue-collar workers in Chicago. His operations were curtailed when war plants commandeered the industry. In 1946 Hoess allied with Metal Building Products of Detroit, a corporation that promoted and sold Hoess siding of Alcoa aluminium. Their product was used on large housing projects in the northeast and was purportedly the siding of choice for a 1947 Pennsylvania development, the first subdivision to solely use aluminium siding. Products such as 4,-6,-8-and-10-inch (100, 150, 200 and 250 mm) by 12-foot (3.7 m) unpainted aluminium panels, starter strips, corner pieces and specialized application clips were assembled in the Indiana shop of the Hoess brothers. Siding could be applied over conventional wooden clapboards, or it could be nailed to studs via special clips affixed to the top of each panel. Insulation was placed between studs. While the Hoess Brothers company continued to function for about twelve more years after the dissolution of the Metal Building Products Corporation in 1948, they were less successful than rising siding companies like Reynolds Metals. [ 1 ] [ 2 ]
Thatch is an ancient and very widespread building material used on roofs and walls. Thatch siding is made with dry vegetation such as longstraw, water reeds, or combed wheat reed. The materials are overlapped and weaved in patterns designed to deflect and direct water.
Stone and masonry veneer is sometimes considered siding , are varied and can accommodate a variety of styles—from formal to rustic. Though masonry can be painted or tinted to match many color palettes, it is most suited to neutral earth tones, and coatings such as roughcast and pebbeldash . Masonry has excellent durability (over 100 years), and minimal maintenance is required. The primary drawback to masonry siding is the initial cost.
Precipitation can threaten the structure of buildings, so it is important that the siding will be able to withstand the weather conditions in the local region. For rainy regions, exterior insulation finishing systems (EIFS) have been known to suffer underlying wood rot problems with excessive moisture exposure.
The environmental impact of masonry depends on the type of material used. In general, concrete and concrete based materials are intensive energy materials to produce. However, the long durability and minimal maintenance of masonry sidings mean that less energy is required over the life of the siding.
Various composite materials are also used for siding: asphalt shingles , asbestos , fiber cement , aluminium (ACM), fiberboard , hardboard , etc. They may be in the form of shingles or boards, in which case they are sometimes called clapboard .
Composite sidings are available in many styles and can mimic the other siding options. Composite materials are ideal for achieving a certain style or 'look' that may not be suited to the local environment (e.g., corrugated aluminium siding in an area prone to severe storms; steel in coastal climates; wood siding in termite-infested regions).
Costs of composites tend to be lower than wood options, but vary widely as do installation, maintenance and repair requirements. Not surprisingly, the durability and environmental impact of composite sidings depends on the specific materials used in the manufacturing process.
Fiber cement siding is a class of composite siding that is usually made from a combination of cement, cellulose (wood), sand, and water. They are either coated or painted in the factory or installed and then painted after installation. Fiber cement is popular for its realistic look, durability, low-maintenance properties, fire resistance, and its lightweight properties compared to traditional wood siding. Composite siding products containing cellulose (wood fibers) have been shown to have problems with deterioration, delamination, or loss of coating adhesion in certain climates or under certain environmental conditions.
A younger class of non-wood synthetic siding has sprouted in the past 15 years. These products are usually made from a combination of non-wood materials such as polymeric resins, fiberglass, stone, sand, and fly ash and are chosen for their durability, curb appeal, and ease of maintenance. Given the newness of such technologies, product lifespan can only be estimated, varieties are limited, and distribution is sporadic. | https://en.wikipedia.org/wiki/Siding_(construction) |
In number theory , a Sidon sequence is a sequence A = { a 0 , a 1 , a 2 , … } {\displaystyle A=\{a_{0},a_{1},a_{2},\dots \}} of natural numbers in which all pairwise sums a i + a j {\displaystyle a_{i}+a_{j}} (for i ≤ j {\displaystyle i\leq j} ) are different. Sidon sequences are also called Sidon sets ; they are named after the Hungarian mathematician Simon Sidon , who introduced the concept in his investigations of Fourier series .
The main problem in the study of Sidon sequences, posed by Sidon, [ 1 ] is to find the maximum number of elements that a Sidon sequence can contain, up to some bound x {\displaystyle x} . Despite a large body of research, [ 2 ] the question has remained unsolved. [ 3 ]
Paul Erdős and Pál Turán proved that, for every x > 0 {\displaystyle x>0} , the number of elements smaller than x {\displaystyle x} in a Sidon sequence is at most x + O ( x 4 ) {\displaystyle {\sqrt {x}}+O({\sqrt[{4}]{x}})} . Several years earlier, James Singer had constructed Sidon sequences with x ( 1 − o ( 1 ) ) {\displaystyle {\sqrt {x}}(1-o(1))} terms less than x . The upper bound was improved to x + x 4 + 1 {\displaystyle {\sqrt {x}}+{\sqrt[{4}]{x}}+1} in 1969 [ 4 ] and to x + 0.998 x 4 {\displaystyle {\sqrt {x}}+0.998{\sqrt[{4}]{x}}} in 2023. [ 5 ]
In 1994 Erdős offered 500 dollars for a proof or disproof of the bound x + o ( x ε ) {\displaystyle {\sqrt {x}}+o(x^{\varepsilon })} . [ 6 ]
A Sidon subset A ⊂ [ n ] := { 1 , 2 , … , n } {\displaystyle A\subset [n]:=\{1,2,\dots ,n\}} is called dense if | A | = max | S | {\displaystyle \left|A\right|=\max \left|S\right|} where the maximum is taken over all Sidon subsets of [ n ] {\displaystyle [n]} . The structure of dense Sidon sets has a rich literature [ 7 ] [ 8 ] and classic constructions by Erdős–Turán, [ 9 ] Singer, [ 10 ] Bose , [ 11 ] Spence, [ 12 ] [ 13 ] Hughes [ 14 ] and Cilleruelo [ 15 ] have established that a dense Sidon set A {\displaystyle A} satisfies | A | ≥ ( 1 − o ( 1 ) ) n {\displaystyle \left|A\right|\geq \left(1-o(1)\right){\sqrt {n}}} . As remarked by Ruzsa , "somehow all known constructions of dense Sidon sets involve the primes". [ 16 ]
A recent result of Balasubramanian and Dutta [ 17 ] shows that if a dense Sidon set A = { a 1 , … , a | A | } ⊂ [ n ] {\displaystyle A=\{a_{1},\dots ,a_{\left|A\right|}\}\subset [n]} has cardinality | A | = n 1 / 2 − L ′ {\displaystyle |A|=n^{1/2}-L^{\prime }} , then
a m = m ⋅ n 1 / 2 + O ( n 7 / 8 ) + O ( L 1 / 2 ⋅ n 3 / 4 ) {\displaystyle a_{m}=m\cdot n^{1/2}+{\mathcal {O}}\left(n^{7/8}\right)+{\mathcal {O}}\left(L^{1/2}\cdot n^{3/4}\right)}
where L = max { 0 , L ′ } {\displaystyle L=\max\{0,L^{\prime }\}} . This directly gives some useful asymptotic results including
∑ a ∈ A a ℓ = 1 ℓ + 1 ⋅ n 2 ℓ + 1 2 + O ( n 8 ℓ + 3 8 ) + O ( L 1 / 2 ⋅ n 4 ℓ + 1 4 ) {\displaystyle \sum _{a\in A}a^{\ell }={\frac {1}{\ell +1}}\cdot n^{\frac {2\ell +1}{2}}+{\mathcal {O}}\left(n^{\frac {8\ell +3}{8}}\right)+{\mathcal {O}}\left(L^{1/2}\cdot n^{\frac {4\ell +1}{4}}\right)}
for any positive integer ℓ {\displaystyle \ell } .
Dense Sidon sets often exhibit surprising symmetries. For example, it is known that dense Sidon sets are uniformly distributed, [ 18 ] [ 19 ] [ 20 ] equidistributed in residue classes, [ 21 ] [ 22 ] and even in smooth Bohr neighbourhoods. [ 23 ]
Erdős also showed that, for any particular infinite Sidon sequence A {\displaystyle A} with A ( x ) {\displaystyle A(x)} denoting the number of its elements up to x {\displaystyle x} , lim inf x → ∞ A ( x ) log x x ≤ 1. {\displaystyle \liminf _{x\to \infty }{\frac {A(x){\sqrt {\log x}}}{\sqrt {x}}}\leq 1.} That is, infinite Sidon sequences are thinner than the densest finite Sidon sequences.
For the other direction, Chowla and Mian observed that the greedy algorithm gives an infinite Sidon sequence with A ( x ) > c x 3 {\displaystyle A(x)>c{\sqrt[{3}]{x}}} for every x {\displaystyle x} . [ 24 ] Ajtai , Komlós , and Szemerédi improved this with a construction [ 25 ] of a Sidon sequence with A ( x ) > x log x 3 . {\displaystyle A(x)>{\sqrt[{3}]{x\log x}}.}
The best lower bound to date was given by Imre Z. Ruzsa , who proved [ 26 ] that a Sidon sequence with A ( x ) > x 2 − 1 − o ( 1 ) {\displaystyle A(x)>x^{{\sqrt {2}}-1-o(1)}} exists. Erdős conjectured that an infinite Sidon set A {\displaystyle A} exists for which A ( x ) > x 1 / 2 − o ( 1 ) {\displaystyle A(x)>x^{1/2-o(1)}} holds. He and Rényi showed [ 27 ] the existence of a sequence { a 0 , a 1 , … } {\displaystyle \{a_{0},a_{1},\dots \}} with the conjectural density but satisfying only the weaker property that there is a constant k {\displaystyle k} such that for every natural number n {\displaystyle n} there are at most k {\displaystyle k} solutions of the equation a i + a j = n {\displaystyle a_{i}+a_{j}=n} . (To be a Sidon sequence would require that k = 1 {\displaystyle k=1} .)
Erdős further conjectured that there exists a nonconstant integer - coefficient polynomial whose values at the natural numbers form a Sidon sequence. Specifically, he asked if the set of fifth powers is a Sidon set. Ruzsa came close to this by showing that there is a real number c {\displaystyle c} with 0 < c < 1 {\displaystyle 0<c<1} such that the range of the function f ( x ) = x 5 + ⌊ c x 4 ⌋ {\displaystyle f(x)=x^{5}+\lfloor cx^{4}\rfloor } is a Sidon sequence, where ⌊ ⌋ {\displaystyle \lfloor \ \rfloor } denotes the integer part . As c {\displaystyle c} is irrational, this function f ( x ) {\displaystyle f(x)} is not a polynomial. The statement that the set of fifth powers is a Sidon set is a special case of the later conjecture of Lander, Parkin and Selfridge .
The existence of Sidon sequences that form an asymptotic basis of order m {\displaystyle m} (meaning that every sufficiently large natural number n {\displaystyle n} can be written as the sum of m {\displaystyle m} numbers from the sequence) has been proved for m = 5 {\displaystyle m=5} in 2010, [ 28 ] m = 4 {\displaystyle m=4} in 2014, [ 29 ] m = 3 + ε {\displaystyle m=3+\varepsilon } (the sum of four terms with one smaller than n ε {\displaystyle n^{\varepsilon }} , for arbitrarily small positive ε {\displaystyle \varepsilon } ) in 2015 [ 30 ] and m = 3 {\displaystyle m=3} in 2024. [ 31 ] [ 32 ] This last one was posed as a problem in a paper of Erdős, Sárközy and Sós in 1994. [ 33 ]
All finite Sidon sets are Golomb rulers , and vice versa.
To see this, suppose for a contradiction that S {\displaystyle S} is a Sidon set and not a Golomb ruler. Since it is not a Golomb ruler, there must be four members such that a i − a j = a k − a l {\displaystyle a_{i}-a_{j}=a_{k}-a_{l}} . It follows that a i + a l = a k + a j {\displaystyle a_{i}+a_{l}=a_{k}+a_{j}} , which contradicts the proposition that S {\displaystyle S} is a Sidon set. Therefore all Sidon sets must be Golomb rulers. By a similar argument, all Golomb rulers must be Sidon sets. | https://en.wikipedia.org/wiki/Sidon_sequence |
The Siegbahn notation is used in X-ray spectroscopy to name the spectral lines that are characteristic to elements. It was introduced by Manne Siegbahn .
The characteristic lines in X-ray emission spectra correspond to atomic electronic transitions where an electron jumps down to a vacancy in one of the inner shells of an atom. Such a hole in an inner shell may have been produced by bombardment with electrons in an X-ray tube , by other particles as in PIXE , by other X-rays in X-ray fluorescence or by radioactive decay of the atom's nucleus.
Although still widely used in spectroscopy, this notation is unsystematic and often confusing. For these reasons, International Union of Pure and Applied Chemistry (IUPAC) recommends another nomenclature .
The use of the letters K and L to denote X-rays originates in a 1911 paper by Charles Glover Barkla , titled The Spectra of the Fluorescent Röntgen Radiations [ 1 ] ("Röntgen radiation" is an archaic name for "X-rays" ). By 1913, Henry Moseley had clearly differentiated two types of X-ray lines for each element, naming them α and β. [ 2 ] In 1914, as part of his thesis, Ivar Malmer ( sv:Ivar Malmer ), a student of Manne Siegbahn , discovered that the α and β lines were not single lines, but doublets. In 1916, Siegbahn published this result in the journal Nature , using what would come to be known as the Siegbahn notation. [ 3 ]
The table below shows a few transitions and their initial and final levels. | https://en.wikipedia.org/wiki/Siegbahn_notation |
Roman–Sasanian wars
Byzantine–Sasanian wars
Year of the Six Emperors (238)
Reign of Gordian III (238–244)
Reign of Philip the Arab (244–249)
Reign of Decius (249–251)
Reign of Trebonianus Gallus (251–253)
Reign of Aemilianus (253)
Reign of Valerian and Gallienus (253–260)
Reign of Gallienus (260–268)
Reign of Claudius Gothicus (268–270)
Reign of Aurelian (270–275)
Reign of Tacitus (275-276)
Reign of Probus (276-282)
Reign of Carus (282-283)
Reign of Carinus (283-285)
The siege of Dura Europos took place when the Sasanians under Shapur I besieged the Roman city of Dura-Europos in 256 after capturing Antioch .
Dura-Europos was an important trading center in Roman Syria. It may or may not be the same as the "Doura" recorded in Shapur I's inscriptions. The town was in Sasanian hands for some time after its fall, and was later abandoned. Intact archaeological evidences at Dura provide details of the Roman presence there, and the dramatic course of the siege. The garrison was determined to resist the siege, and the Sasanians employed a variety of siege warfare techniques to defeat them. Archaeological evidences suggest that the garrison at Dura-Europos was mixed, composed of Cohors XX Palmyrenorum (which is known more than the others), vexillations from Legio IV Scythica Valeriana Galliena , III Cyrenaica , XVI Flavia Firma , and other cohorts, including Cohors II Paphlagonum Galliana Volusiana and possibly Cohors II Equestris . The relationship between these forces are uncertain. XX Palmyrenorum was certainly based in Dura-Europos, and may have been an "inferior" contingent of the garrison relative to the legionaries. The numbers of the legionaries are unknown. [ 2 ] [ 3 ] [ 4 ] [ 5 ]
The siege was notable for the early use of chemical weapons by the attacking Persian army. During the siege the attackers dug several underground shaft mines under the city walls. The Romans dug tunnels to reach the mines and fight the diggers underground. In one such tunnel, when the Romans broke through into the Sasanian tunnel the tunnelers ignited a mixture of sulfur and pitch , producing a cloud of sulfur dioxide , which killed twenty Roman soldiers, one of which was carrying a coin dated 256, allowing the dating of the siege. Archaeologists excavated the scene in the 1930s. In 2009 tests showed the presence of sulfur dioxide inside the tunnel. [ 6 ] [ 7 ] [ 8 ] In 2020, a group of chemistry students in Foxborough, Massachusetts used chemical analysis of the samples in the tunnel compared with the composition of bitumen and deduced that methane was also likely a by-product of the attack. [ 9 ]
This article about a battle or war of ancient Roman history is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Siege_of_Dura-Europos_(256) |
The siege of Fort Pitt took place during June and July 1763 in what is now the city of Pittsburgh , Pennsylvania , United States . The siege was a part of Pontiac's War , an effort by Native Americans to remove the Anglo-Americans from the Ohio Country and Allegheny Plateau after they refused to honor their promises and treaties to leave voluntarily after the defeat of the French. The Native American efforts of diplomacy, and by siege, to remove the Anglo-Americans from Fort Pitt ultimately failed.
This event is known for a possible attempt at biological warfare , in which William Trent and Simeon Ecuyer, a Swiss mercenary in British service, may have given items from a smallpox infirmary as gifts to Native American emissaries with the hope of spreading the deadly disease to nearby tribes. The effectiveness is unknown, although it is known that the method used is inefficient compared to respiratory transmission and these attempts to spread the disease are difficult to differentiate from epidemics occurring from previous contacts with colonists. [ 1 ] [ 2 ]
Fort Pitt was built in 1758 during the French and Indian War , on the site of what was previously Fort Duquesne in what is now the city of Pittsburgh, Pennsylvania, United States. The French abandoned and destroyed Fort Duquesne in November 1758 with the approach of General John Forbes 's expedition. The Forbes expedition was successful in part because of the Treaty of Easton , in which area American Indians agreed to end their alliance with the French. American Indians—primarily the Six Nations , Delawares and Shawnees —made this agreement with the understanding that the British would leave the area after their war with the French. Instead of leaving the territory west of the Appalachian Mountains as they had agreed, the Anglo-Americans remained on Native lands and reinforced their forts while settlers continued to push westward, [ 3 ] despite the Royal Proclamation of 1763 placing a limit upon the westward expansion of the American colonies. The hostilities between the French and British declined significantly after 1760, followed by a final cessation of hostilities and the formal surrender of the French at the Treaty of Paris in February 1763.
The attacks led by Pontiac against the British in early May 1763, near Fort Detroit , mark what is generally considered to be the beginning of Pontiac's War. The siege of Fort Pitt and numerous other British forts during the spring and summer of 1763 were part of an effort by American Indians to reclaim their territory by driving the British out of the Ohio Country and back across the Appalachian Mountains. While many of the forts and outposts in the region were destroyed, the Indian effort to remove the British from Fort Pitt ultimately failed.
By May 27, the uprising reached the tribes near Fort Pitt, and there were many signs of impending hostilities. The captain of the Fort Pitt militia learned that the Delaware tribe just north of the fort had abandoned their dwellings and cornfields overnight. The Mingo had also abandoned their villages further up the river. The proprietor of the Pennsylvania provincial store reported that numerous Delaware warriors had arrived "in fear and haste" to exchange their skins for gunpowder and lead. The western Delaware warrior leaders Wolf and Keekyuscung had fewer than 100 warriors, so did not immediately attack the well-fortified Fort Pitt. Instead, on May 29, they attacked the supporting farms, plantations and villages in the vicinity of the fort. Panicked settlers crowded into the already overcrowded fort. Captain Simeon Ecuyer, a 22-year veteran Swiss mercenary in British service, [ 4 ] tried to ready his fort after this news of expanding hostilities, putting his 230 men, half regulars and half quickly organized militia, on alert. The fort's exceptional structural defenses, made of stone with bastions covering all angles of attack, were supported by 16 cannons which he had permanently loaded. Ecuyer demolished the nearby village houses and structures to deny cover for attackers. He had trenches dug outside the fort, and set out beaver traps. Smallpox had been discovered within the fort, prompting Ecuyer to build a makeshift hospital in which to quarantine those infected. [ 5 ]
On the June 16, four Shawnee visited Fort Pitt and warned Alexander McKee and Captain Simeon Ecuyer that several Indian nations had accepted Pontiac's war belt and bloody hatchet and were going on the offensive against the British, but that the Delaware were still divided, with the older Delaware chiefs advising against war. The following day, however, the Shawnee returned and reported a more threatening situation, saying that all the nations "had taken up the hatchet" against the British, and were going to attack Fort Pitt. Even the local Shawnee themselves "were afraid to refuse" to join the uprising, a subtle hint that the occupants of Fort Pitt should leave. Ecuyer dismissed the warnings and ignored the requests to leave. On June 22, Fort Pitt was attacked on three sides by Shawnee, western Delaware, Mingo and Seneca, which prompted return fire from Ecuyer's artillery. [ 5 ] This initial attack on the fort was repelled. Since the Indians were unfamiliar with siege warfare, they opted to try diplomacy yet again. On June 24, Turtleheart spoke with McKee and Trent outside the fort, informing them that all of the other forts had fallen, and that Fort Pitt "is the only one you have left in our country." He warned McKee that "six different nations of Indians" were ready to attack if the garrison at the fort did not retreat immediately. They thanked Turtleheart and assured him that Fort Pitt could withstand "all nations of Indians", and they presented the Indian dignitaries with two small blankets and a handkerchief from the smallpox hospital. [ 6 ] For the next several days it remained relatively quiet, although reports were coming in about fort after fort falling before large bands of attacking warriors. [ 5 ]
July 3, four Ottawa newcomers requested a parley and tried to trick the occupants of Fort Pitt into surrender, but the ruse failed. This was followed by several weeks of relative quiet, through July 18 when a large group of warriors arrived, likely from the Fort Ligonier area. McKee was informed by the Shawnee that the Indians were still hopeful of an amicable outcome, similar to agreements just made at Detroit. On July 26, a large conference headed by Ecuyer was convened with several leaders of the Ohioan tribes outside the walls of Fort Pitt. The Indian delegation, Shingas , Wingenum and Grey Eyes among them, came to the fort under a flag of truce to parley, and again requested that the British leave this place. They explained that by taking the Indian's country the British caused this war, and Tessecumme of the Delaware noted that the British were the cause of the trouble since they had broken their promises and treaties. They had come onto Indian land and built forts, despite being asked not to, so now the tribes in the area have amassed to take back their lands. He informed Ecuyer that there was still a short time remaining to leave peacefully. [ 5 ] [ 6 ] The Delaware and Shawnee chiefs made sure Captain Ecuyer at Fort Pitt understood the cause of the conflict. Turtleheart told him, "You marched your armies into our country, and built forts here, though we told you, again and again, that we wished you to move, this land is ours, and not yours." [ 7 ] The Delaware also let it be known, "that all the country was theirs; that they had been cheated out of it, and that they would carry on the war till they burnt Philadelphia". [ 5 ] The British refused to leave, claiming that this was their home now. They bluffed that they could hold out for three years, and bragged that several large armies were coming to their aid. This "very much enraged" the Indian delegation, Trent wrote, "White Eyes and Wingenum seemed to be very much irritated and would not shake hands with our people at parting." On July 28, the siege began in earnest and continued for several days. Seven of the fort garrison were wounded, at least one mortally; Ecuyer was wounded in the leg by an arrow. [ 3 ] [ 8 ]
For Commander-in-Chief, North America Jeffery Amherst , who before the war had dismissed the possibility that the Indians would offer any effective resistance to British rule, the military situation over the summer had become increasingly grim. The frustration was so great, he wrote to Colonel Henry Bouquet and instructed him not to take any Indian prisoners. He proposed that they should be intentionally exposed to smallpox, hunted down with dogs, and "Every other method that can serve to Extirpate this Execrable Race." Amherst had directed Bouquet to take his troops to relieve Fort Pitt, a march that would take several weeks. At Fort Pitt, the siege didn't let up until August 1, 1763, when most of the Indians broke off their attack in order to intercept the body of almost 500 British troops marching to the fort under Colonel Bouquet. On August 5, these two forces met at Edge Hill in the Battle of Bushy Run . Bouquet survived the attack and the Indians were unable to prevent his command from relieving Fort Pitt on August 10. [ 3 ] [ 8 ]
More than 500 British troops and perhaps a couple thousand settlers had died in the Ohio Valley, and of more than a dozen British forts, only Detroit, Niagara and Pitt remained standing at the height of this uprising. [ 7 ] On October 7, 1763, the Crown issued Royal Proclamation of 1763 , which forbade all settlement west of the Appalachian Mountains—a proclamation ignored by British settlers, and unenforced by the British military. Fort Pitt would remain in British hands, and would become a central hub for migrant settlers as they pushed west in ever larger numbers over the next decade.
Out of our regard to them we gave them two Blankets and an Handkerchief out of the Small Pox Hospital. I hope it will have the desired effect.
Sometime in the spring of 1763, a smallpox epidemic broke out near Fort Pitt and subsequently spread there. A smallpox hospital was then also established there to treat sick troops. [ 9 ] [ 10 ] [ 11 ] [ 12 ] There had also been an earlier epidemic among Ohio tribes in the early 1750s, [ 13 ] [ 12 ] as smallpox outbreaks occurred every dozen or so years. [ 14 ] According to John McCullough, who was held captive, some of the Mahoning village warriors raiding a Juniata settlement caught smallpox from there that then killed some of them. [ 15 ]
In 1924 the Mississippi Valley Historical Review published a journal written by William Trent , a fur trader and merchant commissioned as a captain at Fort Pitt. For June 24, 1763, Trent wrote about a meeting with two Delaware Indians at the fort. "Out of our regard to them we gave them two Blankets and an Handkerchief out of the Small Pox Hospital. I hope it will have the desired effect." [ 16 ] (It was commonly believed in past centuries that smallpox could be readily spread at a distance through infected clothing or bedding. However, in the 1960s A. R. Rao’s detailed research, during the last years that smallpox was sufficiently prevalent for its mode of transmission to be studied, found no evidence for this mode of transmission. He concluded that it was a breath-borne disease, transmitted by "inhalation".) [ 17 ]
The two blankets and the handkerchief from the infirmary were seemingly wrapped in a piece of linen. [ 18 ] The blankets and handkerchief were unwashed and dirty. [ 19 ] In 1955 a record of Trent's trading firm was found. It had an invoice for the handkerchief, two blankets and the linen to be given to the Natives, and the expense was signed by Ecuyer. [ 16 ] Ecuyer was relatively inexperienced, having only been a captain since April the year before and having taken over the command of the fort the same November. [ 19 ] Trent was likely the main orchestrator of the idea, considering he had more experience with the disease and had even helped out setting the smallpox hospital. [ 20 ] Half-Native Alexander McKee also played a part in parlaying messages, [ 21 ] but he possibly didn't know about the items. [ 19 ] [ 22 ] This plan was carried out independently from General Amherst and Colonel Bouquet. [ 23 ] [ 24 ] [ 25 ] [ 26 ]
The meeting happened on June 24. The night before "Two Delawares called for Mr. McKee and told him they wanted to speak to him in the Morning." The conference took place just outside of Fort Pitt. The participants were Ecuyer, McKee, Turtle's Heart, and another Delaware, "Mamaltee a Chief." The two Delaware men tried to coax the people holed up in the fort to leave, an option that Ecuyer promptly rejected and stated that reinforcements were coming to Fort Pitt and that the stronghold could easily hold out. After conferring with their chiefs, the two "returned and said they would hold fast of the Chain of friendship", but they were not genuinely believable. The messengers had asked for presents such as food and alcohol, "to carry us Home." Requesting gifts was common, but Ecuyer in this case seemed especially generous. Turtle's Heart and his companion received food in "large quantities", some "600 Rations." Included among this was the linen bundle containing the handkerchief and two blankets. [ 27 ]
To Sundries got to Replace in kind those which were taken from people in the Hospital to Convey the Smallpox to the Indians Vizt: 2 Blankets @ 20/ £2" 0" 0 1 Silk Handkerchef 10/ & 1 linnen do: 3/6 0" 13" 6
A month after meeting on July 22, Trent met with the same delegates again and they seemingly had not contracted smallpox: "Gray Eyes, Wingenum, Turtle's Heart and Mamaultee, came over the River told us their Chiefs were in Council, that they waited for Custaluga who they expected that Day." [ 29 ] [ 18 ]
Gershom Hicks, who was fluent in the Delaware language and also knew some Shawnee, testified that starting from spring 1763 up to April 1764 around a hundred Natives from different tribes such as Lenni Lenape (Delaware) and Shawnee died in the smallpox epidemic, making it a relatively minor smallpox outbreak. [ 12 ] [ 30 ] After visiting Pittsburgh a few years later, David McClure would write in his journal published in 1899, "I was informed at Pittsburgh, that when the Delawares, Shawanese & others, laid siege suddenly and most traitorously to Fort Pitt, in 1764, in a time of peace, the people within, found means of conveying the small pox to them, which was far more destructive than the guns from the walls, or all the artillery of Colonel Boquet's army, which obliged them to abandon the enterprise." [ 31 ]
General Amherst, July 8: P.S. Could it not be contrived to Send the Small Pox among those Disaffected Tribes of Indians? We must, on this occasion, Use Every Stratagem in our power to Reduce them. Colonel Bouquet, July 13: P.S. I will try to inocculate the Indians by means of Blankets that may fall in their hands, taking care however not to get the disease myself. Amherst, July 16: P.S. You will Do well to try to Innoculate the Indians by means of Blanketts, as well as to try Every other method that can serve to Extirpate this Execreble Race. Bouquet, July 19: The signal for Indian Messengers, and all your Directions will be observed.
A month later in July Colonel Bouquet discussed Pontiac's War in detail with General Amherst via letters, [ 32 ] and in postscripts of three letters in more freeform style Amherst also briefly broached the subject of using of smallpox as a weapon. Bouquet brought up blankets as a means without going into specifics, and Amherst supported the idea "to Extirpate this Execreble Race". [ 11 ] [ 33 ]
Bouquet himself probably never had the opportunity to "Send the Small Pox." [ 24 ] He was very concerned about smallpox, having never had it. [ 34 ] When Bouquet wrote to Ecuyer, he didn't mention the disease. [ 23 ] He died only two years later in 1765 of yellow fever . [ 34 ]
This event is usually described as an early attempt at biological warfare. [ 35 ] [ 36 ] [ 37 ] [ 38 ] However the plan's effectiveness is generally questioned. [ 35 ] [ 1 ] [ 2 ] [ 18 ] [ 15 ]
The account of the British infecting Natives with smallpox during Pontiac's War of 1763 originated with nineteenth century historian Francis Parkman . [ 13 ] His account has been relied on by later writers. [ 25 ] [ 16 ] He described Amherst's reply to Bouquet as a “detestable suggestion” and concluded "There is no direct evidence that Bouquet carried into effect the shameful plan of infecting the Indians though, a few months after, the small-pox was known to have made havoc among the tribes of the Ohio." [ 25 ] Parkman had the impression that Amherst had planned the gifting, although Amherst approached the matter only a month later. [ 26 ] [ 25 ] Following Parkman was Howard Peckham who was more interested in the overall war and paid only cursory glance to the incident, briefly describing Ecuyer handing over the handkerchief and blankets from the smallpox hospital. He quoted a testimony of a smallpox outbreak and stated that it certainly affected the Natives' ability to wage war. [ 39 ] Bernhard Knollenberg was more critical and pointed out that both Parkman and Peckham hadn't noticed that the smallpox epidemic among the tribes had been reported to have begun in the spring of 1763, quite some time before the meeting. [ 40 ] [ 12 ] [ 10 ] Knollenberg even doubted the authenticity of the documents at first before he was contacted via letter by historian Donald H. Kent who had found a record of Trent's sundries list signed by Ecuyer. [ 12 ]
Francis Jennings , a historian who extensively studied Parkman's writings, had a more damning view. He indicated that the fighting strength of the Natives was greatly compromised by the plan. [ 41 ] Microbiologist Mark Wheelis says the act of biological aggression at Fort Pitt is indisputable, but that at the time the rare attempts to transmit infection rarely worked and they were probably made redundant with natural routes of transmission. The practice was restrained by lack of knowledge. [ 42 ] Elizabeth A. Fenn writes that "the actual effectiveness of an attempt to spread smallpox remains impossible to ascertain: the possibility always exists that infection occurred by some natural route." [ 35 ] Philip Ranlet describes as a clear sign that the blankets had no effect the fact that the same delegates were met a month later, [ 18 ] and that nearly all of the met natives were recorded to have lived for decades afterwards. [ 43 ] He also questions why Trent didn't gloat about any possible success in his journal if there was such. [ 18 ] David Dixon holds likely that the transmission happened via some other route and possibly from the event described by John McCullough. [ 15 ] Barbara Mann holds that the distribution worked, describing that Gershom Hick's testimony of the epidemic starting by spring is explainable by Hicks lacking a calendar. [ 44 ] Mann also estimates that papers related to the incident have been destroyed. [ 45 ]
Researchers James W. Martin, George W. Christopher and Edward M. Eitzen writing in a publication for the US Army Medical Department Center & School , Borden Institute , found that "In retrospect, it is difficult to evaluate the tactical success of Captain Ecuyer's biological attack because smallpox may have been transmitted after other contacts with colonists, as had previously happened in New England and the South. Although scabs from smallpox patients are thought to be of low infectivity as a result of binding of the virus in fibrin metric, and transmission by fomites has been considered inefficient compared with respiratory droplet transmission." [ 2 ] In an article published in the journal Clinical Microbiology and Infection researchers Vincent Barras and Gilbert Greub conclude that “in the light of contemporary knowledge, it remains doubtful whether his hopes were fulfilled, given the fact that the transmission of smallpox through this kind of vector is much less efficient than respiratory transmission, and that Native Americans had been in contact with smallpox >200 years before Ecuyer’s trickery, notably during Pizarro ’s conquest of South America in the 16th century. As a whole, the analysis of the various ‘pre-microbiological” attempts at BW illustrate the difficulty of differentiating attempted biological attack from naturally occurring epidemics.” [ 1 ] | https://en.wikipedia.org/wiki/Siege_of_Fort_Pitt |
The siege of Laghouat was an episode of the French pacification of Algeria . General Aimable Pélissier commanding an army of 6,000, besieged the city of Laghouat from 21 November until 4 December 1852, when the city capitulated. The brutal treatment of the inhabitants was part of the scorched earth tactic of the French army and one of the first instances of recorded use of chemical weapon on civilians. [ 1 ]
The storming of Laghouat [ 2 ] [ 3 ] [ 4 ] [ 5 ] turned quickly into several days of massacres to punish the population that was treated as combating enemies. The battle also witness the several deaths on the French side including that of general Bouscaren, that added to the fervor of the French soldiers to want to take revenge on the population setting an example for other towns and cities throughout the south of Algeria. About two thirds (2,500 to 3,000 out of a total of 4,500 inhabitants remaining in the besieged city) including women and children were massacred. [ 6 ] [ 7 ] [ 8 ]
The massacre left a deep trauma in the Laghouati population that endures to this day. [ 5 ] [ 4 ] The year when the city was emptied of its population is still known to the inhabitants of Laghouat as "the year of the Khalya ", meaning "emptiness" in Arabic. It is also commonly known as "the year of Hessian sacks ", referring to the way the captured surviving men and boys were put alive in sacks and thrown into trenches. Many reports of the battle were written by army chiefs and soldiers as well as visitors of the city after the massacre reported the morbid atmosphere of the city following the siege.
Surviving women were so afraid for their young sons of being collected by the French forces that they came up with a ruse to hide them. They dressed them as girls and put an earring on one ear. The tradition of protecting young boys from evil with an earring has survived until today. [ citation needed ]
The level of brutality of the massacre of Laghouat was a show of force as well as part of the long scorched earth tactic of the three French generals that took the fortified city. By ordering the massacre of the population, [ citation needed ] the French were eyeing all the remaining Saharian territories beyond Laghouat. During the battle of Laghouat several tribes and other city republics and fortresses delivered help to try to stop the advance of the French, namely Ghardaïa (and therefore the whole of the Mozabite confederation), Metlili , and Ouargla . The nobles of the latter cities, after witnessing or hearing of the atrocities committed in Laghouat, quickly sought a peaceful agreement to surrender their cities or sign treaties to keep their autonomy under the protection of France.
A few months after Laghouat, on 29 April 1853, general Randon , the French governor of Algeria, signed a treaty of protectorate with the nobles of the cities of M'zab, known in France as the capitulation of the Mzab. [ 9 ] | https://en.wikipedia.org/wiki/Siege_of_Laghouat |
In mathematics , specifically in transcendental number theory and Diophantine approximation , Siegel's lemma refers to bounds on the solutions of linear equations obtained by the construction of auxiliary functions . The existence of these polynomials was proven by Axel Thue ; [ 1 ] Thue's proof used what would be translated from German as Dirichlet's Drawers principle, which is widely known as the Pigeonhole principle . Carl Ludwig Siegel published his lemma in 1929. [ 2 ] It is a pure existence theorem for a system of linear equations .
Siegel's lemma has been refined in recent years to produce sharper bounds on the estimates given by the lemma. [ 3 ]
Suppose we are given a system of M linear equations in N unknowns such that N > M , say
where the coefficients are integers, not all 0, and bounded by B . The system then has a solution
with the X s all integers, not all 0, and bounded by
Bombieri & Vaaler (1983) gave the following sharper bound for the X' s:
where D is the greatest common divisor of the M × M minors of the matrix A , and A T is its transpose . Their proof involved replacing the pigeonhole principle by techniques from the geometry of numbers . | https://en.wikipedia.org/wiki/Siegel's_lemma |
Siegel's paradox is the phenomenon that uncertainty about future prices can theoretically push rational consumers to temporarily trade away their preferred consumption goods (or currency) for non-preferred goods (or currency), as part of a plan to trade back to the preferred consumption goods after prices become clearer. For example, in some models, Americans can expect to earn more American dollars on average by investing in Euros, while Europeans can expect to earn more Euros on average by investing in American dollars. The paradox was identified by economist Jeremy Siegel in 1972. [ 1 ]
Like the related two envelopes problem , the phenomenon is sometimes labeled a paradox because an agent can seem to trade for something of equal monetary value and yet, paradoxically, seem at the same time to gain monetary value from the trade. Closer analysis shows that the "monetary value" of the trade is ambiguous but that nevertheless such trades are often favorable, depending on the scenario.
Economist Fischer Black gave the following illustration in 1995. Suppose that the exchange rate between an "apple" country where consumers prefer apples, and an "orange" country where consumers prefer valuable oranges, is currently 1:1, but will change next year to 2:1 or 1:2 with equal probability. Suppose an apple consumer trades an apple to an orange consumer in exchange for an orange. The apple consumer now has given up an apple for an orange, which next year has an expected value of 1.25 apples. The orange consumer now has given up an orange for an apple, which next year has an expected value of 1.25 oranges. Thus both appear to have benefited from the exchange on average. [ 1 ] Mathematically, the apparent surplus is related to Jensen's inequality . [ 2 ] [ 3 ]
A more detailed example is a simplified efficient market with two wines, an American wine and a German wine. In November the wines trade 1:1. In December, most consumers will put exactly twice as much value on the trendier wine than the non-trendy wine; there is a 50/50 chance that either wine will become the trendy one in December. Thus, the wines are equally likely to trade 1:2 or 2:1 in December. Most consumers care about the nationality only insofar as it influences which wine is trendy. The only exceptions are a single loyalist American consumer, who only drinks American wine and is indifferent to trendiness, and a single loyalist German consumer, whose only drinks German wine and is likewise indifferent to trendiness.
The American loyalist counter-intuitively prefers to hold a German rather than an American wine in November, as it has a 50% chance of being tradeable for 0.5 American wines, and a 50% chance of being tradeable for 2 American wines, and thus has an expected value of 1.25 American wines. (All the consumers in this scenario are risk-neutral ). Similarly, the German, if she holds an American wine, can be considered to be in possession of an expected value of 1.25 German wines. In this case, the gains from Seigel's paradox are real, and each loyalist gains utility on average by temporarily trading away from their preferred consumption good, due to the large utility gain should they succeed in the gambit of saving up in hopes of buying multiple bottles of the preferred wine should the price plummet in December.
Analyzing the case of the trendy consumers, who are indifferent to the nationality apart from its trendiness, is more complex. Such a consumer, if in possession of American wine, might fallaciously reason: "I currently have 1 American wine. If I trade for a German wine, I will have an expected value of 1.25 American wines. Therefore, I will be better off on average if I adopt a strategy to temporarily trade away, as the American loyalist did." However, this is similar to the " two envelopes problem ", and the gains from Seigel's paradox in this case are illusory. The trendy consumer who uses the American loyalist's strategy is left with a 50% chance of 0.5 bottles of a newly popular trendy American wine, and a 50% chance of 2 bottles of a newly unpopular non-trendy American wine; to the trendy consumer this is not a material improvement over having a 50% chance of a bottle of trendy American wine and a 50% chance of having a bottle of non-trendy American wine. Thus, the trendy consumer has merely broken even, on average. Similarly, the trendy consumer also would not gain utility from adopting the German loyalist's strategy. [ 4 ]
While the wine and the apples are toy examples, the paradox has a real-world application to what currencies investors should choose to hold. Fischer Black concluded from analyses similar to the apple/orange example that when investing overseas, investors should not seek to hedge all their currency risk. [ 1 ] Other researchers consider such an analysis simplistic. In many circumstances, Seigel's paradox should indeed drive a rational investor to become more willing to embrace modest currency risk. In many other circumstances, they should not; for example, if the exchange rate uncertainty is due to differing rates of inflation with the imposition of purchasing power parity, then something like the "two envelopes" analysis applies, and there may be no particular reason to embrace currency risk. [ 4 ]
A different approach to Seigel's paradox is proposed by K. Mallahi-Karai and P. Safari, [ 5 ] where they show that the only possible way to avoid making risk-less money in such future-based currency exchanges is to settle on the (weighted) geometric mean of the future exchange rates, or more generally a product of the weighted geometric mean and a so-called reciprocity function . The weights of the geometric mean depend on the probability of the rates occurring in the future, while the reciprocity function can always be taken to be the unit function. What this implies, for instance, in the case of apple/orange example above, is that the consumers should trade their products for √(2)(1/2) = 1 units of the other product to avoid an arbitrage . This method will provide currency traders on both sides with a common exchange rate they can safely agree on. | https://en.wikipedia.org/wiki/Siegel's_paradox |
In mathematics , Siegel's theorem on integral points states that a curve of genus greater than zero has only finitely many integral points over any given number field .
The theorem was first proved in 1929 by Carl Ludwig Siegel and was the first major result on Diophantine equations that depended only on the genus and not any special algebraic form of the equations. For g > 1 it was superseded by Faltings's theorem in 1983.
Siegel's theorem on integral points: For a smooth algebraic curve C of genus g defined over a number field K , presented in affine space in a given coordinate system, there are only finitely many points on C with coordinates in the ring of integers O of K , provided g > 0.
In 1926, Siegel proved the theorem effectively in the special case g = 1 {\displaystyle g=1} , so that he proved this theorem conditionally, provided the Mordell's conjecture is true.
In 1929, Siegel proved the theorem unconditionally by combining a version of the Thue–Siegel–Roth theorem , from diophantine approximation , with the Mordell–Weil theorem from diophantine geometry (required in Weil's version, to apply to the Jacobian variety of C ).
In 2002, Umberto Zannier and Pietro Corvaja gave a new proof by using a new method based on the subspace theorem . [ 1 ]
Siegel's result was ineffective for g ≥ 2 {\displaystyle g\geq 2} (see effective results in number theory ), since Thue 's method in diophantine approximation also is ineffective in describing possible very good rational approximations to almost all algebraic numbers of degree d ≥ 5 {\displaystyle d\geq 5} . Siegel proved it effectively only in the special case g = 1 {\displaystyle g=1} in 1926. Effective results in some cases derive from Baker's method . | https://en.wikipedia.org/wiki/Siegel's_theorem_on_integral_points |
In mathematics , Siegel's identity refers to one of two formulae that are used in the resolution of Diophantine equations .
The first formula is
The second is
The identities are used in translating Diophantine problems connected with integral points on hyperelliptic curves into S-unit equations . | https://en.wikipedia.org/wiki/Siegel_identity |
In mathematics , the Siegel–Weil formula , introduced by Weil ( 1964 , 1965 ) as an extension of the results of Siegel ( 1951 , 1952 ), expresses an Eisenstein series as a weighted average of theta series of lattices in a genus , where the weights are proportional to the inverse of the order of the automorphism group of the lattice.
For the constant terms this is essentially the Smith–Minkowski–Siegel mass formula .
This number theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Siegel–Weil_formula |
Siemens A50 is a mobile phone manufactured by Siemens Mobile . [ 1 ] [ 2 ] It was one of the best sold mobile phones from 2002. [ 3 ] The phone was announced in October 2002. [ 4 ]
The phone included a WAP browser and two games: Stack Attack and Balloon Shooter. [ 5 ]
This mobile technology –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Siemens_A50 |
Siemens Mobility GmbH is a division of Siemens . With its global headquarters in Munich , Siemens Mobility has four core business units: Mobility Management, dedicated to rail technology and intelligent traffic systems, Railway Electrification, Rolling Stock, and Customer Services. [ 3 ]
Innovations from the late 19th century, such as the world's first electric train, when Siemens & Halske unveiled a train in which power was supplied through the rails, and the world's first electric tram, with the implementation of 2.5-kilometer-long electric tramway located in Berlin, built at the company's own expense, cemented the use of electric power in transportation systems.
In the following years, inventions such as the first electric trolleybus , mine locomotives, and the first underground railway in continental Europe (in Budapest ), set the path from trams and subways to today's high-speed trains . [ 5 ]
Siemens , alongside ThyssenKrupp and Transrapid International , was part of the German consortium that built the Shanghai Maglev , inaugurated in 2002 by the German chancellor, Gerhard Schröder , and the Chinese premier, Zhu Rongji . [ 6 ] It was the world's first commercial high-speed magnetic levitation train, which holds the title of the fastest commercial service, travelling up to 430 km/h. [ 7 ]
In November 2012, Siemens acquired Invensys Rail for £1.7 billion. [ 8 ]
In July 2017, Siemens confirmed it had taken over Hannover -based software company HaCon , to be managed as a separate legal entity. The financial details were not disclosed. [ 9 ]
In September 2017, Siemens announced a proposal to merge its transportation division with Alstom , with the objective of creating "a new European champion in the rail industry". [ 10 ] The combined rail business, to be named Siemens Alstom and headquartered in Paris, would have had $18 billion U.S. in revenue and employed 62,300 people in more than 60 countries. [ 11 ] It was seen as a measure to counter the rise of China's CRRC with support from both the French and German governments. [ 12 ] However, in February 2019, the European Commission refused permission for the merger to proceed. [ 13 ]
During Innotrans in September 2018, Siemens Mobility unveiled the world's first driverless tram in Berlin , the result of a joint research and development project with ViP Verkehrsbetriebe Potsdam , on a six-kilometre section of the tram network in Potsdam, Germany .
Customer Services
Rolling Stock
Rail Technology
Customer Services
Locomotives
EMU and DMU
Passenger coaches
Light Rail/Trams
People Mover
Metro/Subway
Maglev
Railway Signalling
Digital Services
Notes
Some R160 cars were installed with Siemens propulsions. This was done after the New York City Subway tested a propulsion variant on its R143 cars.
Competitors: | https://en.wikipedia.org/wiki/Siemens_Mobility |
Sierpiński's constant is a mathematical constant usually denoted as K . One way of defining it is as the following limit:
where r 2 ( k ) is a number of representations of k as a sum of the form a 2 + b 2 for integer a and b .
It can be given in closed form as:
where ϖ {\displaystyle \varpi } is the lemniscate constant and γ {\displaystyle \gamma } is the Euler-Mascheroni constant .
Another way to define/understand Sierpiński's constant is,
Let r(n) [ 1 ] denote the number of representations of n {\displaystyle n} by k {\displaystyle k} squares, then the Summatory Function [ 2 ] of r 2 ( k ) / k {\displaystyle r_{2}(k)/k} has the Asymptotic [ 3 ] expansion
∑ k = 1 n r 2 ( k ) k = K + π ln n + o ( 1 n ) {\displaystyle \sum _{k=1}^{n}{r_{2}(k) \over k}=K+\pi \ln n+o\!\left({\frac {1}{\sqrt {n}}}\right)} ,
where K = 2.5849817596 {\displaystyle K=2.5849817596} is the Sierpinski constant. The above plot shows
( ∑ k = 1 n r 2 ( k ) k ) − π ln n {\displaystyle \left(\sum _{k=1}^{n}{r_{2}(k) \over k}\right)-\pi \ln n} ,
with the value of K {\displaystyle K} indicated as the solid horizontal line.
This article about a number is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Sierpiński's_constant |
In mathematics , Sierpiński's theorem is an isomorphism theorem concerning certain metric spaces , named after Wacław Sierpiński who proved it in 1920. [ 1 ]
It states that any countable metric space without isolated points is homeomorphic to Q {\displaystyle \mathbb {Q} } (with its standard topology). [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ]
As a consequence of the theorem, the metric space Q 2 {\displaystyle \mathbb {Q} ^{2}} (with its usual Euclidean distance ) is homeomorphic to Q {\displaystyle \mathbb {Q} } , which may seem counterintuitive. This is in contrast to, e.g., R 2 {\displaystyle \mathbb {R} ^{2}} , which is not homeomorphic to R {\displaystyle \mathbb {R} } . As another example, Q ∩ [ 0 , 1 ] {\displaystyle \mathbb {Q} \cap [0,1]} is also homeomorphic to Q {\displaystyle \mathbb {Q} } , again in contrast to the closed real interval [ 0 , 1 ] {\displaystyle [0,1]} , which is not homeomorphic to R {\displaystyle \mathbb {R} } (whereas the open interval ( 0 , 1 ) {\displaystyle (0,1)} is). | https://en.wikipedia.org/wiki/Sierpiński's_theorem_on_metric_spaces |
Sierra Wireless (a subsidiary of Semtech Corporation) is a Canadian multinational wireless communications equipment designer, manufacturer and services provider headquartered in Richmond, British Columbia , Canada. It also maintains offices and operations in the United States, Korea, Japan, Taiwan, India, France, Australia and New Zealand. [ 2 ]
The company sells mobile computing and machine-to-machine (M2M) communications products that work over cellular networks, 2G , 3G , 4G and 5G mobile broadband wireless routers and gateways, modules, as well as software, tools, and services.
Sierra Wireless products and technologies are used in a variety of markets and industries, including automotive and transportation , energy , field service , healthcare , industrial and infrastructure , mobile computing and consumers, networking , sales and payment, and security . It also maintains a network of experts in mobile broadband and M2M integration to support customers worldwide.
The company's products are sold directly to original equipment manufacturers (OEMs), as well as indirectly through distributors and resellers. [ 3 ]
Sierra Wireless was founded in 1993 in Vancouver, Canada. In August 2003, it completed an acquisition of privately held, high-speed CDMA wireless modules supplier, AirPrime, [ 4 ] issuing approximately 3.7 million shares to AirPrime shareholders. [ 5 ] On March 6, 2007, the company announced its purchase of Hayward, California -based AirLink Communications, a privately held developer of high-value fixed, portable, and mobile wireless data solutions. [ buzzword ] [ 6 ] Prior to the May 2007 completion of its sale to Sierra Wireless for a total of $27 million in cash and stock, AirLink had reported $24.8 million in revenues and gross margin of 44 percent. [ 7 ]
In August 2008, Sierra Wireless purchased the assets of Junxion, a Seattle based producer of Linux -based mobile wireless access points and network routers for enterprise and government customers. [ 8 ] In December 2008, Sierra Wireless made a friendly all-cash bid to acquire Wavecom , a French M2M wireless technology developer. The sale was completed for $275 million. [ 9 ]
In August 2012, the company acquired SAGEMCOM's M2M business in a cash transaction of EUR44.9 million plus assumed liabilities. [ 10 ] In November 2012, Sierra Wireless was recognized as an M2M market leader by market research and intelligence firm, ABI Research. Based on the company's aggregated revenues, ABI found that Sierra Wireless held a 34 percent share of the M2M module market. [ 11 ]
In January 2013, Sierra Wireless sold all assets and operations related to its AirCard business to NETGEAR, Inc. for $138 million in cash plus approximately $6.5 million in assumed liabilities. [ 12 ]
In April 2017, Sierra Wireless acquired GlobalTop Technology's GNSS embedded modules business for $3.2 million. [ 13 ] In December, 2017, Sierra Wireless acquired Numerex , in a deal estimated at US$107 million. [ 14 ] [ 15 ] [ 16 ] [ 17 ]
In 2020, Sierra Wireless completed the acquisition of M2M Group in Australia for US$18.4 million and M2M One in New Zealand for US$3.5 million. [ 18 ] In the same year, the company sold its automotive business for US$144 million. [ 19 ] In April 2020, Sierra Wireless appointed Samuel Cochrane as Chief Financial Officer. [ 20 ] In November 2020, Sierra Wireless sold its automotive modules division to Rolling Wireless. [ 21 ]
In July 2021, Sierra Wireless appointed Phil Brace as CEO. [ 22 ]
In August 2022, Semtech agreed to buy Sierra Wireless in an all-cash transaction valued at US$1.2 billion including debt. [ 23 ] The acquisition was completed in January 2023. [ 24 ]
Sierra Wireless has been granted more than 550 unique patents for an array of technologies ranging from built-in antennas and product form factors, to battery power usage and management and network efficiency improvements. The company currently has patents pending in the US , Europe , Asia , Australia , Mexico , and South Africa . [ 25 ]
Sierra Wireless offers IoT products and services including the following: [ 26 ]
Until the 2013 sale of all assets and operations, [ 12 ] Sierra Wireless also manufactured and marketed AirCard, mobile broadband devices permitting users to connect notebooks , netbooks , and other electronics to the Internet over 3G and 4G mobile broadband networks via PC or express card slots, USB ports, or mobile WiFi hotspots .
Sierra Wireless is an active United Way of the Lower Mainland supporter. For its efforts, the company was recognized with United Way Employee Gold Awards and a 2002 Award of Excellence. [ 27 ]
In 2003, Canadian public university Simon Fraser University announced the creation of the Sierra Wireless Chair in Wireless Communication, [ 28 ] which was funded through annual donations for a three-year period. Upon completion of the original three-year term, the company extended its partnership with the university by establishing an endowed Sierra Wireless Professorship in Mobile Communication. [ 29 ] In partnership with the university's School of Engineering Science in the Faculty of Applied Sciences, the Sierra Wireless Mobile Communications Laboratory was opened in November 2012. [ 30 ] | https://en.wikipedia.org/wiki/Sierra_Wireless |
A sieve analysis (or gradation test ) is a practice or procedure used in geology, civil engineering , [ 1 ] and chemical engineering [ 2 ] to assess the particle size distribution (also called gradation ) of a granular material by allowing the material to pass through a series of sieves of progressively smaller mesh size and weighing the amount of material that is stopped by each sieve as a fraction of the whole mass.
The size distribution is often of critical importance to the way the material performs in use. A sieve analysis can be performed on any type of non-organic or organic granular materials including sand , crushed rock , clay , granite , feldspar , coal , soil , a wide range of manufactured powder, grain and seeds , down to a minimum size depending on the exact method. Being such a simple technique of particle sizing , it is probably the most common. [ 3 ]
A gradation test is performed on a sample of aggregate in a laboratory. A typical sieve analysis uses a column of sieves with wire mesh screens of graded mesh size .
A representative weighed sample is poured into the top sieve which has the largest screen openings. Each lower sieve in the column has smaller openings than the one above. At the base is a pan, called the receiver.
The column is typically placed in a mechanical shaker, which shakes the column, usually for a set period, to facilitate exposing all of the material to the screen openings so that particles small enough to fit through the holes can fall through to the next layer. After the shaking is complete the material on each sieve is weighed. The mass of the sample of each sieve is then divided by the total mass to give a percentage retained on each sieve.
The size of the average particle on each sieve is then analysed to get a cut-off point or specific size range, which is then captured on a screen.
The results of this test are used to describe the properties of the aggregate and to see if it is appropriate for various civil engineering purposes such as selecting the appropriate aggregate for concrete mixes and asphalt mixes as well as sizing of water production well screens.
The results of this test are provided in graphical form to identify the type of gradation of the aggregate. The complete procedure for this test is outlined in the American Society for Testing and Materials ( ASTM ) C 136 [ 4 ] and the American Association of State Highway and Transportation Officials ( AASHTO ) T 27 [ 5 ]
A suitable sieve size for the aggregate underneath the nest of sieves to collect the aggregate that passes through the smallest. The entire nest is then agitated, and the material whose diameter is smaller than the mesh opening pass through the sieves. After the aggregate reaches the pan, the amount of material retained in each sieve is then weighed. [ 6 ]
In order to perform the test, a sufficient sample of the aggregate must be obtained from the source. To prepare the sample, the aggregate should be mixed thoroughly and be reduced to a suitable size for testing. The total mass of the sample is also required. [ 6 ]
The results are presented in a graph of percent passing versus the sieve size. On the graph the sieve size scale is logarithmic. To find the percent of aggregate passing through each sieve, first find the percent retained in each sieve. To do so, the following equation is used,
%Retained = W S i e v e W T o t a l {\displaystyle {\frac {W_{Sieve}}{W_{Total}}}} ×100%
where W Sieve is the mass of aggregate in the sieve and W Total is the total mass of the aggregate. The next step is to find the cumulative percent of aggregate retained in each sieve. To do so, add up the total amount of aggregate that is retained in each sieve and the amount in the previous sieves. The cumulative percent passing of the aggregate is found by subtracting the percent retained from 100%.
%Cumulative Passing = 100% - %Cumulative Retained.
The values are then plotted on a graph with cumulative percent passing on the y axis and logarithmic sieve size on the x axis. [ 6 ]
There are two versions of the %Passing equations. the .45 power formula is presented on .45 power gradation chart, whereas the more simple %Passing is presented on a semi-log gradation chart. version of the percent passing graph is shown on .45 power chart and by using the .45 passing formula.
% Passing = P i = S i e v e L a r g e s t A g g r e g a t e m a x − s i z e {\displaystyle {\frac {Sieve_{Largest}}{Aggregate_{max-size}}}} x100%
Where:
Sieve Largest - Largest diameter sieve used in (mm). Aggregate max_size - Largest piece of aggregate in the sample in (mm).
%Passing = W B e l o w W T o t a l {\displaystyle {\frac {W_{Below}}{W_{Total}}}} x100%
Where:
W Below - The total mass of the aggregate within the sieves below the current sieve, not including the current sieve's aggregate.
W Total - The total mass of all of the aggregate in the sample.
There are different methods for carrying out sieve analyses, depending on the material to be measured.
Here a throwing motion acts on the sample. The vertical throwing motion is overlaid with a slight circular motion which results in distribution of the sample amount over the whole sieving surface. The particles are accelerated in the vertical direction (are thrown upwards). In the air they carry out free rotations and interact with the openings in the mesh of the sieve when they fall back. If the particles are smaller than the openings, they pass through the sieve. If they are larger, they are thrown. The rotating motion while suspended increases the probability that the particles present a different orientation to the mesh when they fall back again, and thus might eventually pass through the mesh.
Modern sieve shakers work with an electro-magnetic drive which moves a spring-mass system and transfers the resulting oscillation to the sieve stack. Amplitude and sieving time are set digitally and are continuously observed by an integrated control-unit. Therefore, sieving results are reproducible and precise (an important precondition for a significant analysis). Adjustment of parameters like amplitude and sieving time serves to optimize the sieving for different types of material. This method is the most common in the laboratory sector. [ 7 ]
In horizontal sieve shaker the sieve stack moves in horizontal circles in a plane. Horizontal sieve shakers are preferably used for needle-shaped, flat, long or fibrous samples, as their horizontal orientation means that only a few disoriented particles enter the mesh and the sieve is not blocked so quickly. The large sieving area enables the sieving of large amounts of sample, for example as encountered in the particle-size analysis of construction materials and aggregates.
A horizontal circular motion overlies a vertical motion which is created by a tapping impulse. These motional processes are characteristic of hand sieving and produce a higher degree of sieving for denser particles (e.g. abrasives) than throw-action sieve shakers.
Most sieve analyses are carried out dry. But there are some applications which can only be carried out by wet sieving. This is the case when the sample which has to be analysed is e.g. a suspension which must not be dried; or when the sample is a very fine powder which tends to agglomerate (mostly < 45 μm) – in a dry sieving process this tendency would lead to a clogging of the sieve meshes and this would make a further sieving process impossible. A wet sieving process is set up like a dry process: the sieve stack is clamped onto the sieve shaker and the sample is placed on the top sieve. Above the top sieve a water-spray nozzle is placed which supports the sieving process additionally to the sieving motion. The rinsing is carried out until the liquid which is discharged through the receiver is clear. Sample residues on the sieves have to be dried and weighed. When it comes to wet sieving it is very important not to change the sample in its volume (no swelling, dissolving or reaction with the liquid).
Air jet sieving machines are ideally suited for very fine powders which tend to agglomerate and cannot be separated by vibrational sieving.
The reason for the effectiveness of this sieving method is based on two components:
A rotating slotted nozzle inside the sieving chamber and a powerful industrial vacuum cleaner which is connected to the chamber. The vacuum cleaner generates a vacuum inside the sieving chamber and sucks in fresh air through the slotted nozzle. When passing the narrow slit of the nozzle the air stream is accelerated and blown against the sieve mesh, dispersing the particles. Above the mesh, the air jet is distributed over the complete sieve surface and is sucked in with low speed through the sieve mesh. Thus the finer particles are transported through the mesh openings into the vacuum cleaner.
Woven wire mesh sieves are according to technical requirements of ISO 3310-1. [ 9 ] These sieves usually have nominal aperture ranging from 20 micrometers to 3.55 millimeters, with diameters ranging from 100 to 450 millimeters.
Perforated plate sieves conform to ISO 3310-2 and can have round or square nominal apertures ranging from 1 millimeter to 125 millimeters. [ 10 ] The diameters of the sieves range from 200 to 450 millimeters.
American standard sieves also known as ASTM sieves conform to ASTM E11 standard. [ 11 ] The nominal aperture of these sieves range from 20 micrometers to 200 millimeters, however these sieves have only 8 inches (203 mm) and 12 inches (305 mm) diameter sizes.
Sieve analysis has, in general, been used for decades to monitor material quality based on particle size. For coarse material, sizes that range down to #100 mesh (150 μm), a sieve analysis and particle size distribution is accurate and consistent.
However, for material that is finer than 100 mesh, dry sieving can be significantly less accurate. This is because the mechanical energy required to make particles pass through an opening and the surface attraction effects between the particles themselves and between particles and the screen increase as the particle size decreases. Wet sieve analysis can be utilized where the material analyzed is not affected by the liquid - except to disperse it. Suspending the particles in a suitable liquid transports fine material through the sieve much more efficiently than shaking the dry material.
Sieve analysis assumes that all particle will be round (spherical) or nearly so and will pass through the square openings when the particle diameter is less than the size of the square opening in the screen. For elongated and flat particles a sieve analysis will not yield reliable mass-based results, as the particle size reported will assume that the particles are spherical, where in fact an elongated particle might pass through the screen end-on, but would be prevented from doing so if it presented itself side-on.
Gradation affects many properties of an aggregate, including bulk density, physical stability and permeability. With careful selection of the gradation, it is possible to achieve high bulk density, high physical stability, and low permeability. This is important because in pavement design, a workable, stable mix with resistance to water is important. With an open gradation, the bulk density is relatively low, due to the lack of fine particles, the physical stability is moderate, and the permeability is quite high. With a rich gradation, the bulk density will also be low, the physical stability is low, and the permeability is also low. The gradation can be affected to achieve the desired properties for the particular engineering application. [ 8 ]
Gradation is usually specified for each engineering application it is used for. For example, foundations might only call for coarse aggregates, and therefore an open gradation is needed.
Sieve analysis determines the particle size distribution of a given soil sample and hence helps in easy identification of a soil's mechanical properties. These mechanical properties determine whether a given soil can support the proposed engineering structure. It also helps determine what modifications can be applied to the soil and the best way to achieve maximum soil strength. | https://en.wikipedia.org/wiki/Sieve_analysis |
The sievert (symbol: Sv [ note 1 ] ) is a derived unit in the International System of Units (SI) intended to represent the stochastic health risk of ionizing radiation , which is defined as the probability of causing radiation-induced cancer and genetic damage. The sievert is important in dosimetry and radiation protection . It is named after Rolf Maximilian Sievert , a Swedish medical physicist renowned for work on radiation dose measurement and research into the biological effects of radiation.
The sievert unit is used for radiation dose quantities such as equivalent dose and effective dose , which represent the risk of external radiation from sources outside the body, and committed dose , which represents the risk of internal irradiation due to inhaled or ingested radioactive substances. According to the International Commission on Radiological Protection (ICRP), one sievert results in a 5.5% probability of eventually developing fatal cancer based on the disputed linear no-threshold model of ionizing radiation exposure. [ 1 ] [ 2 ]
To calculate the value of stochastic health risk in sieverts, the physical quantity absorbed dose is converted into equivalent dose and effective dose by applying factors for radiation type and biological context, published by the ICRP and the International Commission on Radiation Units and Measurements (ICRU). One sievert equals 100 rem , which is an older, CGS radiation unit.
Conventionally, deterministic health effects due to acute tissue damage that is certain to happen, produced by high dose rates of radiation, are compared to the physical quantity absorbed dose measured by the unit gray (Gy). [ 3 ]
The SI definition given by the International Committee for Weights and Measures (CIPM) says:
"The quantity dose equivalent H is the product of the absorbed dose D of ionizing radiation and the dimensionless factor Q (quality factor) defined as a function of linear energy transfer by the ICRU "
The value of Q is not defined further by CIPM, but it requires the use of the relevant ICRU recommendations to provide this value.
The CIPM also says that "in order to avoid any risk of confusion between the absorbed dose D and the dose equivalent H , the special names for the respective units should be used, that is, the name gray should be used instead of joules per kilogram for the unit of absorbed dose D and the name sievert instead of joules per kilogram for the unit of dose equivalent H ". [ 4 ]
In summary:
The ICRP definition of the sievert is: [ 5 ]
The sievert is used for a number of dose quantities which are described in this article and are part of the international radiological protection system devised and defined by the ICRP and ICRU.
When the sievert is used to represent the stochastic effects of external ionizing radiation on human tissue, the radiation doses received are measured in practice by radiometric instruments and dosimeters and are called operational quantities. To relate these actual received doses to likely health effects, protection quantities have been developed to predict the likely health effects using the results of large epidemiological studies. Consequently, this has required the creation of a number of different dose quantities within a coherent system developed by the ICRU working with the ICRP.
The external dose quantities and their relationships are shown in the accompanying diagram. The ICRU is primarily responsible for the operational dose quantities, based upon the application of ionising radiation metrology, and the ICRP is primarily responsible for the protection quantities, based upon modelling of dose uptake and biological sensitivity of the human body.
The ICRU/ICRP dose quantities have specific purposes and meanings, but some use common words in a different order. There can be confusion between, for instance, equivalent dose and dose equivalent .
Although the CIPM definition states that the linear energy transfer function (Q) of the ICRU is used in calculating the biological effect, the ICRP in 1990 [ 6 ] developed the "protection" dose quantities effective and equivalent dose which are calculated from more complex computational models and are distinguished by not having the phrase dose equivalent in their name. Only the operational dose quantities which still use Q for calculation retain the phrase dose equivalent . However, there are joint ICRU/ICRP proposals to simplify this system by changes to the operational dose definitions to harmonise with those of protection quantities. These were outlined at the 3rd International Symposium on Radiological Protection in October 2015, and if implemented would make the naming of operational quantities more logical by introducing "dose to lens of eye" and "dose to local skin" as equivalent doses . [ 7 ]
In the USA there are differently named dose quantities which are not part of the ICRP nomenclature. [ 8 ]
These are directly measurable physical quantities in which no allowance has been made for biological effects. Radiation fluence is the number of radiation particles impinging per unit area per unit time, kerma is the ionising effect on air of gamma rays and X-rays and is used for instrument calibration, and absorbed dose is the amount of radiation energy deposited per unit mass in the matter or tissue under consideration.
Operational quantities are measured in practice, and are the means of directly measuring dose uptake due to exposure, or predicting dose uptake in a measured environment. In this way they are used for practical dose control, by providing an estimate or upper limit for the value of the protection quantities related to an exposure. They are also used in practical regulations and guidance. [ 9 ]
The calibration of individual and area dosimeters in photon fields is performed by measuring the collision "air kerma free in air" under conditions of secondary electron equilibrium. Then the appropriate operational quantity is derived applying a conversion coefficient that relates the air kerma to the appropriate operational quantity. The conversion coefficients for photon radiation are published by the ICRU. [ 10 ]
Simple (non-anthropomorphic) "phantoms" are used to relate operational quantities to measured free-air irradiation. The ICRU sphere phantom is based on the definition of an ICRU 4-element tissue-equivalent material which does not really exist and cannot be fabricated. [ 11 ] The ICRU sphere is a theoretical 30 cm diameter "tissue equivalent" sphere consisting of a material with a density of 1 g·cm −3 and a mass composition of 76.2% oxygen, 11.1% carbon, 10.1% hydrogen and 2.6% nitrogen. This material is specified to most closely approximate human tissue in its absorption properties. According to the ICRP, the ICRU "sphere phantom" in most cases adequately approximates the human body as regards the scattering and attenuation of penetrating radiation fields under consideration. [ 12 ] Thus radiation of a particular energy fluence will have roughly the same energy deposition within the sphere as it would in the equivalent mass of human tissue. [ 13 ]
To allow for back-scattering and absorption of the human body, the "slab phantom" is used to represent the human torso for practical calibration of whole body dosimeters. The slab phantom is 300 mm × 300 mm × 150 mm depth to represent the human torso. [ 13 ]
The joint ICRU/ICRP proposals outlined at the 3rd International Symposium on Radiological Protection in October 2015 to change the definition of operational quantities would not change the present use of calibration phantoms or reference radiation fields. [ 7 ]
Protection quantities are calculated models, and are used as "limiting quantities" to specify exposure limits to ensure, in the words of ICRP, "that the occurrence of stochastic health effects is kept below unacceptable levels and that tissue reactions are avoided". [ 14 ] [ 15 ] [ 13 ] These quantities cannot be measured in practice but their values are derived using models of external dose to internal organs of the human body, using anthropomorphic phantoms . These are 3D computational models of the body which take into account a number of complex effects such as body self-shielding and internal scattering of radiation. The calculation starts with organ absorbed dose, and then applies radiation and tissue weighting factors. [ 16 ]
As protection quantities cannot practically be measured, operational quantities must be used to relate them to practical radiation instrument and dosimeter responses. [ 17 ]
This is an actual reading obtained from such as an ambient dose gamma monitor, or a personal dosimeter . Such instruments are calibrated using radiation metrology techniques which will trace them to a national radiation standard, and thereby relate them to an operational quantity. The readings of instruments and dosimeters are used to prevent the uptake of excessive dose and to provide records of dose uptake to satisfy radiation safety legislation; such as in the UK , the Ionising Radiations Regulations 1999 .
The sievert is used in external radiation protection for equivalent dose (the external-source, whole-body exposure effects, in a uniform field), and effective dose (which depends on the body parts irradiated).
These dose quantities are weighted averages of absorbed dose designed to be representative of the stochastic health effects of radiation, and use of the sievert implies that appropriate weighting factors have been applied to the absorbed dose measurement or calculation (expressed in grays). [ 1 ]
The ICRP calculation provides two weighting factors to enable the calculation of protection quantities.
When a whole body is irradiated uniformly only the radiation weighting factor W R is used, and the effective dose equals the whole body equivalent dose. But if the irradiation of a body is partial or non-uniform the tissue factor W T is used to calculate dose to each organ or tissue. These are then summed to obtain the effective dose. In the case of uniform irradiation of the human body, these summate to 1, but in the case of partial or non-uniform irradiation, they will summate to a lower value depending on the organs concerned; reflecting the lower overall health effect. The calculation process is shown on the accompanying diagram. This approach calculates the biological risk contribution to the whole body, taking into account complete or partial irradiation, and the radiation type or types.
The values of these weighting factors are conservatively chosen to be greater than the bulk of experimental values observed for the most sensitive cell types, based on averages of those obtained for the human population.
Since different radiation types have different biological effects for the same deposited energy, a corrective radiation weighting factor W R , which is dependent on the radiation type and on the target tissue, is applied to convert the absorbed dose measured in the unit gray to determine the equivalent dose. The result is given the unit sievert.
The equivalent dose is calculated by multiplying the absorbed energy, averaged by mass over an organ or tissue of interest, by a radiation weighting factor appropriate to the type and energy of radiation. To obtain the equivalent dose for a mix of radiation types and energies, a sum is taken over all types of radiation energy dose. [ 1 ]
H T = ∑ R W R ⋅ D T , R , {\displaystyle H_{T}=\sum _{R}W_{R}\cdot D_{T,R},} where
Thus for example, an absorbed dose of 1 Gy by alpha particles will lead to an equivalent dose of 20 Sv.
This may seem to be a paradox. It implies that the energy of the incident radiation field in joules has increased by a factor of 20, thereby violating the laws of conservation of energy . However, this is not the case. The sievert is used only to convey the fact that a gray of absorbed alpha particles would cause twenty times the biological effect of a gray of absorbed x-rays. It is this biological component that is being expressed when using sieverts rather than the actual energy delivered by the incident absorbed radiation.
The second weighting factor is the tissue factor W T , but it is used only if there has been non-uniform irradiation of a body. If the body has been subject to uniform irradiation, the effective dose equals the whole body equivalent dose, and only the radiation weighting factor W R is used. But if there is partial or non-uniform body irradiation the calculation must take account of the individual organ doses received, because the sensitivity of each organ to irradiation depends on their tissue type. This summed dose from only those organs concerned gives the effective dose for the whole body. The tissue weighting factor is used to calculate those individual organ dose contributions.
The ICRP values for W T are given in the table shown here.
The article on effective dose gives the method of calculation. The absorbed dose is first corrected for the radiation type to give the equivalent dose, and then corrected for the tissue receiving the radiation. Some tissues like bone marrow are particularly sensitive to radiation, so they are given a weighting factor that is disproportionally large relative to the fraction of body mass they represent. Other tissues like the hard bone surface are particularly insensitive to radiation and are assigned a disproportionally low weighting factor.
In summary, the sum of tissue-weighted doses to each irradiated organ or tissue of the body adds up to the effective dose for the body. The use of effective dose enables comparisons of overall dose received regardless of the extent of body irradiation.
The operational quantities are used in practical applications for monitoring and investigating external exposure situations. They are defined for practical operational measurements and assessment of doses in the body. [ 5 ] Three external operational dose quantities were devised to relate operational dosimeter and instrument measurements to the calculated protection quantities. Also devised were two phantoms, The ICRU "slab" and "sphere" phantoms which relate these quantities to incident radiation quantities using the Q(L) calculation.
This is used for area monitoring of penetrating radiation and is usually expressed as the quantity H *(10). This means the radiation is equivalent to that found 10 mm within the ICRU sphere phantom in the direction of origin of the field. [ 20 ] An example of penetrating radiation is gamma rays .
This is used for monitoring of low penetrating radiation and is usually expressed as the quantity H' (0.07). This means the radiation is equivalent to that found at a depth of 0.07 mm in the ICRU sphere phantom. [ 21 ] Examples of low penetrating radiation are alpha particles, beta particles and low-energy photons. This dose quantity is used for the determination of equivalent dose to such as the skin, lens of the eye. [ 22 ] In radiological protection practice value of omega is usually not specified as the dose is usually at a maximum at the point of interest.
This is used for individual dose monitoring, such as with a personal dosimeter worn on the body. The recommended depth for assessment is 10 mm which gives the quantity H p (10). [ 23 ]
In order to simplify the means of calculating operational quantities and assist in the comprehension of radiation dose protection quantities, ICRP Committee 2 & ICRU Report Committee 26 started in 2010 an examination of different means of achieving this by dose coefficients related to Effective Dose or Absorbed Dose.
Specifically;
1. For area monitoring of effective dose of whole body it would be:
The driver for this is that H ∗ (10) is not a reasonable estimate of effective dose due to high energy photons, as a result of the extension of particle types and energy ranges to be considered in ICRP report 116. This change would remove the need for the ICRU sphere and introduce a new quantity called E max .
2. For individual monitoring, to measure deterministic effects on eye lens and skin, it would be:
The driver for this is the need to measure the deterministic effect, which it is suggested, is more appropriate than stochastic effect. This would calculate equivalent dose quantities H lens and H skin .
This would remove the need for the ICRU Sphere and the Q-L function. Any changes would replace ICRU report 51, and part of report 57. [ 7 ]
A final draft report was issued in July 2017 by ICRU/ICRP for consultation. [ 24 ]
The sievert is used for human internal dose quantities in calculating committed dose . This is dose from radionuclides which have been ingested or inhaled into the human body, and thereby "committed" to irradiate the body for a period of time. The concepts of calculating protection quantities as described for external radiation applies, but as the source of radiation is within the tissue of the body, the calculation of absorbed organ dose uses different coefficients and irradiation mechanisms.
The ICRP defines Committed effective dose, E ( t ) {\displaystyle E(t)} as the sum of the products of the committed organ or tissue equivalent doses and the appropriate tissue weighting factors W t {\displaystyle W_{t}} , where t {\displaystyle t} is the integration time in years following the intake. The commitment period is taken to be 50 years for adults, and to age 70 years for children. [ 5 ]
The ICRP further states "For internal exposure, committed effective doses are generally determined from an assessment of the intakes of radionuclides from bioassay measurements or other quantities (e.g., activity retained in the body or in daily excreta). The radiation dose is determined from the intake using recommended dose coefficients". [ 25 ]
A committed dose from an internal source is intended to carry the same effective risk as the same amount of equivalent dose applied uniformly to the whole body from an external source, or the same amount of effective dose applied to part of the body.
Ionizing radiation has deterministic and stochastic effects on human health. Deterministic (acute tissue effect) events happen with certainty, with the resulting health conditions occurring in every individual who received the same high dose. Stochastic (cancer induction and genetic) events are inherently random , with most individuals in a group failing to ever exhibit any causal negative health effects after exposure, while an indeterministic random minority do, often with the resulting subtle negative health effects being observable only after large detailed epidemiology studies.
The use of the sievert implies that only stochastic effects are being considered, and to avoid confusion deterministic effects are conventionally compared to values of absorbed dose expressed by the SI unit gray (Gy).
Stochastic effects are those that occur randomly, such as radiation-induced cancer . The consensus of nuclear regulators, governments and the UNSCEAR is that the incidence of cancers due to ionizing radiation can be modeled as increasing linearly with effective dose at a rate of 5.5% per sievert. [ 1 ] This is known as the linear no-threshold model (LNT model). Some argue that this LNT model is now outdated and should be replaced with a threshold below which the body's natural cell processes repair damage and/or replace damaged cells. [ 26 ] [ 27 ] There is general agreement that the risk is much higher for infants and fetuses than adults, higher for the middle-aged than for seniors, and higher for women than for men, though there is no quantitative consensus about this. [ 28 ] [ 29 ]
The deterministic (acute tissue damage) effects that can lead to acute radiation syndrome only occur in the case of acute high doses (≳ 0.1 Gy) and high dose rates (≳ 0.1 Gy/h) and are conventionally not measured using the unit sievert, but use the unit gray (Gy).
A model of deterministic risk would require different weighting factors (not yet established) than are used in the calculation of equivalent and effective dose.
The ICRP recommends a number of limits for dose uptake in table 8 of report 103. These limits are "situational", for planned, emergency and existing situations. Within these situations, limits are given for the following groups: [ 30 ]
For occupational exposure, the limit is 50 mSv in a single year with a maximum of 100 mSv in a consecutive five-year period, and for the public to an average of 1 mSv (0.001 Sv) of effective dose per year, not including medical and occupational exposures. [ 1 ]
For comparison, natural radiation levels inside the United States Capitol are such that a human body would receive an additional dose rate of 0.85 mSv/a, close to the regulatory limit, because of the uranium content of the granite structure. [ 31 ] According to the conservative ICRP model, someone who spent 20 years inside the capitol building would have an extra one in a thousand chance of getting cancer, over and above any other existing risk (calculated as: 20 a·0.85 mSv/a·0.001 Sv/mSv·5.5%/Sv ≈ 0.1%). However, that "existing risk" is much higher; an average American would have a 10% chance of getting cancer during this same 20-year period, even without any exposure to artificial radiation (see natural Epidemiology of cancer and cancer rates ).
Significant radiation doses are not frequently encountered in everyday life. The following examples can help illustrate relative magnitudes; these are meant to be examples only, not a comprehensive list of possible radiation doses. An "acute dose" is one that occurs over a short and finite period of time, while a "chronic dose" is a dose that continues for an extended period of time so that it is better described by a dose rate.
All conversions between hours and years have assumed continuous presence in a steady field, disregarding known fluctuations, intermittent exposure and radioactive decay . Converted values are shown in parentheses. "/a" is "per annum", which means per year. "/h" means "per hour".
Notes on examples:
The sievert has its origin in the röntgen equivalent man (rem) which was derived from CGS units . The International Commission on Radiation Units and Measurements (ICRU) promoted a switch to coherent SI units in the 1970s, [ 78 ] and announced in 1976 that it planned to formulate a suitable unit for equivalent dose. [ 79 ] The ICRP pre-empted the ICRU by introducing the sievert in 1977. [ 80 ]
The sievert was adopted by the International Committee for Weights and Measures (CIPM) in 1980, five years after adopting the gray. The CIPM then issued an explanation in 1984, recommending when the sievert should be used as opposed to the gray. That explanation was updated in 2002 to bring it closer to the ICRP's definition of equivalent dose, which had changed in 1990. Specifically, the ICRP had introduced equivalent dose, renamed the quality factor (Q) to radiation weighting factor (W R ), and dropped another weighting factor "N" in 1990. In 2002, the CIPM similarly dropped the weighting factor "N" from their explanation but otherwise kept other old terminology and symbols. This explanation only appears in the appendix to the SI brochure and is not part of the definition of the sievert. [ 81 ]
The sievert is named after Rolf Maximilian Sievert . As with every SI unit named after a person, its symbol starts with an upper case letter (Sv), but when written in full, it follows the rules for capitalisation of a common noun ; i.e., sievert becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.
Frequently used SI prefixes are the millisievert (1 mSv = 0.001 Sv) and microsievert (1 μSv = 0.000 001 Sv) and commonly used units for time derivative or "dose rate" indications on instruments and warnings for radiological protection are μSv/h and mSv/h. Regulatory limits and chronic doses are often given in units of mSv/a or Sv/a, where they are understood to represent an average over the entire year. In many occupational scenarios, the hourly dose rate might fluctuate to levels thousands of times higher for a brief period of time, without infringing on the annual limits. The conversion from hours to years varies because of leap years and exposure schedules, but approximate conversions are:
Conversion from hourly rates to annual rates is further complicated by seasonal fluctuations in natural radiation, decay of artificial sources, and intermittent proximity between humans and sources. The ICRP once adopted fixed conversion for occupational exposure, although these have not appeared in recent documents: [ 82 ]
Therefore, for occupation exposures of that time period,
The following table shows radiation quantities in SI and non-SI units:
Although the United States Nuclear Regulatory Commission permits the use of the units curie , rad , and rem alongside SI units, [ 83 ] the European Union European units of measurement directives required that their use for "public health ... purposes" be phased out by 31 December 1985. [ 84 ]
An older unit for the dose equivalent is the rem , [ 85 ] still often used in the United States. One sievert is equal to 100 rem: | https://en.wikipedia.org/wiki/Sievert |
Sieverts's law , in physical metallurgy and in chemistry , is a rule to predict the solubility of gases in metals . It is named after German chemist Adolf Sieverts (1874–1947). [ 1 ] The law states that the solubility of a diatomic gas in metal is proportional to the square root of the partial pressure of the gas in thermodynamic equilibrium . [ 2 ] Hydrogen , oxygen and nitrogen are examples of dissolved diatomic gases of frequent interest in metallurgy.
Sieverts's law can be readily rationalized by considering the reaction of dissolution of the gas in the metal, which involves dissociation of the molecule of the gas. For example, for nitrogen:
For the above reaction, the equilibrium constant is
where:
Therefore, | https://en.wikipedia.org/wiki/Sieverts's_law |
In mass transfer , the sieving coefficient is a measure of equilibration between the concentrations of two mass transfer streams. It is defined as the mean pre- and post-contact concentration of the mass receiving stream divided by the pre- and post-contact concentration of the mass donating stream.
S = C r C d {\displaystyle S={\frac {C_{r}}{C_{d}}}}
where
A sieving coefficient of unity implies that the concentrations of the receiving and donating stream equilibrate, i.e. the out- flow concentrations (post-mass transfer) of the mass donating and receiving stream are equal to one another. Systems with sieving coefficient that are greater than one require an external energy source, as they would otherwise violate the laws of thermodynamics .
Sieving coefficients less than one represent a mass transfer process where the concentrations have not equilibrated.
Contact time between mass streams is important in consider in mass transfer and affects the sieving coefficient.
In renal physiology , the glomerular sieving coefficient (GSC) can be expressed as:
sieving coefficient = clearance / ultrafiltration rate [ 1 ] | https://en.wikipedia.org/wiki/Sieving_coefficient |
SigMF is a standard file format for storing and organizing digitized radio frequency (RF) signals and corresponding metadata, supporting time series real or complex-valued signals. [ 1 ] [ 2 ] A single SigMF "Recording" consists of two files: 1) a binary file containing only the time series digitized samples, and 2) a metadata file describing the contents and capture details of those samples. [ 2 ] The metadata is encapsulated in a JSON file with a .sigmf-meta extension, situated alongside the binary data stored in a file with a .sigmf-data extension. [ 3 ] SigMF "Extensions" enable the addition of hierarchical data to a complete dataset, a capture, or a specific region of the recording. Common applications of SigMF recordings include capturing wireless communications signals, radar , GNSS and electronic warfare .
Before the standardization of SigMF, time series data representing radio signals were commonly stored in flat binary files with external descriptors. Occasionally, researchers used Hierarchical Data Format (HDF5) containers ( .hdf5 ), but these containers lack specificity to any data type. The VITA Radio Transport Standard a.k.a. VITA 49 ( .vrt ) was at times employed for RF data storage, although it is primarily designed as a transport format for RF signals rather than for data storage purposes. [ 4 ] Other proprietary formats were created by industry either to hold specific metadata or encode signals into proprietary containers.
In 2016 at the annual GNU Radio conference, a workshop focused on how a better open source container for RF signals could be constructed and maintained. In the following year the initial release of SigMF was created to provide a portable & annotated container for radio signals. In June 2021 the SigMF specifications and open source software was moved from GNU Radio's GitHub repository to a new SigMF-specific GitHub organization and repository; the project is no longer an effort specific to GNU Radio. [ citation needed ] The SigMF standard has since been incorporated into numerous pieces of software and academic research. [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] | https://en.wikipedia.org/wiki/SigMF |
SigSpoof ( CVE - 2018-12020 ) is a family of security vulnerabilities that affected the software package GNU Privacy Guard ("GnuPG") since version 0.2.2, that was released in 1998. [ 1 ] Several other software packages that make use of GnuPG were also affected, such as Pass and Enigmail . [ 2 ] [ 1 ]
In un- patched versions of affected software, SigSpoof attacks allow cryptographic signatures to be convincingly spoofed , under certain circumstances. [ 1 ] [ 3 ] [ 4 ] [ 2 ] [ 5 ] This potentially enables a wide range of subsidiary attacks to succeed. [ 1 ] [ 3 ] [ 4 ] [ 2 ] [ 5 ]
This computer security article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/SigSpoof |
A sight glass or water gauge is a type of level sensor , a transparent tube through which the operator of a tank or boiler can observe the level of liquid contained within.
Simple sight glasses may be just a plastic or glass tube connected to the bottom of the tank at one end and the top of the tank at the other. The level of liquid in the sight glass will be the same as the level of liquid in the tank. Today, however, sophisticated float switches have replaced sight glasses in many such applications.
If the liquid is hazardous or under pressure, more sophisticated arrangements must be made. In the case of a boiler, the pressure of the water below and the steam above is equal, so any change in the water level will be seen in the gauge. The transparent tube (the “glass” itself) may be mostly enclosed within a metal or toughened glass shroud to prevent it from being damaged through scratching or impact and offering protection to the operators in the case of breakage. This usually has a patterned backplate to make the magnifying effect of the water in the tube more obvious and so allow for easier reading. In some locomotives where the boiler is operated at very high pressures, the tube itself would be made of metal-reinforced toughened glass. [ 1 ] It is important to keep the water at the specified level, otherwise the top of the firebox will be exposed, creating an overheat hazard and causing damage and possibly catastrophic failure.
To check that the device is offering a correct reading and the connecting pipes to the boiler are not blocked by scale , the water level needs to be “bobbed” by quickly opening the taps in turn and allowing a brief spurt of water through the drain cock. [ 2 ]
The National Board of Boiler and Pressure Vessel Inspectors recommends a daily testing procedure described by the American National Standards Institute, chapter 2 part I-204.3 water level gauge. While not strictly required, this procedure is designed to allow an operator to safely verify that all parts of the sight glass are operating correctly and have free flowing connections to the boiler necessary for proper operation.
The gauge glass on a boiler needs to be inspected periodically and replaced if it is seen to have worn thin in the vicinity of the gland nuts , but a failure in service can still occur. Drivers are expected to carry two or three glass tubes, pre-cut to the required length, together with hemp or rubber seals, to replace the tubes on the road. [ 1 ] Familiarity with this disquieting occurrence was considered so important that a glass would often be smashed deliberately while a trainee driver was on the footplate, to give him practice in fitting a new tube. [ 3 ] Although automatic ball valves are fitted in the mounts to limit the release of steam and scalding water, these can fail through accumulation of limescale. It was standard procedure to hold the coal scoop in front of the face while the other hand, holding the cap for protection, reached to turn off the valves at both ends of the glass.
A reflex gauge is more complex in construction but can give a clearer distinction between gas (steam) and liquid (water). Instead of containing the media in a glass tube, the gauge consists of a vertically oriented slotted metal body with a strong glass plate mounted on the open side of the slot facing the operator. The rear of the glass, in contact with the media, has grooves moulded into its surface, running vertically. The grooves form a zig-zag pattern with 90° angles. Incident light entering the glass is refracted at the rear surface in contact with the media. In the region that is contact with the gas, most of the light is reflected from the surface of one groove to the next and back towards the operator, appearing silvery white. In the region that is in contact with the liquid, most of the light is refracted into the liquid causing this region to appear almost black to the operator. Well-known makes of reflex gauge are Clark-Reliance, IGEMA, TGI Ilmadur, Penberthy, Jerguson, Klinger, Cesare-Bonetti and Kenco. Due to the caustic nature of boiler anti-scaling treatments ("water softeners"), reflex gauges tend to become relatively rapidly etched by the water and lose their effectiveness at displaying the liquid level. Therefore, bi-colour gauges are recommended for certain types of boiler, particularly those operating at pressure above 60 bar.
A bi-colour gauge is generally preferred for caustic media in order to afford protection to the glass. The gauge consists of a vertically oriented slotted metal body with a strong plain glass to the front and the rear. The front and rear body surfaces are in non-parallel vertical planes. Behind the gauge body are light sources with two quite different wavelengths, typically red and green. Due to the different refraction of the red and green light, the liquid region appears green to the operator, while the gas region appears red. Unlike the reflex gauge, the glass has a plane surface which it does not need to be in direct contact with the media and can be protected with a layer of a caustic-resistant transparent material such as silica. Well-known manufacturers of the highest quality Bi-Colour Level Gauges are Clark-Reliance, Klinger, FPS-Aquarian, IGEMA and Quest-Tec
In a magnetic indicator is a float on the surface of the liquid contains a permanent magnet. The liquid is contained in a chamber of strong, non-magnetic material, avoiding the use of glass. The level indicator consists of a number of pivoting magnetic vanes arranged one above the other and placed close to the chamber containing the float. The two faces of the vanes are differently coloured. As the magnet passes up and down behind the vanes it cause them to rotate, displaying one colour for the region containing the liquid and another for the region containing gas. Magnetic indicators are stated in various manufacturers' literature to be most suitable for very high pressure and / or temperature and for aggressive liquids.
The first locomotive to be fitted with the device was built in 1829 by John Rastrick at his Stourbridge works. [ 4 ]
Industrial observational instruments have changed with industry itself. More structurally sophisticated than the water gauge, the contemporary sight glass — also called the sight window or sight port — can be found on the media vessel at chemical plants and in other industrial settings, including pharmaceutical, food, beverage and bio gas plants. [ 5 ] Sight glasses enable operators to visually observe processes inside tanks, pipes, reactors and vessels.
The modern industrial sight glass is a glass disk held between two metal frames, which are secured by bolts and gaskets, or the glass disc is fused to the metal frame during manufacture. The glass used for this purpose is either soda lime glass or borosilicate glass , and the metal, usually a type of stainless steel, is chosen for desired properties of strength. Borosilicate glass is superior to other formulations in terms of chemical corrosion resistance and temperature tolerance, as well as transparency. [ 6 ]
Fused sight glasses are also called mechanically prestressed glass, because the glass is strengthened by compression of the metal ring. Heat is applied to a glass disc and its surrounding steel ring, causing a fusion of the materials. [ 7 ] As the steel cools, it contracts, compressing the glass and making it resistant to tension. Because glass typically breaks under tension, mechanically prestressed glass is unlikely to break and endanger workers. The strongest sight glasses are made with borosilicate glass, because of the greater difference in its coefficient of expansions. | https://en.wikipedia.org/wiki/Sight_glass |
In astronavigation , sight reduction is the process of deriving from a sight (in celestial navigation usually obtained using a sextant ) the information needed for establishing a line of position , generally by intercept method .
Sight is defined as the observation of the altitude, and sometimes also the azimuth , of a celestial body for a line of position; or the data obtained by such observation. [ 1 ]
The mathematical basis of sight reduction is the circle of equal altitude . The calculation can be done by computer, or by hand via tabular methods and longhand methods.
Given:
First calculate the altitude of the celestial body H c {\displaystyle Hc} using the equation of circle of equal altitude :
sin ( H c ) = sin ( L a t ) ⋅ sin ( D e c ) + cos ( L a t ) ⋅ cos ( D e c ) ⋅ cos ( L H A ) . {\displaystyle \sin(Hc)=\sin(Lat)\cdot \sin(Dec)+\cos(Lat)\cdot \cos(Dec)\cdot \cos(LHA).}
The azimuth Z {\displaystyle Z} or Z n {\displaystyle Zn} (Zn=0 at North, measured eastward) is then calculated by:
cos ( Z ) = sin ( D e c ) − sin ( H c ) ⋅ sin ( L a t ) cos ( H c ) ⋅ cos ( L a t ) = sin ( D e c ) cos ( H c ) ⋅ cos ( L a t ) − tan ( H c ) ⋅ tan ( L a t ) . {\displaystyle \cos(Z)={\frac {\sin(Dec)-\sin(Hc)\cdot \sin(Lat)}{\cos(Hc)\cdot \cos(Lat)}}={\frac {\sin(Dec)}{\cos(Hc)\cdot \cos(Lat)}}-\tan(Hc)\cdot \tan(Lat).}
These values are contrasted with the observed altitude H o {\displaystyle Ho} . H o {\displaystyle Ho} , Z {\displaystyle Z} , and H c {\displaystyle Hc} are the three inputs to the intercept method (Marcq St Hilaire method), which uses the difference in observed and calculated altitudes to ascertain one's relative location to the assumed point.
The methods included are:
This method is a practical procedure to reduce celestial sights with the needed accuracy, without using electronic tools such as calculator or a computer. And it could serve as a backup in case of malfunction of the positioning system aboard.
The first approach of a compact and concise method was published by R. Doniol in 1955 [ 4 ] and involved haversines . The altitude is derived from sin ( H c ) = n − a ⋅ ( m + n ) {\displaystyle \sin(Hc)=n-a\cdot (m+n)} , in which n = cos ( L a t − D e c ) {\displaystyle n=\cos(Lat-Dec)} , m = cos ( L a t + D e c ) {\displaystyle m=\cos(Lat+Dec)} , a = hav ( L H A ) {\displaystyle a=\operatorname {hav} (LHA)} .
The calculation is:
A practical and friendly method using only haversines was developed between 2014 and 2015, [ 5 ] and published in NavList .
A compact expression for the altitude was derived [ 6 ] using haversines, hav ( ) {\displaystyle \operatorname {hav} ()} , for all the terms of the equation: hav ( Z D ) = hav ( L a t − D e c ) + ( 1 − hav ( L a t − D e c ) − hav ( L a t + D e c ) ) ⋅ hav ( L H A ) {\displaystyle \operatorname {hav} (ZD)=\operatorname {hav} (Lat-Dec)+\left(1-\operatorname {hav} (Lat-Dec)-\operatorname {hav} (Lat+Dec)\right)\cdot \operatorname {hav} (LHA)}
where Z D {\displaystyle ZD} is the zenith distance ,
H c = ( 90 ∘ − Z D ) {\displaystyle Hc=(90^{\circ }-ZD)} is the calculated altitude.
The algorithm if absolute values are used is:
For the azimuth a diagram [ 7 ] was developed for a faster solution without calculation, and with an accuracy of 1°.
This diagram could be used also for star identification. [ 8 ]
An ambiguity in the value of azimuth may arise since in the diagram 0 ∘ ⩽ Z ⩽ 90 ∘ {\displaystyle 0^{\circ }\leqslant Z\leqslant 90^{\circ }} . Z {\displaystyle Z} is E↔W as the name of the meridian angle, but the N↕S name is not determined. In most situations azimuth ambiguities are resolved simply by observation.
When there are reasons for doubt or for the purpose of checking the following formula [ 9 ] should be used:
hav ( Z ) = hav ( 90 ∘ ± | D e c | ) − hav ( | L a t | − H c ) 1 − hav ( | L a t | − H c ) − hav ( | L a t | + H c ) {\displaystyle \operatorname {hav} (Z)={\frac {\operatorname {hav} (90^{\circ }\pm \vert Dec\vert )-\operatorname {hav} (\vert Lat\vert -Hc)}{1-\operatorname {hav} (\vert Lat\vert -Hc)-\operatorname {hav} (\vert Lat\vert +Hc)}}}
The algorithm if absolute values are used is:
This computation of the altitude and the azimuth needs a haversine table. For a precision of 1 minute of arc, a four figure table is enough. [ 10 ] [ 11 ] | https://en.wikipedia.org/wiki/Sight_reduction |
27346
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The sigma-2 receptor ( σ 2 R ) is a sigma receptor subtype that has attracted attention due to its involvement in diseases such as neurological diseases , neurodegenerative , neuro-ophthalmic and cancer . It is currently [ when? ] under investigation for its potential diagnostic and therapeutic uses. [ 5 ]
Although the sigma-2 receptor was identified as a separate pharmacological entity from the sigma-1 receptor in 1990, [ 6 ] the gene that codes for the receptor was identified as TMEM97 only in 2017. [ 7 ] TMEM97 was shown to regulate the cholesterol transporter NPC1 and to be involved in cholesterol homeostasis . [ 8 ] [ 9 ] The sigma-2 receptor is a four-pass transmembrane protein located in the endoplasmic reticulum . It has been found to play a role in both hormone signaling and calcium signaling, in neuronal signaling, in cell proliferation and death, and in binding of antipsychotics. [ 10 ]
The sigma-2 receptor is located in the lipid raft . [ 11 ] The sigma-2 receptor is found in several areas of the brain, including high densities in the cerebellum , motor cortex , hippocampus , and substantia nigra . [ 12 ] It is also highly expressed in the lungs , liver , and kidneys . [ 10 ]
The sigma-2 receptor takes part in a number of normal-function roles such as cholesterol homeostasis. [ 13 ] [ 14 ] [ 15 ]
Binding of a number of hormones and steroids , including testosterone , progesterone , and cholesterol , has been found to occur with sigma-2 receptors, [ 10 ] though in some cases with lower affinity than to the sigma-1 receptor . [ 12 ] Signaling caused by this binding is thought to occur via a calcium secondary messenger [ 16 ] and calcium-dependent phosphorylation, [ 12 ] and in association with sphingolipids [ 16 ] following endoplasmic reticulum release of calcium . [ 17 ] Known effects include decrease of expression of effectors in the mTOR pathway, and suppression of cyclin D1 and PARP-1 . [ 17 ]
Signaling action in neurons by sigma-2 receptors and their associated ligands results in modulation of action potential firing by regulation of calcium channels and potassium channels . [ 16 ] They also are involved in synaptic vesicular release and modulation of dopamine , serotonin , and glutamate , [ 16 ] with activation and increase of the dopaminergic , serotonergic , and noradrenergic activity of neurons. [ 12 ] [ 18 ]
Sigma-2 receptors have been found to be highly expressed in proliferating cells, including tumor cells , [ 19 ] and to play a role in the differentiation, morphology, and survival of those cells. [ 17 ] By interacting with EGFR membrane proteins sigma-2 receptors play a role in the regulation of signals further downstream such as PKC and RAF. Both PKC and Raf kinase up regulate transcription and cell proliferation. [ 17 ]
Ligands of the sigma-2 receptor are exogenous and internalized by endocytosis , and can act as either agonists or antagonists . They can typically be classified into four groups, which are structurally related. It is not entirely understood how binding to the sigma-2 receptor occurs. [ 17 ] Proposed models commonly include one small and one bulky hydrophobic pocket, electrostatic hydrogen interactions, and less commonly a third hydrophobic pocket.
A study of the four groups has revealed that a basic nitrogen and at least one hydrophobic moiety is needed to bind a sigma-2 receptor. In addition, there are molecular characteristics that increase the selectivity for sigma-2 receptors, which include bulky hydrophobic regions, nitrogen-carboxylic interaction, and additional basic nitrogens. [ 17 ]
Since its discovery in 1990, the sigma-2 receptor has been considered an orphan receptor ; however, in 2021 20S-hydroxycholesterol was identified as the putative endogenous ligand . [ 20 ] [ 21 ]
Another ligand is Lu 29-252 .
Sigma-2 receptors are highly expressed in breast, ovarian, lung cancers, brain, bladder, colon cancers, and melanoma . [ 10 ] [ 19 ] This novelty makes them a valuable biomarker for identifying cancerous tissues. Furthermore, studies have shown that they are more highly expressed in malignant tumors than dormant tumors. [ 16 ]
Exogenous sigma-2 receptor ligands have been altered to be neuronal-tracers, used to map cells and their connections. These tracers have high selectivity and affinity for sigma-2 receptors, and high lipophilicity , making them ideal for usage in the brain. [ 5 ] Because sigma-2 receptors are highly expressed in tumor cells and are part of the cell proliferation mechanism, PET scans using sigma-2 targeted tracers can reveal if a tumor is proliferating and what its growth rate is. [ 5 ]
The sigma-2 receptor is expressed in brain [ 22 ] and retinal cells [ 23 ] [ 24 ] where it regulates key pathways involved in age-related diseases such as Alzheimer's disease and synucleinopathies such as Parkinson's disease and dementia with Lewy bodies , [ 25 ] as well as dry age-related macular degeneration ( dry AMD ). The normal activity of processes regulated by sigma-2, such as protein trafficking and autophagy , is impaired by cellular stresses such as oxidative stress and the build-up of amyloid-β and α-synuclein oligomers . [ 25 ] Studies support that sigma-2 modulators can rescue biological processes that are impaired in neurodegenerative diseases. [ 26 ] [ 27 ]
In vitro studies of experimental sigma-2 receptor modulators demonstrated an ability to prevent the binding of amyloid-β oligomers to neurons and also to displace bound amyloid-β oligomers from neuronal receptors. [ 28 ] In addition, transgenic mice treated sigma-2 receptor modulators performed significantly better in the Morris water maze task than did vehicle-treated mice. [ 28 ] Taken together, these studies suggest that sigma-2 receptor modulation may be a viable approach for treating certain neurodegenerative diseases of the CNS and retina .
Due to the binding capabilities of antipsychotic drugs [ 10 ] [ 18 ] and various neurotransmitters associated with mood, [ 16 ] the sigma-2 receptor is a viable target for therapies related to neuropsychiatric disorders and modulation of emotional response. [ 12 ] It is thought to be involved in the pathophysiology of schizophrenia , [ 29 ] and sigma-2 receptors have been shown to be less abundant in schizophrenic patients. [ 18 ] Additionally, PCP, which is an NMDA antagonist, can induce schizophrenia , [ 29 ] while sigma-2 receptor activation has been shown to antagonize effects of PCP , implying antipsychotic capabilities. [ 18 ] Sigma receptors are a potential target for treatment of dystonia , given high densities in affected regions of the brain. [ 29 ] Anti-ischemics ifenprodil and eliprodil , the binding of which increases blood flow, have also shown affinity to sigma receptors. [ 29 ] In experimental trials in mice and rats, the sigma-2 receptor ligand siramesine caused reduced anxiety and displayed antidepressant capabilities, [ 18 ] while other studies have shown inhibition of selective sigma receptor radioligands by antidepressants, in the mouse and rat brain. [ 12 ]
Sigma-2 receptors have been associated with pancreatic cancer , lung cancer , breast cancer , melanoma , prostate cancer , and ovarian cancer . Tumor cells are shown to over-express sigma-2 receptors, allowing for potential cancer therapies as many sigma-2 receptor mediated cell responses happen only in tumor cells. [ 5 ] Tumor cell responses are modulated via ligand binding . Sigma receptor ligands can act as agonists or antagonists , generating different cellular responses. Agonists inhibit tumor cell proliferation and induce apoptosis , which is thought to be triggered by caspase-3 activity. Antagonists promote tumor cell proliferation, but this mechanism is less understood. [ 17 ] Sigma receptor ligands have been conjugated to nanoparticles and peptides to deliver cancer treatment to tumor cells without targeting other tissues. [ 5 ] The success with these methods have been limited to in vitro trials. Additionally, using sigma-2 receptors to target tumor cells allows for synergizing anti-cancer drug therapies. Some studies have shown that certain sigma receptor inhibitors increase cancer cells' susceptibility to chemotherapy . [ 10 ] Other types of binding to sigma-2 receptors increases cytotoxicity of doxorubicin, antinomyocin, and other cancer cell killing drugs. [ 17 ] | https://en.wikipedia.org/wiki/Sigma-2_receptor |
The Sigma-D relation , or Σ-D Relation , is the claimed relation between the radio surface brightness and diameter of a supernova remnant . It is generally regarded as of limited physical use, since it has very large scatter and is dominated by observational selection biases. [ 1 ] [ 2 ]
This astrophysics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Sigma-D_relation |
In organometallic chemistry , sigma-bond metathesis is a chemical reaction wherein a metal-ligand sigma bond undergoes metathesis (exchange of parts) with the sigma bond in some reagent. The reaction is illustrated by the exchange of lutetium (III) methyl complex with a hydrocarbon (R-H): [ 1 ]
This reactivity was first observed by Patricia Watson, a researcher at duPont. [ 2 ]
The reaction is mainly observed for complexes of metals with d 0 configuration, e.g. complexes of Sc(III), Zr(IV), Nb(V), Ta(V), etc. f-Element complexes also participate, regardless of the number of f-electrons. The reaction is thought to proceed via cycloaddition . Indeed, the rate of the reaction is characterized by a highly negative entropy of activation, indicating an ordered transition state . For metals unsuited for redox, sigma bond metathesis provides a pathway for introducing substituents.
The reaction attracted much attention because hydrocarbons are normally unreactive substrates, whereas some sigma-bond metatheses are facile. Unfortunately the reaction does not readily allow the introduction of functional groups. It has been suggested that dehydrocoupling reactions proceed via sigma-bond metathesis. | https://en.wikipedia.org/wiki/Sigma-bond_metathesis |
The σ-π model and equivalent-orbital model refer to two possible representations of molecules in valence bond theory . The σ-π model differentiates bonds and lone pairs of σ symmetry from those of π symmetry, while the equivalent-orbital model hybridizes them . The σ-π treatment takes into account molecular symmetry and is better suited to interpretation of aromatic molecules ( Hückel's rule ), although computational calculations of certain molecules tend to optimize better under the equivalent-orbital treatment. [ 1 ] The two representations produce the same total electron density and are related by a unitary transformation of the occupied molecular orbitals; different localization procedures yield either of the two. Two equivalent orbitals h and h ' can be constructed by taking linear combinations h = c 1 σ + c 2 π and h ' = c 1 σ – c 2 π for an appropriate choice of coefficients c 1 and c 2 .
In a 1996 review, Kenneth B. Wiberg concluded that "although a conclusive statement cannot be made on the basis of the currently available information, it seems likely that we can continue to consider the σ/π and bent-bond descriptions of ethylene to be equivalent. [ 2 ] Ian Fleming goes further in a 2010 textbook, noting that "the overall distribution of electrons [...] is exactly the same" in the two models. [ 3 ] Nevertheless, as pointed out in Carroll's textbook, at lower levels of theory, the two models make different quantitative and qualitative predictions, and there has been considerable debate as to which model is most useful conceptually and pedagogically. [ 4 ]
Two different explanations for the nature of double and triple covalent bonds in organic molecules were proposed in the 1930s. Linus Pauling proposed that the double bond in ethylene results from two equivalent tetrahedral orbitals from each atom, [ 5 ] which later came to be called banana bonds or tau bonds . [ 6 ] Erich Hückel proposed a representation of the double bond as a combination of a sigma bond plus a pi bond . [ 7 ] [ 8 ] [ 9 ] The σ-π representation is the better-known one, and it is the one found in most textbooks since the late-20th century.
Initially, Linus Pauling's scheme of water as presented in his hallmark paper on valence bond theory consists of two inequivalent lone pairs of σ and π symmetry. [ 5 ] As a result of later developments resulting partially from the introduction of VSEPR, an alternative view arose which considers the two lone pairs to be equivalent, colloquially called rabbit ears . [ 10 ]
Weinhold and Landis describe the symmetry adapted use of the orbital hybridization concept within the context of natural bond orbitals , a localized orbital theory containing modernized analogs of classical (valence bond/Lewis structure) bonding pairs and lone pairs. [ 11 ] For the hydrogen fluoride molecule, for example, two F lone pairs are essentially unhybridized p orbitals of π symmetry, while the other is an sp x hydrid orbital of σ symmetry. An analogous consideration applies to water (one O lone pair is in a pure p orbital, another is in an sp x hybrid orbital).
The question of whether it is conceptually useful to derive equivalent orbitals from symmetry-adapted ones, from the standpoint of bonding theory and pedagogy, is still a controversial one, with recent (2014 and 2015) articles opposing [ 12 ] and supporting [ 13 ] the practice. | https://en.wikipedia.org/wiki/Sigma-pi_and_equivalent-orbital_models |
In chemistry , sigma bonds ( σ bonds ) or sigma overlap are the strongest type of covalent chemical bond . [ 1 ] They are formed by head-on overlapping between atomic orbitals along the internuclear axis. Sigma bonding is most simply defined for diatomic molecules using the language and tools of symmetry groups . In this formal approach, a σ-bond is symmetrical with respect to rotation about the bond axis. By this definition, common forms of sigma bonds are s+s, p z +p z , s+p z and d z 2 +d z 2 (where z is defined as the axis of the bond or the internuclear axis). [ 2 ] Quantum theory also indicates that molecular orbitals (MO) of identical symmetry actually mix or hybridize . As a practical consequence of this mixing of diatomic molecules, the wavefunctions s+s and p z +p z molecular orbitals become blended. The extent of this mixing (or hybridization or blending) depends on the relative energies of the MOs of like symmetry.
For homodiatomics ( homonuclear diatomic molecules), bonding σ orbitals have no nodal planes at which the wavefunction is zero, either between the bonded atoms or passing through the bonded atoms. The corresponding antibonding , or σ* orbital, is defined by the presence of one nodal plane between the two bonded atoms.
Sigma bonds are the strongest type of covalent bonds due to the direct overlap of orbitals, and the electrons in these bonds are sometimes referred to as sigma electrons. [ 3 ]
The symbol σ is the Greek letter sigma . When viewed down the bond axis, a σ MO has a circular symmetry , hence resembling a similarly sounding "s" atomic orbital .
Typically, a single bond is a sigma bond while a multiple bond is composed of one sigma bond together with pi or other bonds. A double bond has one sigma plus one pi bond , and a triple bond has one sigma plus two pi bonds.
orbitals
Sigma bonds are obtained by head-on overlapping of atomic orbitals. The concept of sigma bonding is extended to describe bonding interactions involving overlap of a single lobe of one orbital with a single lobe of another. For example, propane is described as consisting of ten sigma bonds, one each for the two C−C bonds and one each for the eight C−H bonds.
Transition metal complexes that feature multiple bonds, such as the dihydrogen complex , have sigma bonds between the multiple bonded atoms. These sigma bonds can be supplemented with other bonding interactions, such as π-back donation , as in the case of W(CO) 3 ( PCy 3 ) 2 (H 2 ), and even δ-bonds, as in the case of chromium(II) acetate . [ 4 ]
Organic molecules are often cyclic compounds containing one or more rings, such as benzene , and are often made up of many sigma bonds along with pi bonds. According to the sigma bond rule , the number of sigma bonds in a molecule is equivalent to the number of atoms plus the number of rings minus one.
This rule is a special-case application of the Euler characteristic of the graph which represents the molecule.
A molecule with no rings can be represented as a tree with a number of bonds equal to the number of atoms minus one (as in dihydrogen , H 2 , with only one sigma bond, or ammonia , NH 3 , with 3 sigma bonds). There is no more than 1 sigma bond between any two atoms.
Molecules with rings have additional sigma bonds, such as benzene rings, which have 6 C−C sigma bonds within the ring for 6 carbon atoms. The anthracene molecule, C 14 H 10 , has three rings so that the rule gives the number of sigma bonds as 24 + 3 − 1 = 26. In this case there are 16 C−C sigma bonds and 10 C−H bonds.
This rule fails in the case of molecules which, when drawn flat on paper, have a different number of rings than the molecule actually has - for example, Buckminsterfullerene , C 60 , which has 32 rings, 60 atoms, and 90 sigma bonds, one for each pair of bonded atoms; however, 60 + 32 − 1 = 91, not 90. This is because the sigma rule is a special case of the Euler characteristic , where each ring is considered a face, each sigma bond is an edge, and each atom is a vertex. Ordinarily, one extra face is assigned to the space not inside any ring, but when Buckminsterfullerene is drawn flat without any crossings , one of the rings makes up the outer pentagon; the inside of that ring is the outside of the graph. This rule fails further when considering other shapes - toroidal fullerenes will obey the rule that the number of sigma bonds in a molecule is exactly the number of atoms plus the number of rings, as will nanotubes - which, when drawn flat as if looking through one from the end, will have a face in the middle, corresponding to the far end of the nanotube, which is not a ring, and a face corresponding to the outside. | https://en.wikipedia.org/wiki/Sigma_bond |
The sEDA parameter ( sigma electron donor-acceptor ) is a sigma-electron substituent effect scale, described also as inductive and electronegativity related effect. There is also a complementary scale - pEDA . The more positive is the value of sEDA the more sigma-electron donating is a substituent. The more negative sEDA, the more sigma-electron withdrawing is the substituent (see the table below).
The sEDA parameter for a given substituent is calculated by means of quantum chemistry methods. The model molecule is the monosubstituted benzene . First the geometry should be optimized at a suitable model of theory, then the natural population analysis within the framework of Natural Bond Orbital theory is performed. The molecule have to be oriented in such a way that the aromatic benzene ring lays in the xy plane and is perpendicular to the z-axis. Then, the 2s, 2p x and 2py orbital occupations of ring carbon atoms are summed up to give the total sigma system occupation. From this value the sum of sigma-occupation for unsubstituted benzene is subtracted resulting in original sEDA parameter. For sigma-electron donating substituents like -Li, -BH 2 , -SiH 3 , the sEDA parameter is positive, and for sigma-electron withdrawing substituents like -F, -OH, -NH 2 , -NO 2 , -COOH the sEDA is negative.
The sEDA scale was invented by Wojciech P. Oziminski and Jan Cz. Dobrowolski and the details are available in the original paper. [ 1 ]
The sEDA scale linearly correlates with experimental substituent constants like Taft-Topsom σR parameter. [ 2 ]
For easy calculation of sEDA the free of charge for academic purposes written in Tcl program with graphical user interface AromaTcl is available.
Sums of sigma-electron occupations and sEDA parameter for substituents of various character are gathered in the following table: | https://en.wikipedia.org/wiki/Sigma_electron_donor-acceptor |
A sigma factor ( σ factor or specificity factor ) is a protein needed for initiation of transcription in bacteria . [ 1 ] [ 2 ] It is a bacterial transcription initiation factor that enables specific binding of RNA polymerase (RNAP) to gene promoters . It is homologous to archaeal transcription factor B and to eukaryotic factor TFIIB . [ 3 ] The specific sigma factor used to initiate transcription of a given gene will vary, depending on the gene and on the environmental signals needed to initiate transcription of that gene. Selection of promoters by RNA polymerase is dependent on the sigma factor that associates with it. [ 4 ] They are also found in plant chloroplasts as a part of the bacteria-like plastid-encoded polymerase (PEP). [ 5 ]
The sigma factor, together with RNA polymerase, is known as the RNA polymerase holoenzyme . Every molecule of RNA polymerase holoenzyme contains exactly one sigma factor subunit, which in the model bacterium Escherichia coli is one of those listed below. The number of sigma factors varies between bacterial species. [ 1 ] [ 6 ] E. coli has seven sigma factors. Sigma factors are distinguished by their characteristic molecular weights . For example, σ 70 is the sigma factor with a molecular weight of 70 kDa .
The sigma factor in the RNA polymerase holoenzyme complex is required for the initiation of transcription, although once that stage is finished, it is dissociated from the complex and the RNAP continues elongation on its own.
Different sigma factors are utilized under different environmental conditions. These specialized sigma factors bind the promoters of genes appropriate to the environmental conditions, increasing the transcription of those genes.
Sigma factors in E. coli :
There are also anti-sigma factors that inhibit the function of sigma factors and anti-anti-sigma factors that restore sigma factor function.
By sequence similarity, most sigma factors are σ 70 -like ( InterPro : IPR000943 ). They have four main regions (domains) that are generally conserved:
The regions are further subdivided. For example, region 2 includes 1.2 and 2.1 through 2.4.
Domain 1.1 is found only in "primary sigma factors" (RpoD, RpoS in E.coli ; "Group 1"). It is involved in ensuring the sigma factor will only bind the promoter when it is complexed with the RNA polymerase. [ 7 ] Domains 2-4 each interact with specific promoter elements and with RNAP. Region 2.4 recognizes and binds to the promoter −10 element (called the " Pribnow box "). Region 4.2 recognizes and binds to the promoter −35 element. [ 7 ]
Not every sigma factor of the σ 70 family contains all the domains. Group 2, which includes RpoS, is very similar to Group 1 but lacks domain 1. Group 3 also lacks domain 1, and includes σ 28 . Group 4, also known as the Extracytoplasmic Function (ECF) group, lack both σ1.1 and σ3. RpoE is a member. [ 7 ]
Other known sigma factors are of the σ 54 /RpoN ( InterPro : IPR000394 ) type. They are functional sigma factors, but they have significantly different primary amino acid sequences. [ 8 ]
The core RNA polymerase (consisting of 2 alpha (α), 1 beta (β), 1 beta-prime (β'), and 1 omega (ω) subunits) binds a sigma factor to form a complex called the RNA polymerase holoenzyme . It was previously believed that the RNA polymerase holoenzyme initiates transcription, while the core RNA polymerase alone synthesizes RNA. Thus, the accepted view was that sigma factor must dissociate upon transition from transcription initiation to transcription elongation (this transition is called "promoter escape"). This view was based on analysis of purified complexes of RNA polymerase stalled at initiation and at elongation. Finally, structural models of RNA polymerase complexes predicted that, as the growing RNA product becomes longer than ~15 nucleotides, sigma must be "pushed out" of the holoenzyme, since there is a steric clash between RNA and a sigma domain. However, σ 70 can remain attached in complex with the core RNA polymerase in early elongation [ 9 ] and sometimes throughout elongation. [ 10 ] Indeed, the phenomenon of promoter-proximal pausing indicates that sigma plays roles during early elongation. All studies are consistent with the assumption that promoter escape reduces the lifetime of the sigma-core interaction from very long at initiation (too long to be measured in a typical biochemical experiment) to a shorter, measurable lifetime upon transition to elongation.
It had long been thought that the sigma factor obligatorily leaves the core enzyme once it has initiated transcription, allowing it to link to another core enzyme and initiate transcription at another site. Thus, the sigma factor would cycle from one core to another.
However, fluorescence resonance energy transfer was used to show that the sigma factor does not obligatorily leave the core. [ 9 ] Instead, it changes its binding with the core during initiation and elongation. Therefore, the sigma factor cycles between a strongly bound state during initiation and a weakly bound state during elongation.
The number of RNAPs in bacterial cells (e.g., E. coli ) have been shown to be smaller than the number of sigma factors. Consequently, if a certain sigma factor is overexpressed, not only will it increase the expression levels of genes whose promoters have preference for that sigma factor, but it will also reduce the probability that genes with promoters with preference for other sigma factors will be expressed. [ 11 ] [ 12 ] [ 13 ] [ 14 ]
Meanwhile, transcription initiation has two major rate limiting steps: the closed and the open complex formation. However, only the dynamics of the first step depends on the concentration of sigma factors. Interestingly, the faster the closed complex formation relative to the open complex formation, the less responsive is a promoter to changes in sigma factors’ concentration (see [ 14 ] for a model and empirical data of this phenomenon).
While most genes of E. coli can be recognized by an RNAP with one and only one type of sigma factor (e.g. sigma 70), a few genes (~ 5%) have what is called a “dual sigma factor preference”, [ 15 ] that is, they can respond to two different sigma factors, as reported in RegulonDB. [ 16 ] The most common ones are those promoters that can respond to both sigma 70 and to sigma 38 (iIlustrated in the figure) . Studies of the dynamics of these genes showed that when the cells enter stationary growth they are almost as induced as those genes that have preference for σ38 alone. This induction level was shown to be predictable from their promoter sequence. [ 15 ] A model of their dynamics is shown in the figure. In the future, these promoters may become useful tools in synthetic genetic constructs in E. coli . | https://en.wikipedia.org/wiki/Sigma_factor |
Sigma heat , denoted S {\displaystyle S} , is a measure of the specific energy of humid air. It is used in the field of mining engineering for calculations relating to the temperature regulation of mine air. Sigma heat is sometimes called total heat , [ 1 ] although total heat may instead mean enthalpy . [ 2 ]
Sigma heat is the energy which would be extracted from a unit mass of humid air if it were cooled to a certain reference temperature under constant pressure while simultaneously removing any condensation formed during the process. Because sigma heat assumes that condensation will be removed, any energy which would be extracted by cooling the water vapor below its condensation point does not count towards sigma heat. [ 3 ] The reference temperature is usually 0 °F (−18 °C), although 32 °F (0 °C) is sometimes used as well. [ 1 ]
Assuming a reference temperature of 0°F, the following formula may be used under standard temperature ranges and pressure: [ note 1 ]
S = 0.24 B T U l b ⋅ ∘ F t + W ( 0.45 B T U l b ⋅ ∘ F t + 1061 B T U l b ) {\displaystyle S=0.24\mathrm {{\tfrac {BTU}{lb\cdot ^{\circ }F}}\;} t+W\;(0.45\mathrm {{\tfrac {BTU}{lb\cdot ^{\circ }F}}\;} t+1061\mathrm {\tfrac {BTU}{lb}} )} [ 3 ]
The equivalent metric formula:
S = 17.86 k J k g + 1.005 k J k g ⋅ K t + W ( 2501 k J k g + 1.884 k J k g ⋅ K t ) {\displaystyle S=17.86\mathrm {\tfrac {kJ}{kg}} +1.005\mathrm {\tfrac {kJ}{kg\cdot K}} t+W\;(2501\mathrm {\tfrac {kJ}{kg}} +1.884\mathrm {\tfrac {kJ}{kg\cdot K}} t)}
Sigma heat is not the same as the enthalpy of the humid air above the reference temperature. (Enthalpy is sometimes called total heat [ 2 ] or true total heat [ 1 ] ) Unlike sigma heat, enthalpy does include the energy which would be extracted in cooling the condensed water vapor all the way to the reference temperature. Essentially, enthalpy assumes that all components of the system must be cooled during the cooling process, whereas sigma heat assumes that some of those components (liquid water) are removed part way through the process. Nevertheless, some writers mistakenly use the term enthalpy when they actually mean sigma heat, creating some confusion. [ 3 ]
Assuming a reference temperature of 0°F, the relationship between enthalpy and sigma heat may be shown mathematically as:
h = S + 1 B T U l b W t ′ {\displaystyle h=S+1\mathrm {{\tfrac {BTU}{lb}}\;} Wt'} [ 3 ]
Assuming constant pressure, sigma heat is solely a function of the wet bulb temperature of the air. For this reason, humidity need not be taken into account unless dry-bulb temperature measurements are used. Like sigma heat, the wet bulb temperature is not directly affected by the temperature of any condensed water vapor (liquid water), and it varies only when there is a net energy change to the system. In contrast, the dry bulb temperature can vary even for processes where there is no such net energy change. This difference may be understood by examining evaporative cooling . During evaporative cooling, all energy lost from air molecules as sensible heat is gained as latent heat by water molecules evaporating into that air. With no net energy gained or lost from the now more humid air, sigma heat remains unchanged. In keeping with this, the wet bulb temperature also remains unchanged, as its reading already represented the maximum possible amount of evaporative cooling. The dry bulb temperature however is in conflict with the sigma heat since it decreases during such evaporative cooling. This is why measurements of sigma heat which use dry bulb temperatures must also take into account the humidity of the air. [ 3 ] | https://en.wikipedia.org/wiki/Sigma_heat |
In chemistry , sigma hole interactions (or σ-hole interactions ) are a family of intermolecular forces that can occur between several classes of molecules and arise from an energetically stabilizing interaction between a positively-charged site, termed a sigma hole , and a negatively-charged site, typically a lone pair , on different atoms that are not covalently bonded to each other. [ 1 ] These interactions are usually rationalized primarily via dispersion , electrostatics , and electron delocalization (similar to Lewis-acid/base coordination) and are characterized by a strong directional preference that allows control over supramolecular chemistry .
The basis of a sigma hole interaction is an energetically stabilizing interaction between a positively charged site (sigma hole) and a negatively charged site ( lone pair ) on different atoms. The positive site is produced by a covalent sigma bond between the atom hosting the sigma hole and a neighboring atom. The presence of the bond results in the distortion of the electron density around the host atom, with the density increasing equatorially (with respect to the bond) about the atom but decreasing along the extension of the bond. Through this mechanism, a region of positive electrostatic potential , termed a sigma hole, can be localized onto the surface of an atom bearing a sigma bond. This sigma hole could then engage in electrostatic interactions with a lone pair associated with a negative electrostatic potential. [ 2 ] [ 3 ]
In addition to the electrostatic interaction described above, dispersive forces are also thought to play a role in the overall interaction. Studies have found electrostatic and dispersive contributions to be roughly comparable in magnitude, and for the dominant contributor to vary from system to system. [ 4 ]
Alternatively, sigma hole pair interactions can be conceptualized in terms of the mixing of molecular orbitals . The occupied sigma bonding orbital associated with the bond would give rise to a corresponding unoccupied sigma antibonding orbital lying on the opposite face of the atom. Mixing between the antibonding orbital and the occupied orbital associated with a lone pair would be expected to result in energetic stabilization. [ 1 ]
Several atoms, including those which are relatively electronegative (such as Chlorine , [ 5 ] Oxygen , [ 6 ] and even Fluorine [ 5 ] ) can act as positive sites in sigma hole pair interactions. Counterintuitively, this can occur even when the atom acting as the positive site has an overall negative partial charge . The solution to this apparent contradiction lies in the anisotropy in the electron cloud introduced by the presence of the sigma bond. If the electronic charge is not evenly distributed around the nucleus , it remains possible for a positive partial charge to develop opposite the sigma bond in the region of electron depletion. This partial positive charge coexists with a partial negative charge of larger magnitude associated with the more electron-rich regions of the atomic surface, which results in an overall negative partial charge. [ 1 ]
Sigma hole interactions exhibit a strong preference for linearity . Theoretical studies have shown that the interaction is most stabilizing when the negative site is colinear with the bond that gives rise to the sigma hole. [ 7 ] As the angle between this bond and the sigma hole interaction is decreased, the strength of the interaction is generally found to decrease rapidly. This finding is consistent with the hypothesis that the sigma hole arises from electronic anisotropy. There are cases in which the angle of interaction does differ somewhat from 180° - in these cases, the influence of additional intermolecular interactions are implicated in determining the overall geometry. [ 1 ]
Consistent with Coulomb's law , There is a very strong relationship between the energetic stabilization associated with a sigma hole interaction and the product of the electrostatic potentials associated with the sigma hole and lone pair sites. [ 1 ] Therefore, factors that increase the electrostatic potential of the sigma hole and decrease the electrostatic potential of the lone pair result in stronger interactions. The main structural factors contributing to the electrostatic potential of the sigma hole are the electronegativity of the host atom, the polarizability of the host atom, and the electron donating or withdrawing character of the group bonded to the host atom, with less electronegative and more polarizable host atoms bound to more electron withdrawing groups associated with the highest electrostatic potential. [ 1 ]
The table below shows the computed strength (in kcal/mol ) of three selected sigma hole interactions at a variety of angles. [ 7 ] At any angle, it can be observed that the interaction is stronger when the Bromine atom hosting the sigma hole is bound to a strongly electron withdrawing cyano group than when this atom is bound to a trifluoromethyl group , which is only moderately electron withdrawing. On the other hand, the interaction is stronger when an ammonia molecule provides the lone pair, as the electrostatic potential associated with this site is more negative than the corresponding site on hydrogen cyanide . In all cases, the interaction is becomes stronger at more linear angles. [ 7 ]
While the formation of a sigma hole pair interaction is associated with energetic stabilization, this process is often thermodynamically disfavored as the energetic stabilization is often offset by a decrease in the entropy of the system. [ 8 ] It has been shown that an enthalpy-entropy compensation relationship exists between the energetic and entropic changes associated with interactions, with more stabilizing interactions tending to result in larger entropy decreases. [ 9 ] However, the decrease in entropy associated with the formation of a sigma hole interaction has been shown to approach a limiting value as the energetic favorability of the process is increased, and as such very energetically stabilizing interactions tend to be thermodynamically favored. [ 1 ] There are additional factors that contribute to thermodynamic stability in the liquid and solid phases, which cannot be as easily modeled as gas phase interactions. As such, the favorability of a given sigma hole interaction in the liquid or solid phase may not necessarily match that of the gas phase equivalent. [ 1 ]
Atoms interacting via a sigma hole interactions are often closer than the sum of their van der waals radii . [ 10 ] In addition, sigma hole interactions are also often associated with changes in the lengths and vibrational stretching frequencies of the covalent bond that gives rise to the sigma hole. Depending on the system engaging in the interaction, either a "blue shift", in which the bond contracts and the vibrational stretching frequency increases, or a "red shift", in which the bond lengthens and the vibrational stretching frequency decreases, is possible. [ 11 ] The extent of these effects are related to the strength of the interaction, with stronger interactions tending to produce shorter interatomic distances between the interacting atoms and stronger red shifts. [ 1 ]
The sigma hole formalism has been applied to a wide range of interactions involving electrostatic and dispersive attraction between positively and negatively charged sites. These interactions are typically classified according to the identity of the atom that hosts the positively charged site. Interaction types that are broadly accepted as subclasses of the sigma hole interaction include tetrel bonding (in which a sigma hole resides on an atom of group IV ), [ 12 ] pnictogen bonding ( group V ), [ 13 ] chalcogen bonding ( group VI ), [ 6 ] [ 14 ] and halogen bonding ( group VII ). [ 1 ] [ 5 ] [ 15 ]
It remains a matter of some debate whether hydrogen bonding is best classified as a sigma hole interaction, in which the sigma hole lies on the Hydrogen atom, or as a distinct class of interactions. While hydrogen bonds and sigma hole interactions of groups IV-VII both exhibit directional preferences towards linearity, the ability of hydrogen bonds to deviate from an ideal 180° angle is much greater. [ 16 ] On the other hand, it has been argued that the underlying mechanism dictating both interactions is identical, and the observed difference in orientational preference can be attributed to a difference in the shape of the sigma holes. [ 15 ] [ 17 ]
Sigma hole interactions have applications in a variety of fields. The ability to induce stabilizing and strongly directional intermolecular interactions which can be easily tuned via minor structural substitutions makes leveraging these interactions particularly value in fields in which control over supramolecular organization is desired. As such, sigma hole interactions have been used in the field of crystal engineering to design molecular building blocks for self-assembly , [ 18 ] to improve the properties of liquid crystals , [ 19 ] and to design magnetic materials . [ 20 ] | https://en.wikipedia.org/wiki/Sigma_hole_interactions |
In physics , a sigma model is a field theory that describes the field as a point particle confined to move on a fixed manifold. This manifold can be taken to be any Riemannian manifold , although it is most commonly taken to be either a Lie group or a symmetric space . The model may or may not be quantized. An example of the non-quantized version is the Skyrme model ; it cannot be quantized due to non-linearities of power greater than 4. In general, sigma models admit (classical) topological soliton solutions, for example, the skyrmion for the Skyrme model. When the sigma field is coupled to a gauge field, the resulting model is described by Ginzburg–Landau theory . This article is primarily devoted to the classical field theory of the sigma model; the corresponding quantized theory is presented in the article titled " non-linear sigma model ".
The name has roots in particle physics, where a sigma model describes the interactions of pions . Unfortunately, the "sigma meson" is not described by the sigma-model, but only a component of it. [ 1 ]
The sigma model was introduced by Gell-Mann & Lévy (1960 , section 5); the name σ-model comes from a field in their model corresponding to a spinless meson called σ , a scalar meson introduced earlier by Julian Schwinger . [ 2 ] The model served as the dominant prototype of spontaneous symmetry breaking of O(4) down to O(3): the three axial generators broken are the simplest manifestation of chiral symmetry breaking , the surviving unbroken O(3) representing isospin .
In conventional particle physics settings, the field is generally taken to be SU(N) , or the vector subspace of quotient ( S U ( N ) L × S U ( N ) R ) / S U ( N ) {\displaystyle (SU(N)_{L}\times SU(N)_{R})/SU(N)} of the product of left and right chiral fields. In condensed matter theories, the field is taken to be O(N) . For the rotation group O(3), the sigma model describes the isotropic ferromagnet ; more generally, the O(N) model shows up in the quantum Hall effect , superfluid Helium-3 and spin chains .
In supergravity models, the field is taken to be a symmetric space . Since symmetric spaces are defined in terms of their involution , their tangent space naturally splits into even and odd parity subspaces. This splitting helps propel the dimensional reduction of Kaluza–Klein theories.
In its most basic form, the sigma model can be taken as being purely the kinetic energy of a point particle; as a field, this is just the Dirichlet energy in Euclidean space.
In two spatial dimensions, the O(3) model is completely integrable .
The Lagrangian density of the sigma model can be written in a variety of different ways, each suitable to a particular type of application. The simplest, most generic definition writes the Lagrangian as the metric trace of the pullback of the metric tensor on a Riemannian manifold . For ϕ : M → Φ {\displaystyle \phi :M\to \Phi } a field over a spacetime M {\displaystyle M} , this may be written as
where the g i j ( ϕ ) {\displaystyle g_{ij}(\phi )} is the metric tensor on the field space ϕ ∈ Φ {\displaystyle \phi \in \Phi } , and the ∂ μ {\displaystyle \partial _{\mu }} are the derivatives on the underlying spacetime manifold .
This expression can be unpacked a bit. The field space Φ {\displaystyle \Phi } can be chosen to be any Riemannian manifold . Historically, this is the "sigma" of the sigma model; the historically-appropriate symbol σ {\displaystyle \sigma } is avoided here to prevent clashes [ which? ] with many other common usages of σ {\displaystyle \sigma } in geometry. Riemannian manifolds always come with a metric tensor g {\displaystyle g} . Given an atlas of charts on Φ {\displaystyle \Phi } , the field space can always be locally trivialized , in that given U ⊂ Φ {\displaystyle U\subset \Phi } in the atlas, one may write a map U → R n {\displaystyle U\to \mathbb {R} ^{n}} giving explicit local coordinates ϕ = ( ϕ 1 , ⋯ , ϕ n ) {\displaystyle \phi =(\phi ^{1},\cdots ,\phi ^{n})} on that patch. The metric tensor on that patch is a matrix having components g i j ( ϕ ) . {\displaystyle g_{ij}(\phi ).}
The base manifold M {\displaystyle M} must be a differentiable manifold ; by convention, it is either Minkowski space in particle physics applications, flat two-dimensional Euclidean space for condensed matter applications, or a Riemann surface , the worldsheet in string theory . The ∂ μ ϕ = ∂ ϕ / ∂ x μ {\displaystyle \partial _{\mu }\phi =\partial \phi /\partial x^{\mu }} is just the plain-old covariant derivative on the base spacetime manifold M . {\displaystyle M.} When M {\displaystyle M} is flat, ∂ μ ϕ = ∇ ϕ {\displaystyle \partial _{\mu }\phi =\nabla \phi } is just the ordinary gradient of a scalar function (as ϕ {\displaystyle \phi } is a scalar field, from the point of view of M {\displaystyle M} itself.) In more precise language, ∂ μ ϕ {\displaystyle \partial _{\mu }\phi } is a section of the jet bundle of M × Φ {\displaystyle M\times \Phi } .
Taking g i j = δ i j {\displaystyle g_{ij}=\delta _{ij}} the Kronecker delta , i.e. the scalar dot product in Euclidean space, one gets the O ( n ) {\displaystyle O(n)} non-linear sigma model. That is, write ϕ = u ^ {\displaystyle \phi ={\hat {u}}} to be the unit vector in R n {\displaystyle \mathbb {R} ^{n}} , so that u ^ ⋅ u ^ = 1 {\displaystyle {\hat {u}}\cdot {\hat {u}}=1} , with ⋅ {\displaystyle \cdot } the ordinary Euclidean dot product. Then u ^ ∈ S n − 1 {\displaystyle {\hat {u}}\in S^{n-1}} the ( n − 1 ) {\displaystyle (n-1)} - sphere , the isometries of which are the rotation group O ( n ) {\displaystyle O(n)} . The Lagrangian can then be written as
For n = 3 {\displaystyle n=3} , this is the continuum limit of the isotropic ferromagnet on a lattice, i.e. of the classical Heisenberg model . For n = 2 {\displaystyle n=2} , this is the continuum limit of the classical XY model . See also the n-vector model and the Potts model for reviews of the lattice model equivalents. The continuum limit is taken by writing
as the finite difference on neighboring lattice locations i , j . {\displaystyle i,j.} Then δ h [ u ^ ] → ∂ μ u ^ {\displaystyle \delta _{h}[{\hat {u}}]\to \partial _{\mu }{\hat {u}}} in the limit h → 0 {\displaystyle h\to 0} , and u ^ i ⋅ u ^ j → ∂ μ u ^ ⋅ ∂ μ u ^ {\displaystyle {\hat {u}}_{i}\cdot {\hat {u}}_{j}\to \partial _{\mu }{\hat {u}}\cdot \partial _{\mu }{\hat {u}}} after dropping the constant terms u ^ i ⋅ u ^ i = 1 {\displaystyle {\hat {u}}_{i}\cdot {\hat {u}}_{i}=1} (the "bulk magnetization").
The sigma model can also be written in a more fully geometric notation, as a fiber bundle with fibers Φ {\displaystyle \Phi } over a differentiable manifold M {\displaystyle M} . Given a section ϕ : M → Φ {\displaystyle \phi :M\to \Phi } , fix a point x ∈ M . {\displaystyle x\in M.} The pushforward at x {\displaystyle x} is a map of tangent bundles
where ∂ μ = ∂ / ∂ x μ {\displaystyle \partial _{\mu }=\partial /\partial x^{\mu }} is taken to be a local orthonormal vector space basis on T M {\displaystyle TM} and ∂ i = ∂ / ∂ q i {\displaystyle \partial _{i}=\partial /\partial q^{i}} the vector space basis on T Φ {\displaystyle T\Phi } . The d ϕ {\displaystyle \mathrm {d} \phi } is a differential form . The sigma model action is then just the conventional inner product on vector-valued k -forms
where the ∧ {\displaystyle \wedge } is the wedge product , and the ⋆ {\displaystyle \star } is the Hodge star . This is an inner product in two different ways. In the first way, given any two differentiable forms α , β {\displaystyle \alpha ,\beta } in M {\displaystyle M} , the Hodge dual defines an invariant inner product on the space of differential forms, commonly written as
The above is an inner product on the space of square-integrable forms, conventionally taken to be the Sobolev space L 2 . {\displaystyle L^{2}.} In this way, one may write
This makes it explicit and plainly evident that the sigma model is just the kinetic energy of a point particle. From the point of view of the manifold M {\displaystyle M} , the field ϕ {\displaystyle \phi } is a scalar, and so d ϕ {\displaystyle \mathrm {d} \phi } can be recognized just the ordinary gradient of a scalar function. The Hodge star is merely a fancy device for keeping track of the volume form when integrating on curved spacetime. In the case that M {\displaystyle M} is flat, it can be completely ignored, and so the action is
which is the Dirichlet energy of ϕ {\displaystyle \phi } . Classical extrema of the action (the solutions to the Lagrange equations ) are then those field configurations that minimize the Dirichlet energy of ϕ {\displaystyle \phi } . Another way to convert this expression into a more easily-recognizable form is to observe that, for a scalar function f : M → R {\displaystyle f:M\to \mathbb {R} } one has d ⋆ f = 0 {\displaystyle \mathrm {d} {\star }f=0} and so one may also write
where Δ {\displaystyle \Delta } is the Laplace–Beltrami operator , i.e. , the ordinary Laplacian when M {\displaystyle M} is flat.
That there is another , second inner product in play simply requires not forgetting that d ϕ {\displaystyle \mathrm {d} \phi } is a vector from the point of view of Φ {\displaystyle \Phi } itself. That is, given any two vectors v , w ∈ T Φ {\displaystyle v,w\in T\Phi } , the Riemannian metric g i j {\displaystyle g_{ij}} defines an inner product
Since d ϕ {\displaystyle \mathrm {d} \phi } is vector-valued d ϕ = ( d ϕ 1 , ⋯ , d ϕ n ) {\displaystyle \mathrm {d} \phi =(\mathrm {d} \phi ^{1},\cdots ,\mathrm {d} \phi ^{n})} on local charts, one also takes the inner product there as well. More verbosely,
The tension between these two inner products can be made even more explicit by noting that
is a bilinear form ; it is a pullback of the Riemann metric g i j {\displaystyle g_{ij}} . The individual ∂ μ ϕ i {\displaystyle \partial _{\mu }\phi ^{i}} can be taken as vielbeins . The Lagrangian density of the sigma model is then
for g μ ν {\displaystyle g_{\mu \nu }} the metric on M . {\displaystyle M.} Given this gluing-together, the d ϕ {\displaystyle \mathrm {d} \phi } can be interpreted as a solder form ; this is articulated more fully below.
Several interpretational and foundational remarks can be made about the classical (non-quantized) sigma model. The first of these is that the classical sigma model can be interpreted as a model of non-interacting quantum mechanics. The second concerns the interpretation of energy.
This follows directly from the expression
given above. Taking Φ = C {\displaystyle \Phi =\mathbb {C} } , the function ϕ : M → C {\displaystyle \phi :M\to \mathbb {C} } can be interpreted as a wave function , and its Laplacian the kinetic energy of that wave function. The ⟨ ⟨ ⋅ , ⋅ ⟩ ⟩ {\displaystyle \langle \!\langle \cdot ,\cdot \rangle \!\rangle } is just some geometric machinery reminding one to integrate over all space. The corresponding quantum mechanical notation is ϕ = | ψ ⟩ . {\displaystyle \phi =|\psi \rangle .} In flat space, the Laplacian is conventionally written as Δ = ∇ 2 {\displaystyle \Delta =\nabla ^{2}} . Assembling all these pieces together, the sigma model action is equivalent to
which is just the grand-total kinetic energy of the wave-function ψ ( x ) {\displaystyle \psi (x)} , up to a factor of ℏ / m {\displaystyle \hbar /m} . To conclude, the classical sigma model on C {\displaystyle \mathbb {C} } can be interpreted as the quantum mechanics of a free, non-interacting quantum particle. Obviously, adding a term of V ( ϕ ) {\displaystyle V(\phi )} to the Lagrangian results in the quantum mechanics of a wave-function in a potential. Taking Φ = C n {\displaystyle \Phi =\mathbb {C} ^{n}} is not enough to describe the n {\displaystyle n} -particle system, in that n {\displaystyle n} particles require n {\displaystyle n} distinct coordinates, which are not provided by the base manifold. This can be solved by taking n {\displaystyle n} copies of the base manifold.
It is very well-known that the geodesic structure of a Riemannian manifold is described by the Hamilton–Jacobi equations . [ 3 ] In thumbnail form, the construction is as follows. Both M {\displaystyle M} and Φ {\displaystyle \Phi } are Riemannian manifolds; the below is written for Φ {\displaystyle \Phi } , the same can be done for M {\displaystyle M} . The cotangent bundle T ∗ Φ {\displaystyle T^{*}\Phi } , supplied with coordinate charts , can always be locally trivialized , i.e.
The trivialization supplies canonical coordinates ( q 1 , ⋯ , q n , p 1 , ⋯ , p n ) {\displaystyle (q^{1},\cdots ,q^{n},p_{1},\cdots ,p_{n})} on the cotangent bundle. Given the metric tensor g i j {\displaystyle g_{ij}} on Φ {\displaystyle \Phi } , define the Hamiltonian function
where, as always, one is careful to note that the inverse of the metric is used in this definition: g i j g j k = δ k i . {\displaystyle g^{ij}g_{jk}=\delta _{k}^{i}.} Famously, the geodesic flow on Φ {\displaystyle \Phi } is given by the Hamilton–Jacobi equations
The geodesic flow is the Hamiltonian flow ; the solutions to the above are the geodesics of the manifold. Note, incidentally, that d H / d t = 0 {\displaystyle dH/dt=0} along geodesics; the time parameter t {\displaystyle t} is the distance along the geodesic.
The sigma model takes the momenta in the two manifolds T ∗ Φ {\displaystyle T^{*}\Phi } and T ∗ M {\displaystyle T^{*}M} and solders them together, in that d ϕ {\displaystyle \mathrm {d} \phi } is a solder form . In this sense, the interpretation of the sigma model as an energy functional is not surprising; it is in fact the gluing together of two energy functionals. Caution: the precise definition of a solder form requires it to be an isomorphism; this can only happen if M {\displaystyle M} and Φ {\displaystyle \Phi } have the same real dimension. Furthermore, the conventional definition of a solder form takes Φ {\displaystyle \Phi } to be a Lie group. Both conditions are satisfied in various applications.
The space Φ {\displaystyle \Phi } is often taken to be a Lie group , usually SU(N) , in the conventional particle physics models, O(N) in condensed matter theories, or as a symmetric space in supergravity models. Since symmetric spaces are defined in terms of their involution , their tangent space (i.e. the place where d ϕ {\displaystyle \mathrm {d} \phi } lives) naturally splits into even and odd parity subspaces. This splitting helps propel the dimensional reduction of Kaluza–Klein theories.
For the special case of Φ {\displaystyle \Phi } being a Lie group , the g i j {\displaystyle g_{ij}} is the metric tensor on the Lie group, formally called the Cartan tensor or the Killing form . The Lagrangian can then be written as the pullback of the Killing form. Note that the Killing form can be written as a trace over two matrices from the corresponding Lie algebra ; thus, the Lagrangian can also be written in a form involving the trace. With slight re-arrangements, it can also be written as the pullback of the Maurer–Cartan form .
A common variation of the sigma model is to present it on a symmetric space . The prototypical example is the chiral model , which takes the product
of the "left" and "right" chiral fields, and then constructs the sigma model on the "diagonal"
Such a quotient space is a symmetric space, and so one can generically take Φ = G / H {\displaystyle \Phi =G/H} where H ⊂ G {\displaystyle H\subset G} is the maximal subgroup of G {\displaystyle G} that is invariant under the Cartan involution . The Lagrangian is still written exactly as the above, either in terms of the pullback of the metric on G {\displaystyle G} to a metric on G / H {\displaystyle G/H} or as a pullback of the Maurer–Cartan form.
In physics, the most common and conventional statement of the sigma model begins with the definition
Here, the g − 1 ∂ μ g {\displaystyle g^{-1}\partial _{\mu }g} is the pullback of the Maurer–Cartan form , for g ∈ G {\displaystyle g\in G} , onto the spacetime manifold. The π m {\displaystyle \pi _{\mathfrak {m}}} is a projection onto the odd-parity piece of the Cartan involution. That is, given the Lie algebra g {\displaystyle {\mathfrak {g}}} of G {\displaystyle G} , the involution decomposes the space into odd and even parity components g = m ⊕ h {\displaystyle {\mathfrak {g}}={\mathfrak {m}}\oplus {\mathfrak {h}}} corresponding to the two eigenstates of the involution. The sigma model Lagrangian can then be written as
This is instantly recognizable as the first term of the Skyrme model .
The equivalent metric form of this is to write a group element g ∈ G {\displaystyle g\in G} as the geodesic g = exp ( θ i T i ) {\displaystyle g=\exp(\theta ^{i}T_{i})} of an element θ i T i ∈ g {\displaystyle \theta ^{i}T_{i}\in {\mathfrak {g}}} of the Lie algebra g {\displaystyle {\mathfrak {g}}} . The [ T i , T j ] = f i j k T k {\displaystyle [T_{i},T_{j}]={f_{ij}}^{k}T_{k}} are the basis elements for the Lie algebra; the f i j k {\displaystyle {f_{ij}}^{k}} are the structure constants of g {\displaystyle {\mathfrak {g}}} .
Plugging this directly into the above and applying the infinitesimal form of the Baker–Campbell–Hausdorff formula promptly leads to the equivalent expression
where t r ( T m T n ) {\displaystyle \mathrm {tr} (T_{m}T_{n})} is now obviously (proportional to) the Killing form, and the W i m {\displaystyle {W_{i}}^{m}} are the vielbeins that express the "curved" metric g i j {\displaystyle g_{ij}} in terms of the "flat" metric t r ( T m T n ) {\displaystyle \mathrm {tr} (T_{m}T_{n})} . The article on the Baker–Campbell–Hausdorff formula provides an explicit expression for the vielbeins. They can be written as
where M {\displaystyle M} is a matrix whose matrix elements are M j k = θ i f i j k {\displaystyle {M_{j}}^{k}=\theta ^{i}{f_{ij}}^{k}} .
For the sigma model on a symmetric space, as opposed to a Lie group, the T i {\displaystyle T_{i}} are limited to span the subspace m {\displaystyle {\mathfrak {m}}} instead of all of g = m ⊕ h {\displaystyle {\mathfrak {g}}={\mathfrak {m}}\oplus {\mathfrak {h}}} . The Lie commutator on m {\displaystyle {\mathfrak {m}}} will not be within m {\displaystyle {\mathfrak {m}}} ; indeed, one has [ m , m ] ⊂ h {\displaystyle [{\mathfrak {m}},{\mathfrak {m}}]\subset {\mathfrak {h}}} and so a projection is still needed.
The model can be extended in a variety of ways. Besides the aforementioned Skyrme model , which introduces quartic terms, the model may be augmented by a torsion term to yield the Wess–Zumino–Witten model .
Another possibility is frequently seen in supergravity models. Here, one notes that the Maurer–Cartan form g − 1 d g {\displaystyle g^{-1}dg} looks like "pure gauge". In the construction above for symmetric spaces, one can also consider the other projection
where, as before, the symmetric space corresponded to the split g = m ⊕ h {\displaystyle {\mathfrak {g}}={\mathfrak {m}}\oplus {\mathfrak {h}}} . This extra term can be interpreted as a connection on the fiber bundle M × H {\displaystyle M\times H} (it transforms as a gauge field). It is what is "left over" from the connection on G {\displaystyle G} . It can be endowed with its own dynamics, by writing
with F i = d A i {\displaystyle F^{i}=dA^{i}} . Note that the differential here is just "d", and not a covariant derivative; this is not the Yang–Mills stress-energy tensor. This term is not gauge invariant by itself; it must be taken together with the part of the connection that embeds into L μ {\displaystyle L_{\mu }} , so that taken together, the L μ {\displaystyle L_{\mu }} , now with the connection as a part of it, together with this term, forms a complete gauge invariant Lagrangian (which does have the Yang–Mills terms in it, when expanded out). | https://en.wikipedia.org/wiki/Sigma_model |
Sigma non-innocence is a special form of non-innocence , an oxidation characteristic in metal complexes . It is mainly discussed in coordination complexes of late transition metals in their high formal oxidation states. Complexes exhibiting sigma non-innocence differ from classical Werner coordination complexes in that their bonding and antibonding orbitals have an inverted distribution of metal and ligand character (cf. inverted ligand field ). The oxidation of the ligand and a lowered charge at the metal center renders the assignment of the oxidation state non-trivial.
Sigma non-innocence has been extensively discussed for the prototypical example of a copper complex [Cu(CF 3 ) 4 ] − [ 2 ] in conjunction with the concept of an inverted ligand field . [ 3 ] In 1995, Snyder suggested, based on his quantum chemical calculations, that this formal Cu(III) (d 8 ) complex would be more appropriately represented as a Cu(I) (d 10 ) complex. [ 1 ] Snyder pointed out that the frontier molecular orbitals of [Cu(CF 3 ) 4 ] − are dominated by ligand parentage due to the higher-lying ligand orbitals compared to the metal orbitals, and this inversion of the ligand field causes the d x2‑y2 orbital to be occupied and the lowest unoccupied molecular orbital (LUMO) to be ligand centered.
Later, Lancaster et al. experimentally validated this inverted ligand field electronic structure of [Cu(CF 3 ) 4 ] − using core spectroscopy techniques. [ 4 ] Their findings revealed that the 3d orbitals are nearly fully occupied, supporting the formulation of this ion as a Cu(I) species. The assignment of what would be typically called a Cu(III) species as Cu(I) indicates the sigma non-innocence of the perfluoromethyl ligands in the complex.
The researchers also examined the electronic structure of other formally Cu(III) complexes using Cu L 2,3 -edge X-ray absorption spectroscopy together with computational techniques. [ 5 ] They reported that all the Cu(III) species they studied except CuF 6 3– have significantly diminished metal d-character in their LUMOs compared to the formal d 8 assignment. This implies that ligand field inversion and sigma non-innocence are not unique to [Cu(CF 3 ) 4 ] − but is general in many systems.
Klein et al. computationally analyzed the electronic structure of a high valent Nickel complex "1". [ 7 ] This complex was previously reported to readily undergo aryl-CF 3 bond-forming reductive elimination. [ 6 ]
Klein et al. reported that this formally Ni(IV) complex is best described as Ni approaching the +II oxidation state. They used intrinsic bond orbital method to analyze the bonding of the complex and identified that the bond between C Ar and Ni is polarized to Ni with the partial charge on Ni (0.988) larger than the one on C Ar (0.973). They attributed the +II oxidation state of Ni to the oxidation of the aryl ligand due to sigma non-innocence.
Based on calculations, they also asserted that the formal reductive elimination from this complex is essentially redox neutral, with the Ni center retaining its Ni(II) state throughout the C-C bond-forming event. They interpreted the bond-formation mechanism as the nucleophilic CF 3 group attacking the electrophilic aryl group. | https://en.wikipedia.org/wiki/Sigma_non-innocence |
In organic chemistry , a sigmatropic reaction (from Greek τρόπος (trópos) ' turn ' ) is a pericyclic reaction wherein the net result is one sigma bond (σ-bond) is changed to another σ-bond in an intramolecular reaction . [ 1 ] In this type of rearrangement reaction , a substituent moves from one part of a π-system to another part with simultaneous rearrangement of the π-system. [ 2 ] True sigmatropic reactions are usually uncatalyzed , although Lewis acid catalysis is possible. Sigmatropic reactions often have transition-metal catalysts that form intermediates in analogous reactions. The most well-known of the sigmatropic rearrangements are the [3,3] Cope rearrangement , Claisen rearrangement , Carroll rearrangement , and the Fischer indole synthesis .
Sigmatropic rearrangements are concisely described by an order term [i,j] , which is defined as the migration of a σ-bond adjacent to one or more π systems to a new position (i−1) and (j−1) atoms removed from the original location of the σ-bond. [ 3 ] When the sum of i and j is an even number, this is an indication of the involvement of a neutral, all C atom chain. An odd number is an indication of the involvement of a charged C atom or of a heteroatom lone pair replacing a CC double bond. Thus, [1,5] and [3,3] shifts become [1,4] and [2,3] shifts with heteroatoms, while preserving symmetry considerations. Hydrogens are omitted in the third example for clarity.
A convenient means of determining the order of a given sigmatropic rearrangement is to number the atoms of the bond being broken as atom 1, and then count the atoms in each direction from the broken bond to the atoms that form the new σ-bond in the product, numbering consecutively. The numbers that correspond to the atoms forming the new bond are then separated by a comma and placed within brackets to create the sigmatropic reaction order descriptor. [ 4 ]
In the case of hydrogen atom migrations, a similar technique may be applied. When determining the order of a sigmatropic shift involving a hydrogen atom migration it is critical to count across all atoms involved in the reaction rather than only across the closest atoms. For example, the following hydrogen atom migration is of order [1,5], attained by counting counterclockwise through the π system, rather than the [1,3] order designation through the ring CH 2 group that would mistakenly result if counted clockwise.
As a general approach, one can simply draw the transition state of the reaction. For a sigmatropic reaction, the transition state will consist of two fragments, joined by the forming and breaking σ-bonds. The sigmatropic reaction is named as a [ i , j ]-sigmatropic rearrangement ( i ≤ j ) if these two fragments consist of i and j atoms. This is illustrated below, with the relevant fragments shown in color.
In principle, all sigmatropic shifts can occur with either a retention or inversion of the geometry of the migrating group, depending upon whether the original bonding lobe of the migrating atom or its other lobe is used to form the new bond. [ 4 ]
In cases of stereochemical retention, the migrating group translates without rotation into the bonding position, while in the case of stereochemical inversion the migrating group both rotates and translates to reach its bonded conformation.
However, another stereochemical transition effect equally capable of producing inversion or retention products is whether the migrating group remains on the original face of the π system after rebonding or instead transfers to the opposite face of the π system. If the migrating group remains on the same face of the π system, the shift is known as suprafacial , while if the migrating group transfers to the opposite face is called an antarafacial shift, [ 3 ] which are impossible for transformations that occur within small- or medium-sized rings.
In a thermal [1,3] hydride shift, a hydride moves three atoms. The Woodward–Hoffmann rules dictate that it would proceed in an antarafacial shift. Although such a shift is symmetry allowed, the Mobius topology required in the transition state prohibits such a shift because it is geometrically impossible, which accounts for the fact that enols do not isomerize without an acid or base catalyst . [ 4 ]
Thermal alkyl [1,3] shifts, similar to [1,3] hydride shifts, must proceed antarafacially. Here the geometry of the transition state is prohibitive, but an alkyl group , due to the nature of its orbitals, can invert its geometry, form a new bond with the back lobe of its sp 3 orbital, and therefore proceed via a suprafacial shift. These reactions are still not common in open-chain compounds because of the highly ordered nature of the transition state, which is more readily achieved in cyclic molecules. [ 4 ]
Photochemical [1,3] shifts should proceed through suprafacial shifts; however, most are non-concerted because they proceed through a triplet state (i.e., have a diradical mechanism, to which the Woodward-Hoffmann rules do not apply). [ 4 ]
A [1,5] shift involves the shift of 1 substituent (hydride, alkyl, or aryl ) down 5 atoms of a π system. Hydrogen has been shown to shift in both cyclic and open-chain compounds at temperatures at or above 200 ˚C. [ 4 ] These reactions are predicted to proceed suprafacially, via a Hückel-topology transition state.
Photoirradiation would require an antarafacial shift of hydrogen. Although rare, there are examples where antarafacial shifts are favored: [ 5 ]
In contrast to hydrogen [1,5] shifts, there have never been any observed [1,5] alkyl shifts in an open-chain compound. [ 4 ] Several studies have, however, been done to determine rate preferences for [1,5] alkyl shifts in cyclic systems: carbonyl and carboxyl > hydride> phenyl and vinyl >> alkyl. [ 6 ] [ 7 ]
Alkyl groups undergo [1,5] shifts very poorly, usually requiring high temperatures, however, for cyclohexadiene , the temperature for alkyl shifts isn't much higher than that for carbonyls, the best migratory group. A study showed that this is because alkyl shifts on cyclohexadienes proceed through a different mechanism. First the ring opens, followed by a [1,7] shift, and then the ring reforms electrocyclically : [ 8 ]
This same mechanistic process is seen below, without the final electrocyclic ring-closing reaction, in the interconversion of lumisterol to vitamin D 2 .
[1,7] sigmatropic shifts are predicted by the Woodward–Hoffmann rules to proceed in an antarafacial fashion, via a Mobius topology transition state. An antarafacial [1,7] shift is observed in the conversion of lumisterol to vitamin D 2 , where following an electrocyclic ring opening to previtamin D 2 , a methyl hydrogen shifts. [ 9 ]
Bicyclic nonatrienes also undergo [1,7] shifts in a so-called walk rearrangement , [ 10 ] which is the shift of divalent group, as part of a three-membered ring, in a bicyclic molecule .
[3,3] sigmatropic shifts are well studied sigmatropic rearrangements. The Woodward–Hoffman rules predict that these six- electron reactions would proceed suprafacially, via a Hückel topology transition state.
Discovered in 1912 by Rainer Ludwig Claisen , the Claisen rearrangement is the first recorded example of a [3,3]-sigmatropic rearrangement. [ 11 ] [ 12 ] [ 13 ] This rearrangement is a useful carbon -carbon bond -forming reaction . An example of Claisen rearrangement is the [3,3] rearrangement of an allyl vinyl ether , which upon heating yields a γ,δ-unsaturated carbonyl. The formation of a carbonyl group makes this reaction, unlike other sigmatropic rearrangements, inherently irreversible.
The ortho-Claisen rearrangement involves the [3,3] shift of an allyl phenyl ether to an intermediate which quickly tautomerizes to an ortho-substituted phenol .
When both the ortho positions on the benzene ring are blocked, a second [3,3] rearrangement will occur. This para-Claisen rearrangement ends with the tautomerization to a tri-substituted phenol.
The Cope rearrangement is an extensively studied organic reaction involving the [3,3] sigmatropic rearrangement of 1,5-dienes. [ 14 ] [ 15 ] [ 16 ] It was developed by Arthur C. Cope . For example, 3,4-dimethyl-1,5-hexadiene heated to 300 °C yields 2,6-octadiene.
In the oxy-Cope rearrangement , a hydroxyl group is added at C3 forming an enal or enone after keto-enol tautomerism of the intermediate enol: [ 17 ]
The Carroll rearrangement is a rearrangement reaction in organic chemistry and involves the transformation of a β- keto allyl ester into a α-allyl-β-ketocarboxylic acid. [ 18 ] This organic reaction is accompanied by decarboxylation and the final product is a γ,δ-allylketone. The Carroll rearrangement is an adaptation of the Claisen rearrangement and effectively a decarboxylative allylation .
The Fischer indole synthesis is a chemical reaction that produces the aromatic heterocycle indole from a (substituted) phenylhydrazine and an aldehyde or ketone under acidic conditions. [ 19 ] [ 20 ] The reaction was discovered in 1883 by Hermann Emil Fischer .
The choice of acid catalyst is very important. Brønsted acids such as HCl , H 2 SO 4 , polyphosphoric acid and p-toluenesulfonic acid have been used successfully. Lewis acids such as boron trifluoride , zinc chloride , iron(III) chloride , and aluminium chloride are also useful catalysts.
Several reviews have been published. [ 21 ] [ 22 ] [ 23 ]
Similar to [3,3] shifts, the Woodward-Hoffman rules predict that [5,5] sigmatropic shifts would proceed suprafacially, Hückel topology transition state. These reactions are rarer than [3,3] sigmatropic shifts, but this is mainly a function of the fact that molecules that can undergo [5,5] shifts are rarer than molecules that can undergo [3,3] shifts. [ 4 ]
An example of a 2,3-sigmatropic rearrangement is the 2,3-Wittig rearrangement :
The migration of a divalent group, such as O , S , N –R, or C–R 2 , which is part of a three-membered ring in a bicyclic molecule, is commonly referred to as a walk rearrangement. This can be formally characterized according to the Woodward-Hofmann rules as being a (1, n) sigmatropic shift. [ 24 ] An example of such a rearrangement is the shift of substituents on tropilidenes (1,3,5-cycloheptatrienes). When heated, the pi-system goes through an electrocyclic ring closing to form bicycle[4,1,0]heptadiene (norcaradiene). Thereafter follows a [1,5] alkyl shift and an electrocyclic ring opening.
Proceeding through a [1,5] shift, the walk rearrangement of norcaradienes is expected to proceed suprafacially with a retention of stereochemistry. Experimental observations, however, show that the 1,5-shifts of norcaradienes proceed antarafacially. [ 25 ] Theoretical calculations found the [1,5] shift to be a diradical process, but without involving any diradical minima on the potential energy surface . [ 26 ] | https://en.wikipedia.org/wiki/Sigmatropic_reaction |
A sign-value notation represents numbers using a sequence of numerals which each represent a distinct quantity, regardless of their position in the sequence. Sign-value notations are typically additive, subtractive, or multiplicative depending on their conventions for grouping signs together to collectively represent numbers. [ 1 ]
Although the absolute value of each sign is independent of its position, the value of the sequence as a whole may depend on the order of the signs, as with numeral systems which combine additive and subtractive notation, such as Roman numerals . There is no need for zero in sign-value notation.
Additive notation represents numbers by a series of numerals that added together equal the value of the number represented, much as tally marks are added together to represent a larger number. To represent multiples of the sign value, the same sign is simply repeated. In Roman numerals, for example, X means ten and L means fifty, so LXXX means eighty (50 + 10 + 10 + 10).
Although signs may be written in a conventional order the value of each sign does not depend on its place in the sequence, and changing the order does not affect the total value of the sequence in an additive system. Frequently used large numbers are often expressed using unique symbols to avoid excessive repetition. Aztec numerals , for example, use a tally of dots for numbers less than twenty alongside unique symbols for powers of twenty, including 400 and 8,000. [ 1 ]
Subtractive notation represents numbers by a series of numerals in which signs representing smaller values are typically subtracted from those representing larger values to equal the value of the number represented. In Roman numerals, for example, I means one and X means ten, so IX means nine (10 − 1). The consistent use of the subtractive system with Roman numerals was not standardised until after the widespread adoption of the printing press in Europe. [ 1 ]
Sign-value notation was the ancient way of writing numbers and only gradually evolved into place-value notation, also known as positional notation . Sign-value notations have been used across the world by a variety of cultures throughout history.
When ancient people wanted to write "two sheep" in clay, they could inscribe in clay a picture of two sheep; however, this would be impractical when they wanted to write "twenty sheep". In Mesopotamia they used small clay tokens to represent a number of a specific commodity, and strung the tokens like beads on a string, which were used for accounting. There was a token for one sheep and a token for ten sheep, and a different token for ten goats, etc.
To ensure that nobody could alter the number and type of tokens, they invented the bulla ; a clay envelope shaped like a hollow ball into which the tokens on a string were placed and then baked. If anybody contested the number, they could break open the clay envelope and do a recount. To avoid unnecessary damage to the record, they pressed archaic number signs on the outside of the envelope before it was baked, each sign similar in shape to the tokens they represented. Since there was seldom any need to break open the envelope, the signs on the outside became the first written language for writing numbers in clay, using sign-value notation. [ 2 ]
Initially, different systems of counting were used in relation to specific kinds of measurement. [ 3 ] Much like counting tokens, early Mesopotamian proto-cuneiform numerals often utilised different signs to count or measure different things, and identical signs could be used to represent different quantities depending on what was being counted or measured. [ 4 ] Eventually, the sexagesimal system was widely adopted by cuneiform -using cultures. [ 3 ] The sexagesimal sign-value system used by the Sumerians and the Akkadians would later evolve into the place-value system of Babylonian cuneiform numerals . | https://en.wikipedia.org/wiki/Sign-value_notation |
In computer science , the sign bit is a bit in a signed number representation that indicates the sign of a number. Although only signed numeric data types have a sign bit, it is invariably located in the most significant bit position, [ 1 ] so the term may be used interchangeably with "most significant bit" in some contexts.
Almost always, if the sign bit is 0, the number is non-negative (positive or zero). [ 1 ] If the sign bit is 1 then the number is negative. Formats other than two's complement integers allow a signed zero : distinct "positive zero" and "negative zero" representations, the latter of which does not correspond to the mathematical concept of a negative number .
When using a complement representation, to convert a signed number to a wider format the additional bits must be filled with copies of the sign bit in order to preserve its numerical value, [ 2 ] : 61–62 a process called sign extension or sign propagation . [ 3 ]
Two's complement is by far the most common format for signed integers. In Two's complement, the sign bit has the weight -2 w-1 where w is equal to the bits position in the number. [ 1 ] With an 8-bit integer, the sign bit would have the value of -2 8 -1 , or -128. Due to this value being larger than all the other bits combined, having this bit set would ultimately make the number negative, thus changing the sign.
Ones' complement is similar to Two's Complement, but the sign bit has the weight -(2 w-1 +1) where w is equal to the bits position in the number. [ citation needed ] With an 8-bit integer, the sign bit would have a value of -(2 8 -1 +1) , or -127. This allows for two types of zero : positive and negative, which is not possible with Two's complement.
Using sign magnitude , the sign bit directly determines the sign. If the sign bit is 0, the number is positive; if the sign bit is 1, the number is negative. [ 2 ] : 52–54 Similarly with Ones' Complement, this allows for both a positive and a negative zero.
Floating-point numbers, such as IEEE format , IBM format , VAX format, and even the format used by the Zuse Z1 and Z3 use a Sign and magnitude representation. [ citation needed ]
This computer science article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Sign_bit |
Sign extension (sometimes abbreviated as sext , particularly in mnemonics ) is the operation, in computer arithmetic , of increasing the number of bits of a binary number while preserving the number's sign (positive/negative) and value. This is done by appending digits to the most significant side of the number, following a procedure dependent on the particular signed number representation used.
For example, if six bits are used to represent the number " 00 1010 " (decimal positive 10) and the sign extends operation increases the word length to 16 bits, then the new representation is simply " 0000 0000 0000 1010 ". Thus, both the value and the fact that the value was positive are maintained.
If ten bits are used to represent the value " 11 1111 0001 " (decimal negative 15) using two's complement , and this is sign extended to 16 bits, the new representation is " 1111 1111 1111 0001 ". Thus, by padding the left side with ones, the negative sign and the value of the original number are maintained.
In the Intel x86 instruction set , for example, there are two ways of doing sign extension:
A similar concept is zero extension (sometimes abbreviated as zext ). In a move or convert operation, zero extension refers to setting the high bits of the destination to zero, rather than setting them to a copy of the most significant bit of the source. If the source of the operation is an unsigned number, then zero extension is usually the correct way to move it to a larger field while preserving its numeric value, while sign extension is correct for signed numbers.
In the x86 and x64 instruction sets, the movzx instruction ("move with zero extension") performs this function. For example, movzx ebx, al copies a byte from the al register to the low-order byte of ebx and then fills the remaining bytes of ebx with zeroes.
On x64, most instructions that write to the entirety of lower 32 bits of any of the general-purpose registers will zero the upper half of the destination register. For example, the instruction mov eax, 1234 will clear the upper 32 bits of the rax [ a ] register. | https://en.wikipedia.org/wiki/Sign_extension |
The sign of the horns is a hand gesture with a variety of meanings and uses in various cultures. It is formed by extending the index and little fingers while holding the middle and ring fingers down with the thumb.
In Hatha Yoga , a similar hand gesture – with the tips of middle and ring finger touching the thumb – is known as Apāna Mudrā , a gesture believed to rejuvenate the body. [ 1 ] In Indian classical dance forms, it symbolizes the lion . [ 1 ] In Buddhism , the Karana Mudrā is seen as an apotropaic gesture to expel demons , remove negative energy, and ward off evil . It is commonly found on depictions of Gautama Buddha . [ 1 ] [ 2 ] It is also found on the Song dynasty statue of Laozi , the founder of Taoism , on Mount Qingyuan , China. [ 3 ]
An apotropaic usage of the sign can be seen in Italy and in other Mediterranean cultures where, when confronted with unfortunate events, or simply when these events are mentioned, the sign of the horns may be given to ward off further bad luck. It is also used traditionally to counter or ward off the " evil eye " ( Italian : malocchio ). In Italy specifically, the gesture is known as the corna ('horns'). With fingers pointing down, it is a common Mediterranean apotropaic gesture, by which people seek protection in unlucky situations (a Mediterranean equivalent of knocking on wood ). The President of the Italian Republic , Giovanni Leone , startled the media when, while in Naples during an outbreak of cholera , he shook the hands of patients with one hand while with the other behind his back he superstitiously made the corna , presumably to ward off the disease or in reaction to being confronted by such misfortune. Very often it is accompanied by a characteristic superstitious invocation: "Tèee!", a slang form derived from "Tiè!", "Tieni!", ("Hold it !"), second person of the imperative of the verb "Tenere" ("To Hold").
In Italy and other parts of the Mediterranean region , the gesture must usually be performed with the fingers tilting downward or in a leveled position not pointed at someone and without movement to signify the warding off of bad luck; in the same region and elsewhere, the gesture may take a different, offensive, and insulting meaning if it is performed with fingers upward or if directed aggressively towards someone especially in a swiveling motion (see section below).
The sign of the horns is used during religious rituals in Wicca , to invoke or represent the Horned God . [ 4 ]
In LaVeyan Satanism , the sign of the horns is used as a traditional salutation, either for informal or ritual purposes. [ 5 ]
In many Mediterranean and Latin countries, such as Colombia, Greece, Italy, Portugal, Spain and Mexico, [ 6 ] [ 7 ] [ 8 ] [ 9 ] when directed towards someone, pointed upward, and/or swiveled back and forth, the sign offensively implies cuckoldry in regard to the targeted individual; the common words for cuckolded in Greek, Italian, Spanish, and Portuguese are, respectively, κερατάς ( keratas ), cornuto , cornudo and corno , literally meaning "horned [one]". In this particular case, in Italy, the gesture is often accompanied by the invocation: "Cornuto!" ("Cuckold!"). As previously stated above, in Italy and certain other Mediterranean countries, the sign, often when pointing downwards, but occasionally also upwards, can serve also as a talismanic gesture to ward off bad luck . [ 10 ] However, the positioning of the hand sign and the context in which it is used generally renders obvious to Italian and other Mediterranean people the meaning of the sign in a particular situation. During a European Union meeting in February 2002, Italian prime minister Silvio Berlusconi was photographed performing in a jocular manner the offensive " cornuto " version of gesture behind the back of Josep Piqué , the Spanish foreign minister. [ 11 ]
There is a 1927 jazz recording by the New Orleans Owls , "Throwin' the Horns", on 78 rpm , Columbia 1261-D. It has a humorous vocal by two of the band members. [ 12 ]
Ike Turner told in an interview that he used the sign in his piano playing on Howlin' Wolf 's blues song " How Many More Years " in 1951. [ 13 ]
Marlon Brando makes the sign whilst singing " Luck Be a Lady " in the 1955 film Guys and Dolls , seeming to indicate it was a sign for snake eyes in the craps game he is playing for the gamblers' souls. [ 14 ]
The 1969 back album cover for Witchcraft Destroys Minds & Reaps Souls on Mercury Records by Chicago-based psychedelic- occult rock band Coven , led by singer Jinx Dawson , pictured Coven band members giving the "sign of the horns". According to a Facebook post by Dawson, she used the sign as early as late 1967 when Coven started, to which she posted a photo showing her giving the sign on stage. [ 15 ]
Beginning in the early 1970s, the horns were known as the "P-Funk sign" to fans of Parliament-Funkadelic . It was used by George Clinton and Bootsy Collins as the password to the Mothership, [ 16 ] a central element in Parliament's science-fiction mythology , and fans used it in return to show their enthusiasm for the band. Collins is depicted showing the P-Funk sign on the cover of his 1977 album Ahh... The Name Is Bootsy, Baby! .
Ronnie James Dio was known for popularizing the sign of the horns in heavy metal . [ 16 ] [ 17 ] He claimed his Italian grandmother used it to ward off the evil eye (which is known in Italy as malocchio ). Dio began using the sign soon after joining the metal band Black Sabbath in 1979. The previous singer in the band, Ozzy Osbourne , was rather well known for using the "peace" sign at concerts, raising the index and middle finger in the form of a V. Dio, in an attempt to connect with the fans, wanted to similarly use a hand gesture. However, not wanting to copy Osbourne, he chose to use the sign his grandmother always made. [ 18 ] The horns became famous in metal concerts very soon after Black Sabbath's first tour with Dio. The sign would later be appropriated by heavy metal fans.
Geezer Butler of Black Sabbath can be seen "raising the horns" in a photograph taken in 1969. [ 19 ] The photograph is included in the CD booklet of the Symptom of the Universe: The Original Black Sabbath 1970–1978 2002 compilation album. This would indicate that there had been some association between the "horns" and heavy metal before Dio's popularization of it. Although The Beatles aren’t directly associated with heavy metal, John Lennon can be seen doing the "horn-sign" in a photograph already two years prior to Butler. The photoshoot was done for the promotion for their upcoming cartoon movie Yellow Submarine in late 1967. The official movie poster of 1968 showing the Beatles in cartoon form depicts Lennon performing the same gesture.
When asked if he was the one who introduced the hand gesture to metal subculture, Dio said in a 2001 interview:
I doubt very much if I would be the first one who ever did that. That's like saying I invented the wheel, I'm sure someone did that at some other point. I think you'd have to say that I made it fashionable. I used it so much and all the time and it had become my trademark until the Britney Spears audience decided to do it as well. So it kind of lost its meaning with that. But it was ... I was in Sabbath at the time. It was a symbol that I thought was reflective of what that band was supposed to be all about. It's not the devil's sign like we're here with the devil. It's an Italian thing I got from my Grandmother called the "Malocchio". It's to ward off the Evil Eye or to give the Evil Eye, depending on which way you do it. It's just a symbol but it had magical incantations and attitudes to it and I felt it worked very well with Sabbath. So I became very noted for it and then everybody else started to pick up on it and away it went. But I would never say I take credit for being the first to do it. I say because I did it so much that it became the symbol of rock and roll of some kind.
Gene Simmons of the rock group KISS attempted to claim the "devil horns" hand gesture for his own. According to CBS News, Simmons filed an application on June 16, 2017, with the United States Patent and Trademark Office for a trademark on the hand gesture he regularly shows during concerts and public appearances—thumb, index, and pinky fingers extended, with the middle and ring fingers folded down (like the ILY sign meaning "I love you" in the American Sign Language ). According to Simmons, this hand gesture was first commercially used—by him—on November 14, 1974. He claimed the hand gesture should be trademarked for "entertainment, namely live performances by a musical artist [and] personal appearances by a musical artist." [ 20 ] Simmons abandoned this application on June 21, 2017. [ 21 ]
The Japanese kawaii metal band Babymetal uses the kitsune sign, their own variation of the sign of the horns, symbolizing their personal deity, the Fox God. The middle, ring finger, and thumb join at the tips to form the snout, the extended index and pinky fingers are the ears. [ 22 ] [ 23 ] This gesture is similar in appearance to the salute of the Turanist Grey Wolves movement.
In text-based electronic communication, the sign of the horns is represented with the \../ , \m/ or |m| emoticon and sometimes with /../ . The Unicode character U+1F918 🤘 SIGN OF THE HORNS was introduced in Unicode 8.0 as an emoji , on June 17, 2015. [ 24 ]
The "sign of the horns" hand gesture is used in criminal gang subcultures to indicate membership or affiliation with Mara Salvatrucha . The significance is both the resemblance of an inverted "devil horns" to the Latin letter 'M', and in the broader demonic connotation, of fierceness and nonconformity.
Fans of Houston sports teams use the hand signal as a sign of support for the city's sports teams. Rising to prominence through Houston's hip-hop culture, this signal has become the defacto hand signal for the city. Referred to as "H's up" by the Houston Texans , this signal has been described as "featur[ing] the back of the hand facing out, hand held in front of the chest, and both middle and ring fingers curled under the thumb, with the index and pinky fingers straight like a bull's horns." [ 25 ] This signal has also been promoted by the Houston Astros , Houston Rockets , Houston Cougars , and Houston Dynamo FC .
Hook 'em Horns is the slogan and hand signal of the University of Texas at Austin (UT). Students and alumni of the university employ a greeting consisting of the phrase "Hook 'em" or "Hook 'em Horns" and also use the phrase as a parting good-bye or as the closing line in a letter or story. The gesture is meant to approximate the shape of the head and horns of the UT mascot, the Texas Longhorn Bevo . Rival schools such as the Oklahoma Sooners or Texas A&M Aggies will turn the horns upside down meaning "Horns Down" as an insult.
Fans of the University of South Florida Bulls use the same hand sign at their athletic events, except that the hand is turned around and facing the other way. With the middle and ring finger extending towards the person presenting the "Go Bulls" sign.
Fans of North Dakota State University Bison athletics also use a similar hand gesture, known as "Go Bison!" The pinky and index fingers are usually slightly bent, however, to mimic the shape of a bison 's horns.
Fans of North Carolina State University Wolfpack athletics use a similar gesture with the middle and ring fingers moving up and down over the thumb to mimic a wolf's jaw.
Fans of University of California, Irvine Anteaters use a similar sign with the middle and ring fingers out to resemble the head of an anteater.
Fans of University of Nevada, Reno Wolf Pack athletics use a similar sign with the middle and ring fingers out to resemble the wolf's snout.
A variation of this hand gesture is also used in the professional wrestling industry, which fans dub the "Too Sweet". It was possibly innovated by Scott Hall and the other members of The Kliq based on the Turkish Grey Wolves organization hand gesture according to Sean Waltman , and has since been attributed to other wrestling groups such as the nWo and Bullet Club , as well as individual wrestlers such as Finn Bálor .
Fans of University of Utah athletics, particularly football and gymnastics, use a gesture where the index and pinky finger are straight and parallel to each other, forming a block "U." [ 26 ]
Fans of Northwestern State University Demon athletics also use a similar hand gesture, known as "Fork 'em!" The pinky and index fingers are extended but a little more parallel to each other resembling the horns on a demon.
Arizona State University Sun Devil fans make a pitchfork sign by extending the index and middle fingers, as well as the pinky. The thumb holds down the ring finger to complete the gesture.
Fans of the Wichita State University Shockers frequently hold up their middle finger in addition to the pointer and pinky fingers as a reference to the comic sexual act .
Fans of the Grand Canyon University Antelopes use this hand gesture with a slight variation by touching the tips of the ring and middle finger with the thumb to form the shape of an antelope and its horns. Often followed by the phrase "Lopes up".
Fans of the Universidad de Chile soccer team use this gesture to represent their support for the team by forming a U-shaped hand gesture, often followed by the phrase "Grande la U".
Fans of University at Buffalo Buffalo Bulls athletics use the same hand sign at their athletic events. This gesture is meant to resemble a bull's horns.
In Russian children's folklore the sign of the horns (called koza , "goat") is associated with the nursery rhyme "Идёт коза рогатая" ("Here comes a horned goat"). When telling the rhyme to a toddler, the narrator tickles the child with the "horns" at the end of the rhyme. [ 27 ] [ 28 ] | https://en.wikipedia.org/wiki/Sign_of_the_horns |
In mathematics , a sign sequence , or ±1–sequence or bipolar sequence , is a sequence of numbers, each of which is either 1 or −1. One example is the sequence (1, −1, 1, −1, ...).
Such sequences are commonly studied in discrepancy theory .
Around 1932, mathematician Paul Erdős conjectured that for any infinite ±1-sequence ( x 1 , x 2 , … ) {\displaystyle (x_{1},x_{2},\ldots )} and any integer C , there exist integers k and d such that
The Erdős discrepancy problem asks for a proof or disproof of this conjecture.
In February 2014, Alexei Lisitsa and Boris Konev of the University of Liverpool showed that every sequence of 1161 or more elements satisfies the conjecture in the special case C = 2, which proves the conjecture for C ≤ 2. [ 1 ] This was the best such bound available at the time. Their proof relied on a SAT-solver computer algorithm whose output takes up 13 gigabytes of data, more than the entire text of Wikipedia at that time, so it cannot be independently verified by human mathematicians without further use of a computer. [ 2 ]
In September 2015, Terence Tao announced a proof of the conjecture, building on work done in 2010 during Polymath5 (a form of crowdsourcing applied to mathematics) and a suggestion made by German mathematician Uwe Stroinski on Tao's blog. [ 3 ] [ 4 ] His proof was published in 2016, as the first paper in the new journal Discrete Analysis . [ 5 ]
Erdős discrepancy of finite sequences has been proposed as a measure of local randomness in DNA sequences. [ 6 ] This is based on the fact that in the case of finite-length sequences discrepancy is bounded, and therefore one can determine the finite sequences with discrepancy less than a certain value. Those sequences will also be those that "avoid" certain periodicities. By comparing the expected versus observed distribution in the DNA or using other correlation measures, one can make conclusions related to the local behavior of DNA sequences.
A Barker code is a sequence of N values of +1 and −1,
such that
for all 1 ≤ v < N {\displaystyle 1\leq v<N} . [ 7 ]
Barker codes of lengths 11 and 13 are used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties. | https://en.wikipedia.org/wiki/Sign_sequence |
A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing , information theory and biology .
In signal processing, a signal is a function that conveys information about a phenomenon. [ 1 ] Any quantity that can vary over space or time can be used as a signal to share messages between observers. [ 2 ] The IEEE Transactions on Signal Processing includes audio , video , speech, image , sonar , and radar as examples of signals. [ 3 ] A signal may also be defined as any observable change in a quantity over space or time (a time series ), even if it does not carry information. [ a ]
In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with cell signaling . Signaling theory , in evolutionary biology , proposes that a substantial driver for evolution is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typically provided by a sensor , and often the original form of a signal is converted to another form of energy using a transducer . For example, a microphone converts an acoustic signal to a voltage waveform, and a speaker does the reverse. [ 1 ]
Another important property of a signal is its entropy or information content . Information theory serves as the formal study of signals and their content. The information of a signal is often accompanied by noise , which primarily refers to unwanted modifications of signals, but is often extended to include unwanted signals conflicting with desired signals ( crosstalk ). The reduction of noise is covered in part under the heading of signal integrity . The separation of desired signals from background noise is the field of signal recovery , [ 5 ] one branch of which is estimation theory , a probabilistic approach to suppressing random disturbances.
Engineering disciplines such as electrical engineering have advanced the design, study, and implementation of systems involving transmission , storage , and manipulation of information. In the latter half of the 20th century, electrical engineering itself separated into several disciplines: electronic engineering and computer engineering developed to specialize in the design and analysis of systems that manipulate physical signals, while design engineering developed to address the functional design of signals in user–machine interfaces .
Definitions specific to sub-fields are common:
Signals can be categorized in various ways. The most common [ verification needed ] distinction is between discrete and continuous spaces that the functions are defined over, for example, discrete and continuous-time domains. Discrete-time signals are often referred to as time series in other fields. Continuous-time signals are often referred to as continuous signals .
A second important distinction is between discrete-valued and continuous-valued. Particularly in digital signal processing , a digital signal may be defined as a sequence of discrete values, typically associated with an underlying continuous-valued physical process. In digital electronics , digital signals are the continuous-time waveform signals in a digital system, representing a bit-stream.
Signals may also be categorized by their spatial distributions as either point source signals (PSSs) or distributed source signals (DSSs). [ 2 ]
In Signals and Systems, signals can be classified according to many criteria, mainly: according to the different feature of values, classified into analog signals and digital signals ; according to the determinacy of signals, classified into deterministic signals and random signals; according to the strength of signals , classified into energy signals and power signals.
Two main types of signals encountered in practice are analog and digital . The figure shows a digital signal that results from approximating an analog signal by its values at particular time instants. Digital signals are quantized , while analog signals are continuous.
An analog signal is any continuous signal for which the time-varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. For example, in an analog audio signal , the instantaneous voltage of the signal varies continuously with the sound pressure . It differs from a digital signal , in which the continuous quantity is a representation of a sequence of discrete values which can only take on one of a finite number of values. [ 6 ] [ 7 ]
The term analog signal usually refers to electrical signals ; however, analog signals may use other mediums such as mechanical , pneumatic or hydraulic . An analog signal uses some property of the medium to convey the signal's information. For example, an aneroid barometer uses rotary position as the signal to convey pressure information. In an electrical signal, the voltage , current , or frequency of the signal may be varied to represent the information.
Any information may be conveyed by an analog signal; often such a signal is a measured response to changes in physical phenomena, such as sound , light , temperature , position, or pressure . The physical variable is converted to an analog signal by a transducer . For example, in sound recording, fluctuations in air pressure (that is to say, sound ) strike the diaphragm of a microphone which induces corresponding electrical fluctuations. The voltage or the current is said to be an analog of the sound.
A digital signal is a signal that is constructed from a discrete set of waveforms of a physical quantity so as to represent a sequence of discrete values. [ 8 ] [ 9 ] [ 10 ] A logic signal is a digital signal with only two possible values, [ 11 ] [ 12 ] and describes an arbitrary bit stream . Other types of digital signals can represent three-valued logic or higher valued logics.
Alternatively, a digital signal may be considered to be the sequence of codes represented by such a physical quantity. [ 13 ] The physical quantity may be a variable electric current or voltage, the intensity, phase or polarization of an optical or other electromagnetic field , acoustic pressure, the magnetization of a magnetic storage media, etc. Digital signals are present in all digital electronics , notably computing equipment and data transmission .
With digital signals, system noise, provided it is not too great, will not affect system operation whereas noise always degrades the operation of analog signals to some degree.
Digital signals often arise via sampling of analog signals, for example, a continually fluctuating voltage on a line that can be digitized by an analog-to-digital converter circuit, wherein the circuit will read the voltage level on the line, say, every 50 microseconds and represent each reading with a fixed number of bits. The resulting stream of numbers is stored as digital data on a discrete-time and quantized-amplitude signal. Computers and other digital devices are restricted to discrete time.
According to the strengths of signals, practical signals can be classified into two categories: energy signals and power signals. [ 14 ]
Energy signals: Those signals' energy are equal to a finite positive value, but their average powers are 0;
0 < E = ∫ − ∞ ∞ s 2 ( t ) d t < ∞ {\displaystyle 0<E=\int _{-\infty }^{\infty }s^{2}(t)dt<\infty }
Power signals: Those signals' average power are equal to a finite positive value, but their energy are infinite .
P = lim T → ∞ 1 T ∫ − T / 2 T / 2 s 2 ( t ) d t {\displaystyle P=\lim _{T\rightarrow \infty }{\frac {1}{T}}\int _{-T/2}^{T/2}s^{2}(t)dt}
Deterministic signals are those whose values at any time are predictable and can be calculated by a mathematical equation.
Random signals are signals that take on random values at any given time instant and must be modeled stochastically . [ 15 ]
An even signal satisfies the condition x ( t ) = x ( − t ) {\displaystyle x(t)=x(-t)}
or equivalently if the following equation holds for all t {\displaystyle t} and − t {\displaystyle -t} in the domain of x {\displaystyle x} :
An odd signal satisfies the condition x ( t ) = − x ( − t ) {\displaystyle x(t)=-x(-t)}
or equivalently if the following equation holds for all t {\displaystyle t} and − t {\displaystyle -t} in the domain of x {\displaystyle x} :
A signal is said to be periodic if it satisfies the condition:
x ( t ) = x ( t + T ) ∀ t ∈ [ t 0 , t m a x ] {\displaystyle x(t)=x(t+T)\quad \forall t\in [t_{0},t_{max}]} or x ( n ) = x ( n + N ) ∀ n ∈ [ n 0 , n m a x ] {\displaystyle x(n)=x(n+N)\quad \forall n\in [n_{0},n_{max}]}
Where:
T {\displaystyle T} = fundamental time period ,
1 / T = f {\displaystyle 1/T=f} = fundamental frequency .
The same can be applied to N {\displaystyle N} . A periodic signal will repeat for every period.
Signals can be classified as continuous or discrete time . In the mathematical abstraction, the domain of a continuous-time signal is the set of real numbers (or some interval thereof), whereas the domain of a discrete-time (DT) signal is the set of integers (or other subsets of real numbers). What these integers represent depends on the nature of the signal; most often it is time.
A continuous-time signal is any function which is defined at every time t in an interval, most commonly an infinite interval. A simple source for a discrete-time signal is the sampling of a continuous signal, approximating the signal by a sequence of its values at particular time instants.
If a signal is to be represented as a sequence of digital data, it is impossible to maintain exact precision – each number in the sequence must have a finite number of digits. As a result, the values of such a signal must be quantized into a finite set for practical representation. Quantization is the process of converting a continuous analog audio signal to a digital signal with discrete numerical values of integers.
Naturally occurring signals can be converted to electronic signals by various sensors . Examples include:
Signal processing is the manipulation of signals. A common example is signal transmission between different locations. The embodiment of a signal in electrical form is made by a transducer that converts the signal from its original form to a waveform expressed as a current or a voltage , or electromagnetic radiation , for example, an optical signal or radio transmission . Once expressed as an electronic signal, the signal is available for further processing by electrical devices such as electronic amplifiers and filters , and can be transmitted to a remote location by a transmitter and received using radio receivers .
In electrical engineering (EE) programs, signals are covered in a class and field of study known as signals and systems . Depending on the school, undergraduate EE students generally take the class as juniors or seniors, normally depending on the number and level of previous linear algebra and differential equation classes they have taken. [ 19 ]
The field studies input and output signals, and the mathematical representations between them known as systems, in four domains: time, frequency, s and z . Since signals and systems are both studied in these four domains, there are 8 major divisions of study. As an example, when working with continuous-time signals ( t ), one might transform from the time domain to a frequency or s domain; or from discrete time ( n ) to frequency or z domains. Systems also can be transformed between these domains like signals, with continuous to s and discrete to z .
Signals and systems is a subset of the field of mathematical modeling . It involves circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago with dynamical systems tools including differential equations, and recently, Lagrangians . Students are expected to understand the modeling tools as well as the mathematics, physics, circuit analysis, and transformations between the 8 domains.
Because mechanical engineering (ME) topics like friction, dampening etc. have very close analogies in signal science (inductance, resistance, voltage, etc.), many of the tools originally used in ME transformations (Laplace and Fourier transforms, Lagrangians, sampling theory, probability, difference equations, etc.) have now been applied to signals, circuits, systems and their components, analysis and design in EE. Dynamical systems that involve noise, filtering and other random or chaotic attractors and repellers have now placed stochastic sciences and statistics between the more deterministic discrete and continuous functions in the field. (Deterministic as used here means signals that are completely determined as functions of time).
EE taxonomists are still not decided where signals and systems falls within the whole field of signal processing vs. circuit analysis and mathematical modeling, but the common link of the topics that are covered in the course of study has brightened boundaries with dozens of books, journals, etc. called "Signals and Systems", and used as text and test prep for the EE, as well as, recently, computer engineering exams. [ 20 ] | https://en.wikipedia.org/wiki/Signal |
A signal-flow graph or signal-flowgraph ( SFG ), invented by Claude Shannon , [ 1 ] but often called a Mason graph after Samuel Jefferson Mason who coined the term, [ 2 ] is a specialized flow graph , a directed graph in which nodes represent system variables, and branches (edges, arcs, or arrows) represent functional connections between pairs of nodes. Thus, signal-flow graph theory builds on that of directed graphs (also called digraphs ), which includes as well that of oriented graphs . This mathematical theory of digraphs exists, of course, quite apart from its applications. [ 3 ] [ 4 ]
SFGs are most commonly used to represent signal flow in a physical system and its controller(s), forming a cyber-physical system . Among their other uses are the representation of signal flow in various electronic networks and amplifiers, digital filters , state-variable filters and some other types of analog filters. In nearly all literature, a signal-flow graph is associated with a set of linear equations .
Wai-Kai Chen wrote: "The concept of a signal-flow graph was originally worked out by Shannon [1942] [ 1 ] in dealing with analog computers. The greatest credit for the formulation of signal-flow graphs is normally extended to Mason [1953], [ 2 ] [1956]. [ 5 ] He showed how to use the signal-flow graph technique to solve some difficult electronic problems in a relatively simple manner. The term signal flow graph was used because of its original application to electronic problems and the association with electronic signals and flowcharts of the systems under study." [ 6 ]
Lorens wrote: "Previous to Mason 's work, C. E. Shannon [ 1 ] worked out a number of the properties of what are now known as flow graphs. Unfortunately, the paper originally had a restricted classification and very few people had access to the material." [ 7 ]
"The rules for the evaluation of the graph determinant of a Mason Graph were first given and proven by Shannon [1942] using mathematical induction. His work remained essentially unknown even after Mason published his classical work in 1953. Three years later, Mason [1956] rediscovered the rules and proved them by considering the value of a determinant and how it changes as variables are added to the graph. [...]" [ 8 ]
Robichaud et al. identify the domain of application of SFGs as follows: [ 9 ]
The following illustration and its meaning were introduced by Mason to illustrate basic concepts: [ 2 ]
In the simple flow graphs of the figure, a functional dependence of a node is indicated by an incoming arrow, the node originating this influence is the beginning of this arrow, and in its most general form the signal flow graph indicates by incoming arrows only those nodes that influence the processing at the receiving node, and at each node, i , the incoming variables are processed according to a function associated with that node, say F i . The flowgraph in (a) represents a set of explicit relationships:
Node x 1 is an isolated node because no arrow is incoming; the equations for x 2 and x 3 have the graphs shown in parts (b) and (c) of the figure.
These relationships define for every node a function that processes the input signals it receives. Each non-source node combines the input signals in some manner, and broadcasts a resulting signal along each outgoing branch. "A flow graph, as defined originally by Mason, implies a set of functional relations, linear or not." [ 9 ]
However, the commonly used Mason graph is more restricted, assuming that each node simply sums its incoming arrows, and that each branch involves only the initiating node involved. Thus, in this more restrictive approach, the node x 1 is unaffected while:
and now the functions f ij can be associated with the signal-flow branches ij joining the pair of nodes x i , x j , rather than having general relationships associated with each node. A contribution by a node to itself like f 33 for x 3 is called a self-loop . Frequently these functions are simply multiplicative factors (often called transmittances or gains ), for example, f ij (x j )=c ij x j , where c is a scalar, but possibly a function of some parameter like the Laplace transform variable s . Signal-flow graphs are very often used with Laplace-transformed signals, because then they represent systems of Linear differential equations . In this case the transmittance, c(s) , often is called a transfer function .
In general, there are several ways of choosing the variables in a complex system. Corresponding to each choice, a system of equations can be written and each system of equations can be represented in a graph. This formulation of the equations becomes direct and automatic if one has at his disposal techniques which permit the drawing of a graph directly from the schematic diagram of the system under study. The structure of the graphs thus obtained is related in a simple manner to the topology of the schematic diagram , and it becomes unnecessary to consider the equations , even implicitly, to obtain the graph. In some cases, one has simply to imagine the flow graph in the schematic diagram and the desired answers can be obtained without even drawing the flow graph.
Robichaud et al. wrote: "The signal flow graph contains the same information as the equations from which it is derived; but there does not exist a one-to-one correspondence between the graph and the system of equations. One system will give different graphs according to the order in which the equations are used to define the variable written on the left-hand side." [ 9 ] If all equations relate all dependent variables, then there are n! possible SFGs to choose from. [ 12 ]
Linear signal-flow graph (SFG) methods only apply to linear time-invariant systems , as studied by their associated theory . When modeling a system of interest, the first step is often to determine the equations representing the system's operation without assigning causes and effects (this is called acausal modeling). [ 13 ] A SFG is then derived from this system of equations.
A linear SFG consists of nodes indicated by dots and weighted directional branches indicated by arrows. The nodes are the variables of the equations and the branch weights are the coefficients. Signals may only traverse a branch in the direction indicated by its arrow. The elements of a SFG can only represent the operations of multiplication by a coefficient and addition, which are sufficient to represent the constrained equations. When a signal traverses a branch in its indicated direction, the signal is multiplied the weight of the branch. When two or more branches direct into the same node, their outputs are added.
For systems described by linear algebraic or differential equations, the signal-flow graph is mathematically equivalent to the system of equations describing the system, and the equations governing the nodes are discovered for each node by summing incoming branches to that node. These incoming branches convey the contributions of the other nodes, expressed as the connected node value multiplied by the weight of the connecting branch, usually a real number or function of some parameter (for example a Laplace transform variable s ).
For linear active networks, Choma writes: [ 14 ] "By a 'signal flow representation' [or 'graph', as it is commonly referred to] we mean a diagram that, by displaying the algebraic relationships among relevant branch variables of network, paints an unambiguous picture of the way an applied input signal ‘flows’ from input-to-output ... ports."
A motivation for a SFG analysis is described by Chen: [ 15 ]
A linear signal flow graph is related to a system of linear equations [ 16 ] of the following form:
The figure to the right depicts various elements and constructs of a signal flow graph (SFG). [ 17 ]
Terms used in linear SFG theory also include: [ 17 ]
A signal-flow graph may be simplified by graph transformation rules. [ 19 ] [ 20 ] [ 21 ] These simplification rules are also referred to as signal-flow graph algebra . [ 22 ] The purpose of this reduction is to relate the dependent variables of interest (residual nodes, sinks) to its independent variables (sources).
The systematic reduction of a linear signal-flow graph is a graphical method equivalent to the Gauss-Jordan elimination method for solving linear equations. [ 23 ]
The rules presented below may be applied over and over until the signal flow graph is reduced to its "minimal residual form". Further reduction can require loop elimination or the use of a "reduction formula" with the goal to directly connect sink nodes representing the dependent variables to the source nodes representing the independent variables. By these means, any signal-flow graph can be simplified by successively removing internal nodes until only the input and output and index nodes remain. [ 24 ] [ 25 ] Robichaud described this process of systematic flow-graph reduction:
The reduction of a graph proceeds by the elimination of certain nodes to obtain a residual graph showing only the variables of interest. This elimination of nodes is called " node absorption ". This method is close to the familiar process of successive eliminations of undesired variables in a system of equations. One can eliminate a variable by removing the corresponding node in the graph. If one reduces the graph sufficiently, it is possible to obtain the solution for any variable and this is the objective which will be kept in mind in this description of the different methods of reduction of the graph. In practice, however, the techniques of reduction will be used solely to transform the graph to a residual graph expressing some fundamental relationships. Complete solutions will be more easily obtained by application of Mason's rule . [ 26 ] The graph itself programs the reduction process. Indeed a simple inspection of the graph readily suggests the different steps of the reduction which are carried out by elementary transformations, by loop elimination, or by the use of a reduction formula. [ 26 ]
For digitally reducing a flow graph using an algorithm, Robichaud extends the notion of a simple flow graph to a generalized flow graph:
Before describing the process of reduction...the correspondence between the graph and a system of linear equations ... must be generalized... The generalized graphs will represent some operational relationships between groups of variables ...To each branch of the generalized graph is associated a matrix giving the relationships between the variables represented by the nodes at the extremities of that branch... [ 27 ] The elementary transformations [defined by Robichaud in his Figure 7.2, p. 184] and the loop reduction permit the elimination of any node j of the graph by the reduction formula :[described in Robichaud's Equation 7-1]. With the reduction formula, it is always possible to reduce a graph of any order... [After reduction] the final graph will be a cascade graph in which the variables of the sink nodes are explicitly expressed as functions of the sources. This is the only method for reducing the generalized graph since Mason's rule is obviously inapplicable. [ 28 ]
The definition of an elementary transformation varies from author to author:
Parallel edges. Replace parallel edges with a single edge having a gain equal to the sum of original gains.
The graph on the left has parallel edges between nodes. On the right, these parallel edges have been replaced with a single edge having a gain equal to the sum of the gains on each original edge.
The equations corresponding to the reduction between N and node I 1 are:
Outflowing edges. Replace outflowing edges with edges directly flowing from the node's sources.
The graph on the left has an intermediate node N between nodes from which it has inflows, and nodes to which it flows out.
The graph on the right shows direct flows between these node sets, without transiting via N .
For the sake of simplicity, N and its inflows are not represented. The outflows from N are eliminated.
The equations corresponding to the reduction directly relating N' s input signals to its output signals are:
Zero-signal nodes.
Eliminate outflowing edges from a node determined to have a value of zero.
If the value of a node is zero, its outflowing edges can be eliminated.
Nodes without outflows.
Eliminate a node without outflows.
In this case, N is not a variable of interest, and it has no outgoing edges; therefore, N , and its inflowing edges, can be eliminated.
Self-looping edge. Replace looping edges by adjusting the gains on the incoming edges.
The graph on the left has a looping edge at node N , with a gain of g . On the right, the looping edge has been eliminated, and all inflowing edges have their gain divided by (1-g) .
The equations corresponding to the reduction between N and all its input signals are:
The above procedure for building the SFG from an acausal system of equations and for solving the SFG's gains have been implemented [ 31 ] as an add-on to MATHLAB 68 , [ 32 ] an on-line system providing machine aid for the mechanical symbolic processes encountered in analysis .
Signal flow graphs can be used to solve sets of simultaneous linear equations. [ 33 ] The set of equations must be consistent and all equations must be linearly independent.
For M equations with N unknowns where each y j is a known value and each x j is an unknown value, there is equation for each known of the following form.
Although it is feasible, particularly for simple cases, to establish a signal flow graph using the equations in this form, some rearrangement allows a general procedure that works easily for any set of equations, as now is presented. To proceed, first the equations are rewritten as
and further rewritten as
and finally rewritten as
The signal-flow graph is now arranged by selecting one of these equations and addressing the node on the right-hand side. This is the node for which the node connects to itself with the branch of weight including a '+1', making a self-loop in the flow graph. The other terms in that equation connect this node first to the source in this equation and then to all the other branches incident on this node. Every equation is treated this way, and then each incident branch is joined to its respective emanating node. For example, the case of three variables is shown in the figure, and the first equation is:
where the right side of this equation is the sum of the weighted arrows incident on node x 1 .
As there is a basic symmetry in the treatment of every node, a simple starting point is an arrangement of nodes with each node at one vertex of a regular polygon. When expressed using the general coefficients { c in }, the environment of each node is then just like all the rest apart from a permutation of indices. Such an implementation for a set of three simultaneous equations is seen in the figure. [ 34 ]
Often the known values, y j are taken as the primary causes and the unknowns values, x j to be effects, but regardless of this interpretation, the last form for the set of equations can be represented as a signal-flow graph. This point is discussed further in the subsection Interpreting 'causality' .
In the most general case, the values for all the x k variables can be calculated by computing Mason's gain formula for the path from each y j to each x k and using superposition.
In general, there are N-1 paths from y j to variable x k so the computational effort to calculated G kj is proportional to N-1.
Since there are M values of y j , G kj must be computed M times for a single value of x k . The computational effort to calculate a single x k variable is proportional to (N-1)(M). The effort to compute all the x k variables is proportional to (N)(N-1)(M). If there are N equations and N unknowns, then the computation effort is on the order of N 3 .
For some authors, a linear signal-flow graph is more constrained than a block diagram , [ 35 ] in that the SFG rigorously describes linear algebraic equations represented by a directed graph.
For other authors, linear block diagrams and linear signal-flow graphs are equivalent ways of depicting a system, and either can be used to solve the gain. [ 36 ]
A tabulation of the comparison between block diagrams and signal-flow graphs is provided by Bakshi & Bakshi, [ 37 ] and another tabulation by Kumar. [ 38 ] According to Barker et al. : [ 39 ]
In the figure, a simple block diagram for a feedback system is shown with two possible interpretations as a signal-flow graph. The input R(s) is the Laplace-transformed input signal; it is shown as a source node in the signal-flow graph (a source node has no input edges). The output signal C(s) is the Laplace-transformed output variable. It is represented as a sink node in the flow diagram (a sink has no output edges). G(s) and H(s) are transfer functions, with H(s) serving to feed back a modified version of the output to the input, B(s) . The two flow graph representations are equivalent.
The term "cause and effect" was applied by Mason to SFGs: [ 2 ]
and has been repeated by many later authors: [ 40 ]
However, Mason's paper is concerned to show in great detail how a set of equations is connected to an SFG, an emphasis unrelated to intuitive notions of "cause and effect". Intuitions can be helpful for arriving at an SFG or for gaining insight from an SFG, but are inessential to the SFG. The essential connection of the SFG is to its own set of equations, as described, for example, by Ogata: [ 41 ]
There is no reference to "cause and effect" here, and as said by Barutsky: [ 42 ]
The term "cause and effect" may be misinterpreted as it applies to the SFG, and taken incorrectly to suggest a system view of causality, [ 43 ] rather than a computationally based meaning. To keep discussion clear, it may be advisable to use the term "computational causality", as is suggested for bond graphs : [ 44 ]
The term "computational causality" is explained using the example of current and voltage in a resistor: [ 45 ]
A computer program or algorithm can be arranged to solve a set of equations using various strategies. They differ in how they prioritize finding some of the variables in terms of the others, and these algorithmic decisions, which are simply about solution strategy, then set up the variables expressed as dependent variables earlier in the solution to be "effects", determined by the remaining variables that now are "causes", in the sense of "computational causality".
Using this terminology, it is computational causality, not system causality, that is relevant to the SFG. There exists a wide-ranging philosophical debate, not concerned specifically with the SFG, over connections between computational causality and system causality. [ 46 ]
Signal-flow graphs can be used for analysis, that is for understanding a model of an existing system, or for synthesis, that is for determining the properties of a design alternative.
When building a model of a dynamic system, a list of steps is provided by Dorf & Bishop: [ 47 ]
In this workflow, equations of the physical system's mathematical model are used to derive the signal-flow graph equations.
Signal-flow graphs have been used in Design Space Exploration (DSE) , as an intermediate representation towards a physical implementation. The DSE process seeks a suitable solution among different alternatives. In contrast with the typical analysis workflow, where a system of interest is first modeled with the physical equations of its components, the specification for synthesizing a design could be a desired transfer function. For example, different strategies would create different signal-flow graphs, from which implementations are derived. [ 48 ] Another example uses an annotated SFG as an expression of the continuous-time behavior, as input to an architecture generator [ 49 ]
Shannon's formula is an analytic expression for calculating the gain of an interconnected set of amplifiers in an analog computer. During World War II, while investigating the functional operation of an analog computer, Claude Shannon developed his formula. Because of wartime restrictions, Shannon's work was not published at that time, and, in 1952, Mason rediscovered the same formula.
William W. Happ generalized the Shannon formula for topologically closed systems. [ 50 ] The Shannon-Happ formula can be used for deriving transfer functions, sensitivities, and error functions. [ 51 ]
For a consistent set of linear unilateral relations, the Shannon-Happ formula expresses the solution using direct substitution (non-iterative). [ 51 ] [ 52 ]
NASA's electrical circuit software NASAP is based on the Shannon-Happ formula. [ 51 ] [ 52 ]
The amplification of a signal V 1 by an amplifier with gain a 12 is described mathematically by
This relationship represented by the signal-flow graph of Figure 1. is that V 2 is dependent on V 1 but it implies no dependency of V 1 on V 2 . See Kou page 57. [ 53 ]
A possible SFG for the asymptotic gain model for a negative feedback amplifier is shown in Figure 3, and leads to the equation for the gain of this amplifier as
The interpretation of the parameters is as follows: T = return ratio , G ∞ = direct amplifier gain, G 0 = feedforward (indicating the possible bilateral nature of the feedback, possibly deliberate as in the case of feedforward compensation ). Figure 3 has the interesting aspect that it resembles Figure 2 for the two-port network with the addition of the extra feedback relation x 2 = T y 1 .
From this gain expression an interpretation of the parameters G 0 and G ∞ is evident, namely:
There are many possible SFG's associated with any particular gain relation. Figure 4 shows another SFG for the asymptotic gain model that can be easier to interpret in terms of a circuit. In this graph, parameter β is interpreted as a feedback factor and A as a "control parameter", possibly related to a dependent source in the circuit. Using this graph, the gain is
To connect to the asymptotic gain model, parameters A and β cannot be arbitrary circuit parameters, but must relate to the return ratio T by:
and to the asymptotic gain as:
Substituting these results into the gain expression,
which is the formula of the asymptotic gain model.
The figure to the right depicts a circuit that contains a y -parameter two-port network . V in is the input of the circuit and V 2 is the output. The two-port equations impose a set of linear constraints between its port voltages and currents. The terminal equations impose other constraints. All these constraints are represented in the SFG (Signal Flow Graph) below the circuit. There is only one path from input to output which is shown in a different color and has a (voltage) gain of -R L y 21 . There are also three loops: -R in y 11 , -R L y 22 , R in y 21 R L y 12 . Sometimes a loop indicates intentional feedback but it can also indicate a constraint on the relationship of two variables. For example, the equation that describes a resistor says that the ratio of the voltage across the resistor to the current through the resistor is a constant which is called the resistance. This can be interpreted as the voltage is the input and the current is the output, or the current is the input and the voltage is the output, or merely that the voltage and current have a linear relationship. Virtually all passive two terminal devices in a circuit will show up in the SFG as a loop.
The SFG and the schematic depict the same circuit, but the schematic also suggests the circuit's purpose. Compared to the schematic, the SFG is awkward but it does have the advantage that the input to output gain can be written down by inspection using Mason's rule .
This example is representative of a SFG (signal-flow graph) used to represent a servo control system and illustrates several features of SFGs. Some of the loops (loop 3, loop 4 and loop 5) are extrinsic intentionally designed feedback loops. These are shown with dotted lines. There are also intrinsic loops (loop 0, loop1, loop2) that are not intentional feedback loops, although they can be analyzed as though they were. These loops are shown with solid lines. Loop 3 and loop 4 are also known as minor loops because they are inside a larger loop.
See Mason's rule for development of Mason's Gain Formula for this example.
There is some confusion in literature about what a signal-flow graph is; Henry Paynter , inventor of bond graphs , writes: "But much of the decline of signal-flow graphs [...] is due in part to the mistaken notion that the branches must be linear and the nodes must be summative. Neither assumption was embraced by Mason, himself !" [ 55 ]
A state transition SFG or state diagram is a simulation diagram for a system of equations, including the initial conditions of the states. [ 56 ]
Closed flowgraphs describe closed systems and have been utilized to provide a rigorous theoretical basis for topological techniques of circuit analysis. [ 50 ]
Mason introduced both nonlinear and linear flow graphs. To clarify this point, Mason wrote : "A linear flow graph is one whose associated equations are linear." [ 2 ]
It we denote by x j the signal at node j , the following are examples of node functions that do not pertain to a linear time-invariant system : | https://en.wikipedia.org/wiki/Signal-flow_graph |
The signal-to-crosstalk ratio at a specified point in a circuit is the ratio of the power of the wanted signal to the power of the unwanted signal from another channel .
The signals are adjusted in each channel so that they are of equal power at the zero transmission level point in their respective channels.
The signal-to- crosstalk ratio is usually expressed in dB .
This electronics-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Signal-to-crosstalk_ratio |
In information theory and telecommunication engineering, the signal-to-interference-plus-noise ratio ( SINR [ 1 ] ) (also known as the signal-to-noise-plus-interference ratio ( SNIR ) [ 2 ] ) is a quantity used to give theoretical upper bounds on channel capacity (or the rate of information transfer) in wireless communication systems such as networks. Analogous to the signal-to-noise ratio (SNR) used often in wired communications systems, the SINR is defined as the power of a certain signal of interest divided by the sum of the interference power (from all the other interfering signals) and the power of some background noise. If the power of noise term is zero, then the SINR reduces to the signal-to-interference ratio (SIR). Conversely, zero interference reduces the SINR to the SNR, which is used less often when developing mathematical models of wireless networks such as cellular networks . [ 3 ]
The complexity and randomness of certain types of wireless networks and signal propagation has motivated the use of stochastic geometry models in order to model the SINR, particularly for cellular or mobile phone networks. [ 4 ]
SINR is commonly used in wireless communication as a way to measure the quality of wireless connections. Typically, the energy of a signal fades with distance, which is referred to as a path loss in wireless networks. Conversely, in wired networks the existence of a wired path between the sender or transmitter and the receiver determines the correct reception of data. In a wireless network one has to take other factors into account (e.g. the background noise, interfering strength of other simultaneous transmission). The concept of SINR attempts to create a representation of this aspect.
The definition of SINR is usually defined for a particular receiver (or user). In particular, for a receiver located at some point x in space (usually, on the plane), then its corresponding SINR given by
where P is the power of the incoming signal of interest, I is the interference power of the other (interfering) signals in the network, and N is some noise term, which may be a constant or random. Like other ratios in electronic engineering and related fields, the SINR is often expressed in decibels or dB.
To develop a mathematical model for estimating the SINR, a suitable mathematical model is needed to represent the propagation of the incoming signal and the interfering signals. A common model approach is to assume the propagation model consists of a random component and non-random (or deterministic) component. [ 5 ] [ 6 ]
The deterministic component seeks to capture how a signal decays or attenuates as it travels a medium such as air, which is done by introducing a path-loss or attenuation function. A common choice for the path-loss function is a simple power-law. For example, if a signal travels from point x to point y , then it decays by a factor given by the path-loss function
where the path-loss exponent α>2 , and |x-y| denotes the distance between point y of the user and the signal source at point x . Although this model suffers from a singularity (when x=y ), its simple nature results in it often being used due to the relatively tractable models it gives. [ 3 ] Exponential functions are sometimes used to model fast decaying signals. [ 1 ]
The random component of the model entails representing multipath fading of the signal, which is caused by signals colliding with and reflecting off various obstacles such as buildings. This is incorporated into the model by introducing a random variable with some probability distribution . The probability distribution is chosen depending on the type of fading model and include Rayleigh , Rician , log-normal shadow (or shadowing), and Nakagami .
The propagation model leads to a model for the SINR. [ 2 ] [ 6 ] [ 4 ] Consider a collection of n {\displaystyle n} base stations located at points x 1 {\displaystyle x_{1}} to x n {\displaystyle x_{n}} in the plane or 3D space. Then for a user located at, say x = 0 {\displaystyle x=0} , then the SINR for a signal coming from base station, say, x i {\displaystyle x_{i}} , is given by
where F i {\displaystyle F_{i}} are fading random variables of some distribution. Under the simple power-law path-loss model becomes
In wireless networks, the factors that contribute to the SINR are often random (or appear random) including the signal propagation and the positioning of network transmitters and receivers. Consequently, in recent years this has motivated research in developing tractable stochastic geometry models in order to estimate the SINR in wireless networks. The related field of continuum percolation theory has also been used to derive bounds on the SINR in wireless networks. [ 2 ] [ 4 ] [ 7 ] | https://en.wikipedia.org/wiki/Signal-to-interference-plus-noise_ratio |
The signal-to-interference ratio ( SIR or S/I ), also known as the carrier-to-interference ratio ( CIR or C/I ), is the quotient between the average received modulated carrier power S or C and the average received co-channel interference power I , i.e. crosstalk , from other transmitters than the useful signal. [ 1 ] [ 2 ]
The CIR resembles the carrier-to-noise ratio (CNR or C/N ), which is the signal-to-noise ratio (SNR or S/N ) of a modulated signal before demodulation. A distinction is that interfering radio transmitters contributing to I may be controlled by radio resource management , while N involves noise power from other sources, typically additive white Gaussian noise (AWGN).
The CIR ratio is studied in interference limited systems, i.e. where I dominates over N , typically in cellular radio systems and broadcasting systems where frequency channels are reused in view to achieve high level of area coverage. The C/N is studied in noise limited systems. If both situations can occur, the carrier-to-noise-and-interference ratio (CNIR or C/(N+I) ) may be studied.
This article related to telecommunications is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Signal-to-interference_ratio |
Signal-to-noise ratio ( SNR or S/N ) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise . SNR is defined as the ratio of signal power to noise power , often expressed in decibels . A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise.
SNR is an important parameter that affects the performance and quality of systems that process or transmit signals, such as communication systems , audio systems , radar systems , imaging systems , and data acquisition systems. A high SNR means that the signal is clear and easy to detect or interpret, while a low SNR means that the signal is corrupted or obscured by noise and may be difficult to distinguish or recover. SNR can be improved by various methods, such as increasing the signal strength, reducing the noise level, filtering out unwanted noise, or using error correction techniques.
SNR also determines the maximum possible amount of data that can be transmitted reliably over a given channel, which depends on its bandwidth and SNR. This relationship is described by the Shannon–Hartley theorem , which is a fundamental law of information theory.
SNR can be calculated using different formulas depending on how the signal and noise are measured and defined. The most common way to express SNR is in decibels, which is a logarithmic scale that makes it easier to compare large or small values. Other definitions of SNR may use different factors or bases for the logarithm, depending on the context and application.
One definition of signal-to-noise ratio is the ratio of the power of a signal (meaningful input) to the power of background noise (meaningless or unwanted input):
where P is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system bandwidth .
The signal-to-noise ratio of a random variable ( S ) to random noise N is: [ 1 ]
S N R = E [ S 2 ] E [ N 2 ] , {\displaystyle \mathrm {SNR} ={\frac {\mathrm {E} [S^{2}]}{\mathrm {E} [N^{2}]}}\,,}
where E refers to the expected value , which in this case is the mean square of N .
If the signal is simply a constant value of s , this equation simplifies to:
S N R = s 2 E [ N 2 ] . {\displaystyle \mathrm {SNR} ={\frac {s^{2}}{\mathrm {E} [N^{2}]}}\,.}
If the noise has expected value of zero, as is common, the denominator is its variance , the square of its standard deviation σ N .
The signal and the noise must be measured the same way, for example as voltages across the same impedance . Their root mean squares can alternatively be used according to:
where A is root mean square (RMS) amplitude (for example, RMS voltage).
Because many signals have a very wide dynamic range , signals are often expressed using the logarithmic decibel scale. Based upon the definition of decibel, signal and noise may be expressed in decibels (dB) as
and
In a similar manner, SNR may be expressed in decibels as
Using the definition of SNR
Using the quotient rule for logarithms
Substituting the definitions of SNR, signal, and noise in decibels into the above equation results in an important formula for calculating the signal to noise ratio in decibels, when the signal and noise are also in decibels:
In the above formula, P is measured in units of power, such as watts (W) or milliwatts (mW), and the signal-to-noise ratio is a pure number.
However, when the signal and noise are measured in volts (V) or amperes (A), which are measures of amplitude, [ note 1 ] they must first be squared to obtain a quantity proportional to power, as shown below:
The concepts of signal-to-noise ratio and dynamic range are closely related. Dynamic range measures the ratio between the strongest un- distorted signal on a channel and the minimum discernible signal, which for most purposes is the noise level. SNR measures the ratio between an arbitrary signal level (not necessarily the most powerful signal possible) and noise. Measuring signal-to-noise ratios requires the selection of a representative or reference signal. In audio engineering , the reference signal is usually a sine wave at a standardized nominal or alignment level , such as 1 kHz at +4 dBu (1.228 V RMS ).
SNR is usually taken to indicate an average signal-to-noise ratio, as it is possible that instantaneous signal-to-noise ratios will be considerably different. The concept can be understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 'stands out'.
In physics, the average power of an AC signal is defined as the average value of voltage times current; for resistive (non- reactive ) circuits, where voltage and current are in phase, this is equivalent to the product of the rms voltage and current:
But in signal processing and communication, one usually assumes that R = 1 Ω {\displaystyle R=1\Omega } [ 3 ] so that factor is usually not included while measuring power or energy of a signal. This may cause some confusion among readers, but the resistance factor is not significant for typical operations performed in signal processing, or for computing power ratios. For most cases, the power of a signal would be considered to be simply
An alternative definition of SNR is as the reciprocal of the coefficient of variation , i.e., the ratio of mean to standard deviation of a signal or measurement: [ 4 ] [ 5 ]
where μ {\displaystyle \mu } is the signal mean or expected value and σ {\displaystyle \sigma } is the standard deviation of the noise, or an estimate thereof. [ note 2 ] Notice that such an alternative definition is only useful for variables that are always non-negative (such as photon counts and luminance ), and it is only an approximation since E [ X 2 ] = σ 2 + μ 2 {\displaystyle \operatorname {E} \left[X^{2}\right]=\sigma ^{2}+\mu ^{2}} . It is commonly used in image processing , [ 6 ] [ 7 ] [ 8 ] [ 9 ] where the SNR of an image is usually calculated as the ratio of the mean pixel value to the standard deviation of the pixel values over a given neighborhood.
Sometimes [ further explanation needed ] SNR is defined as the square of the alternative definition above, in which case it is equivalent to the more common definition :
This definition is closely related to the sensitivity index or d ' , when assuming that the signal has two states separated by signal amplitude μ {\displaystyle \mu } , and the noise standard deviation σ {\displaystyle \sigma } does not change between the two states.
The Rose criterion (named after Albert Rose ) states that an SNR of at least 5 is needed to be able to distinguish image features with certainty. An SNR less than 5 means less than 100% certainty in identifying image details. [ 5 ] [ 10 ]
Yet another alternative, very specific, and distinct definition of SNR is employed to characterize sensitivity of imaging systems; see Signal-to-noise ratio (imaging) .
Related measures are the " contrast ratio " and the " contrast-to-noise ratio ".
Channel signal-to-noise ratio is given by
where W is the bandwidth and k a {\displaystyle k_{a}} is modulation index
Output signal-to-noise ratio (of AM receiver) is given by
Channel signal-to-noise ratio is given by
Output signal-to-noise ratio is given by
All real measurements are disturbed by noise. This includes electronic noise , but can also include external events that affect the measured phenomenon — wind, vibrations, the gravitational attraction of the moon, variations of temperature, variations of humidity, etc., depending on what is measured and of the sensitivity of the device. It is often possible to reduce the noise by controlling the environment.
Internal electronic noise of measurement systems can be reduced through the use of low-noise amplifiers .
When the characteristics of the noise are known and are different from the signal, it is possible to use a filter to reduce the noise. For example, a lock-in amplifier can extract a narrow bandwidth signal from broadband noise a million times stronger.
When the signal is constant or periodic and the noise is random, it is possible to enhance the SNR by averaging the measurements. In this case the noise goes down as the square root of the number of averaged samples.
When a measurement is digitized, the number of bits used to represent the measurement determines the maximum possible signal-to-noise ratio. This is because the minimum possible noise level is the error caused by the quantization of the signal, sometimes called quantization noise . This noise level is non-linear and signal-dependent; different calculations exist for different signal models. Quantization noise is modeled as an analog error signal summed with the signal before quantization ("additive noise").
This theoretical maximum SNR assumes a perfect input signal. If the input signal is already noisy (as is usually the case), the signal's noise may be larger than the quantization noise. Real analog-to-digital converters also have other sources of noise that further decrease the SNR compared to the theoretical maximum from the idealized quantization noise, including the intentional addition of dither .
Although noise levels in a digital system can be expressed using SNR, it is more common to use E b /N o , the energy per bit per noise power spectral density.
The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal.
For n -bit integers with equal distance between quantization levels ( uniform quantization ) the dynamic range (DR) is also determined.
Assuming a uniform distribution of input signal values, the quantization noise is a uniformly distributed random signal with a peak-to-peak amplitude of one quantization level, making the amplitude ratio 2 n /1. The formula is then:
This relationship is the origin of statements like " 16-bit audio has a dynamic range of 96 dB". Each extra quantization bit increases the dynamic range by roughly 6 dB.
Assuming a full-scale sine wave signal (that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal), the quantization noise approximates a sawtooth wave with peak-to-peak amplitude of one quantization level [ 11 ] and uniform distribution. In this case, the SNR is approximately
Floating-point numbers provide a way to trade off signal-to-noise ratio for an increase in dynamic range. For n-bit floating-point numbers, with n-m bits in the mantissa and m bits in the exponent :
The dynamic range is much larger than fixed-point but at a cost of a worse signal-to-noise ratio. This makes floating-point preferable in situations where the dynamic range is large or unpredictable. Fixed-point's simpler implementations can be used with no signal quality disadvantage in systems where dynamic range is less than 6.02m. The very large dynamic range of floating-point can be a disadvantage, since it requires more forethought in designing algorithms. [ 12 ] [ note 3 ] [ note 4 ]
Optical signals have a carrier frequency (about 200 THz and more) that is much higher than the modulation frequency. This way the noise covers a bandwidth that is much wider than the signal itself. The resulting signal influence relies mainly on the filtering of the noise. To describe the signal quality without taking the receiver into account, the optical SNR (OSNR) is used. The OSNR is the ratio between the signal power and the noise power in a given bandwidth. Most commonly a reference bandwidth of 0.1 nm is used. This bandwidth is independent of the modulation format, the frequency and the receiver. For instance an OSNR of 20 dB/0.1 nm could be given, even the signal of 40 GBit DPSK would not fit in this bandwidth. OSNR is measured with an optical spectrum analyzer .
Signal to noise ratio may be abbreviated as SNR and less commonly as S/N. PSNR stands for peak signal-to-noise ratio . GSNR stands for geometric signal-to-noise ratio. [ 13 ] SINR is the signal-to-interference-plus-noise ratio .
While SNR is commonly quoted for electrical signals, it can be applied to any form of signal, for example isotope levels in an ice core , biochemical signaling between cells, or financial trading signals . The term is sometimes used metaphorically to refer to the ratio of useful information to false or irrelevant data in a conversation or exchange. For example, in online discussion forums and other online communities, off-topic posts and spam are regarded as noise that interferes with the signal of appropriate discussion. [ 14 ]
SNR can also be applied in marketing and how business professionals manage information overload. Managing a healthy signal to noise ratio can help business executives improve their KPIs (Key Performance Indicators). [ 15 ]
The signal-to-noise ratio is similar to Cohen's d given by the difference of estimated means divided by the standard deviation of the data d = X ¯ 1 − X ¯ 2 SD = X ¯ 1 − X ¯ 2 σ = t N {\displaystyle d={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{\text{SD}}}={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{\sigma }}={\frac {t}{\sqrt {N}}}} and is related to the test statistic t {\displaystyle t} in the t-test . [ 16 ] | https://en.wikipedia.org/wiki/Signal-to-noise_ratio |
Signal-to-noise ratio ( SNR ) is used in imaging to characterize image quality . The sensitivity of a (digital or film) imaging system is typically described in the terms of the signal level that yields a threshold level of SNR.
Industry standards define sensitivity in terms of the ISO film speed equivalent, using SNR thresholds (at average scene luminance) of 40:1 for "excellent" image quality and 10:1 for "acceptable" image quality. [ 1 ]
SNR is sometimes quantified in decibels (dB) of signal power relative to noise power, though in the imaging field the concept of "power" is sometimes taken to be the power of a voltage signal proportional to optical power; so a 20 dB SNR may mean either 10:1 or 100:1 optical power, depending on which definition is in use.
Traditionally, SNR is defined to be the ratio of the average signal value μ s i g {\displaystyle \mu _{\mathrm {sig} }} to the standard deviation of the signal σ s i g {\displaystyle \sigma _{\mathrm {sig} }} : [ 2 ] [ 3 ]
when the signal is an optical intensity, or as the square of this value if the signal and noise are viewed as amplitudes (field quantities). [ further explanation needed ]
This engineering-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Signal-to-noise_ratio_(imaging) |
Signal-to-quantization-noise ratio ( SQNR or SN q R ) is widely used quality measure in analysing digitizing schemes such as pulse-code modulation (PCM). The SQNR reflects the relationship between the maximum nominal signal strength and the quantization error (also known as quantization noise) introduced in the analog-to-digital conversion .
The SQNR formula is derived from the general signal-to-noise ratio (SNR) formula:
where:
As SQNR applies to quantized signals, the formulae for SQNR refer to discrete-time digital signals . Instead of m ( t ) {\displaystyle m(t)} , the digitized signal x ( n ) {\displaystyle x(n)} will be used. For N {\displaystyle N} quantization steps, each sample, x {\displaystyle x} requires ν = log 2 N {\displaystyle \nu =\log _{2}N} bits. The probability distribution function (PDF) represents the distribution of values in x {\displaystyle x} and can be denoted as f ( x ) {\displaystyle f(x)} . The maximum magnitude value of any x {\displaystyle x} is denoted by x m a x {\displaystyle x_{max}} .
As SQNR, like SNR, is a ratio of signal power to some noise power, it can be calculated as:
The signal power is:
The quantization noise power can be expressed as:
Giving:
When the SQNR is desired in terms of decibels (dB) , a useful approximation to SQNR is:
where ν {\displaystyle \nu } is the number of bits in a quantized sample, and P x ν {\displaystyle P_{x^{\nu }}} is the signal power calculated above. Note that for each bit added to a sample, the SQNR goes up by approximately 6 dB ( 20 × l o g 10 ( 2 ) {\displaystyle 20\times log_{10}(2)} ). | https://en.wikipedia.org/wiki/Signal-to-quantization-noise_ratio |
Signal/One was a manufacturer of high performance SSB and CW HF radio communications transceivers initially based in St. Petersburg , Florida , United States.
Signal/One's parent company was Electronic Communications, Inc. (ECI), a military division of NCR Corporation located in St. Petersburg, Florida . Key Signal/One executives were general manager Dick Ehrhorn ( amateur radio call sign W4ETO), and project engineer Don Fowler (W4YET). Beginning in the 1960s with the Signal/One CX7, ("S1", as they were called) the company made radios that were priced well above the competition and offered many advanced features for the time, [ 1 ] such as passband tuning, broadband transmission, dual receive, built-in IAMBIC keyer, electronic digital read out, solid state design, QSK and RF clipping. A Signal/One radio was said to be a complete high performance, station in a box. [ 1 ] [ 2 ] [ 3 ]
While marketed to the affluent radio amateur, it has been suggested that the primary market for Signal/One, like Collins , was military, State Department, and government communications. Although prized for the performance and advanced engineering, Signal/One's products did not sell as well as hoped, and the company gradually fell on hard times. From the 1970s though the 1990s, every few years, Signal/One was spun off , sold, and resurfaced at another location. [ 1 ]
The surviving Signal/One products are sought after and actively collected. [ 2 ] These include the CX7, CX7A, CX7B, CX11 and Milspec models. The last Signal/One radio was a re-engineered ICOM IC-781. Information available indicates there were 1152 Signal Ones built: 850 CX7, 112 CX11, 168 MS1030 (number of "C" versions is not known), 6 MilSpec1030C, 15 MilSpec1030CI Icom IC-781 conversions and 1 Milspec1030E DSP Icom IC-756 Pro conversion. [ 4 ]
This United States manufacturing company–related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Signal/One |
A signal analyzer is an instrument that measures the magnitude and phase of the input signal at a single frequency within the IF bandwidth of the instrument. It employs digital techniques to extract useful information that is carried by an electrical signal. [ 1 ] In common usage the term is related to both spectrum analyzers and vector signal analyzers . While spectrum analyzers measure the amplitude or magnitude of signals, a signal analyzer with appropriate software or programming can measure any aspect of the signal such as modulation . Today’s high-frequency signal analyzers achieve good performance by optimizing both the analog front end and the digital back end. [ 2 ]
Modern signal analyzers use a superheterodyne receiver to downconvert a portion of the signal spectrum for analysis. As shown in the figure to the right, the signal is first converted to an intermediate frequency and then filtered in order to band-limit the signal and prevent aliasing . The downconversion can operate in a swept-tuned mode similar to a traditional spectrum analyzer , or in a fixed-tuned mode. In the fixed-tuned mode the range of frequencies downconverted does not change and the downconverter output is then digitized for further analysis. The digitizing process typically involves in-phase/quadrature (I/Q) or complex sampling so that all characteristics of the signal are preserved, as opposed to the magnitude-only processing of a spectrum analyzer . The sampling rate of the digitizing process may be varied in relation to the frequency span under consideration or (more typically) the signal may be digitally resampled.
Signal analyzers can perform the operations of both spectrum analyzers and vector signal analyzers . A signal analyzer can be viewed as a measurement platform, with operations such as spectrum analysis (including phase noise , power , and distortion ) and vector signal analysis (including demodulation or modulation quality analysis) performed as measurement applications. These measurement applications can be built into the analyzer platform as measurement firmware or installed as changeable application software. | https://en.wikipedia.org/wiki/Signal_analyzer |
In electronics and signal processing , signal conditioning is the manipulation of an analog signal in such a way that it meets the requirements of the next stage for further processing.
In an analog-to-digital converter (ADC) application, signal conditioning includes voltage or current limiting and anti-aliasing filtering .
In control engineering applications, it is common to have a sensing stage (which consists of a sensor ), a signal conditioning stage (where usually amplification of the signal is done) and a processing stage (often carried out by an ADC and a micro-controller ). Operational amplifiers (op-amps) are commonly employed to carry out the amplification of the signal in the signal conditioning stage. In some transducers , signal conditioning is integrated with the sensor, for example in Hall effect sensors .
In power electronics , before processing the input sensed signals by sensors like voltage sensor and current sensor, signal conditioning scales signals to level acceptable to the microprocessor.
Signal inputs accepted by signal conditioners include DC voltage and current, AC voltage and current, frequency and electric charge . Sensor inputs can be accelerometer , thermocouple , thermistor , resistance thermometer , strain gauge or bridge, and LVDT or RVDT . Specialized inputs include encoder, counter or tachometer , timer or clock, relay or switch, and other specialized inputs. Outputs for signal conditioning equipment can be voltage, current, frequency, timer or counter, relay, resistance or potentiometer, and other specialized outputs.
Signal conditioning can include amplification , filtering , converting, range matching, isolation and any other processes required to make sensor output suitable for processing after conditioning.
Use AC coupling when the signal contains a large DC component. If you enable AC coupling, you remove the large DC offset for the input amplifier and amplify only the AC component. This configuration makes effective use of the ADC dynamic range
Filtering is the most common signal conditioning function, as usually not all the signal frequency spectrum contains valid data. For example, the 50 or 60 Hz AC power lines, present in most environments induce noise on signals that can cause interference if amplified.
Signal amplification performs two important functions: increases the resolution of the input signal, and increases its signal-to-noise ratio. [ citation needed ] For example, the output of an electronic temperature sensor , which is probably in the millivolts range is probably too low for an analog-to-digital converter (ADC) to process directly. [ citation needed ] In this case it is necessary to bring the voltage level up to that required by the ADC .
Commonly used amplifiers used for signal conditioning include sample and hold amplifiers, peak detectors, log amplifiers, antilog amplifiers, instrumentation amplifiers and programmable gain amplifiers. [ 1 ]
Attenuation, the opposite of amplification, is necessary when voltages to be digitized are beyond the ADC range. This form of signal conditioning decreases the input signal amplitude so that the conditioned signal is within ADC range. Attenuation is typically necessary when measuring voltages that are more than 10 V.
Some sensors require external voltage or current source of excitation, These sensors are called active sensors. (E.g. a temperature sensor like a thermistor & RTD, a pressure sensor (piezo-resistive and capacitive), etc.). The stability and precision of the excitation signal directly relates to the sensor accuracy and stability.
Linearization is necessary when sensors produce voltage signals that are not linearly related to the physical measurement. Linearization is the process of interpreting the signal from the sensor and can be done either with signal conditioning or through software.
Signal isolation may be used to pass the signal from the source to the measuring device without a physical connection. It is often used to isolate possible sources of signal perturbations that could otherwise follow the electrical path from the sensor to the processing circuitry. In some situations, it may be important to isolate the potentially expensive equipment used to process the signal after conditioning from the sensor.
Magnetic or optical isolation can be used. Magnetic isolation transforms the signal from a voltage to a magnetic field so the signal can be transmitted without physical connection (for example, using a transformer). Optical isolation works by using an electronic signal to modulate a signal encoded by light transmission (optical encoding). The decoded light transmission is then used for input for the next stage of processing.
A surge protector absorbs voltage spikes to protect the next stage from damage. | https://en.wikipedia.org/wiki/Signal_conditioning |
A signal passed at danger ( SPAD ) [ 1 ] : 75 is an event on a railway where a train passes a stop signal without authority. [ 2 ] This is also known as running a red , in the United States as a stop signal overrun (SSO) [ 3 ] and in Canada as passing a stop signal . [ 4 ] SPAD is defined by Directive 2014/88/EU as any occasion when any part of a train proceeds beyond its authorised movement. [ 5 ] Unauthorised movement means to pass: [ 5 ]
The name derives from red colour light signals and horizontal semaphore signals in the United Kingdom, which are said to be at danger when they indicate that trains must stop (also known as the signal being on ). This terminology is not used in North America where not all red signals indicate stop. [ 1 ] : 72 In the UK, a signal passed at red ( SPAR ) is used where a signal changes to red directly in front of a train, due to a fault or emergency, meaning it is impossible to stop before the signal.
The high inertia of trains, and the low adhesion between the wheels and track, means it takes a long distance for the train brakes to stop a train. SPADs are most commonly a small overrun of the signal (instead of a long overrun), because the driver has braked too late. The safety consequences for these types of SPADs may be minor. On the other hand, some SPADs involve the driver being unaware they have passed a signal at danger and continue until notified by network controllers, or a collision occurs, as in the Ladbroke Grove rail crash .
The causes and prevention of SPADs is actively researched. Causes of SPADs are always multidimensional. [ citation needed ] Some of the causes of SPADs are:
Automatic train protection (ATP) is an advanced form of train stop which can regulate the speed of trains in situations other than at a signal set at danger. ATP can supervise speed restrictions and distance to danger points. It can also take into account individual train characteristics such as brake performance etc. Therefore ATP can determine when brakes should be applied in order to stop the train before passing a signal at danger. Presently, In the UK, only a small percentage of trains ( Great Western Railway and Chiltern Railways ) are fitted with this equipment.
The driver's reminder appliance (DRA) is an inhibiting switch located on the driver's desk of United Kingdom passenger trains designed specifically to prevent " starting away SPADs ". The driver is required to operate the DRA whenever the train is brought to a stand, [ 10 ] either after passing a signal displaying caution or at a signal displaying danger.
Once applied, the DRA displays a red light and prevents traction power from being taken until the DRA is manually cancelled by the driver.
Whilst the ideal safety system would prevent a SPAD from occurring, most equipment in current use does not stop the train before it has passed the Danger signal. However, provided that the train stops within the designated overlap beyond that signal, a collision should not occur.
On the London Underground (for example), mechanical train stops are fitted beside the track at signals to stop a train, should a SPAD occur.
Train stops are also installed on main line railways in places where tripcock equipped trains run in extensive tunnels, such as the on the Northern City Line where the Automatic warning system and Train Protection & Warning System are not fitted.
On the UK mainline, AWS consists of an on-board receiver/timer connected to the emergency braking system of a train, and magnets located in the center of the track. At each AWS site, a permanent magnet arms the system and an electromagnet connected to the green signal lamp disarms the system and a confirming chime is provided to the driver. If the receiver does not disarm within one second after arming, a warning tone sounds at the driver's desk and if it is not cancelled by the driver, the emergency brakes will be activated. A visual indication remains set to remind the driver that they have passed a restrictive signal aspect .
On the UK mainline, TPWS consists of an on-board receiver/timer connected to the emergency braking system of a train, and radio frequency transmitter loops located on the track. The 'Overspeed Sensor System' pair of loops is located on the approach to the signal, and will activate the train's emergency brake if it approaches faster than the 'trigger speed' when the signal is at danger . The 'Train Stop System' pair of loops is located at the signal, and will activate the emergency brake if the train passes over them at any speed when the signal is at danger .
TPWS has proved to be an effective system in the UK, [ citation needed ] and has prevented several significant collisions. [ citation needed ] However, its deployment is not universal; only those signals where the risk of collision is considered to be significant are fitted with it.
At certain junctions, especially where if the signal protecting the junction was passed at danger a side collision is likely to result, then flank protection [ 11 ] may be used. Derailers and/or facing points beyond the signal protecting the junction will be set in such a position to allow a safe overlap if the signal was passed without authority. This effectively removes the chance of a side-impact collision as the train would be diverted in a parallel path to the approaching train.
Prior to the introduction of TPWS in the UK, "SPAD indicators" were introduced at 'high risk' locations (for example: the entry to a single track section of line). Consisting of three red lamps, they are placed beyond the protecting stop signal and are normally unlit. If a driver passes the signal at 'danger', the top and bottom lamps flash red and the centre lamp, which has the word "STOP" written across the lens in black, is lit continuously. Whenever a SPAD indicator activates, all drivers who observe it are required to stop immediately, even if they can see that the signal pertaining to their own train is showing a proceed aspect. Since the introduction of TPWS, provision of new SPAD indicators has become less common.
In the UK, incidents where a signal is passed at danger without authority are categorised according to principal cause. A SPAD is where the train proceeds beyond its authorised movement to an unauthorised movement. Other types are categorised as SPAR ("signal passed at red").
Prior to December 2012, [ 12 ] the term "SPAD" applied to all such incidents, with a letter specifying cause.
Some SPADs are defined as a;
Signals form part of a complex system, and it is inevitable that faults may occur. They are designed to fail safe , so that when problems occur, the affected signal indicates danger (an example where this did not happen, known as a wrong-side failure , was the Clapham Junction rail crash due primarily to faulty wiring). To keep the network running, safety rules enable trains to pass signals that cannot be cleared to a proceed aspect. Provided that authority for the movement is obtained, a SPAD does not occur. There are two methods of obtaining that authority: [ 14 ]
Once the train has been brought to a stand at a signal which is at danger, the driver should attempt to contact the signaller. If the signal cannot be cleared then the driver must obtain the signaller's authority to pass it at danger. Methods for contacting the signaller may include GSM-R cab radio, signal post telephone or mobile phone .
The signaller can authorise a driver to pass a signal at danger when: [ 15 ]
The driver and signaller must come to a clear understanding, and ensure they agree about how it is to be done. In the UK the signaller tells the driver of a specific train to pass a specific signal at danger, proceed with caution and travel at a speed that enables him to stop short of any obstruction, and then obey all other signals. If the signal is fitted with TPWS, the driver resets the Driver Reminder Appliance, pushes the TPWS Trainstop Override button in the cab, and proceeds cautiously through the section. If the train reaches the next signal without finding an obstruction, they must obey its aspect, at which point they can revert to normal working.
If contact with the signaller cannot be made then the driver must not move the train, unless it is standing at one of the following signals:
After passing a signal at danger under their own authority, the driver must stop at the next signal (even if it is showing a proceed aspect) and inform the signaller of what they have done.
Whenever a signal is passed at danger the driver is required to "proceed with caution, stop short of any obstructions, and drive at speed that will enable you to stop within the distance which you can see to be clear". Failure to do this has caused the following collisions:
Except where permissive working is in use, interlocking usually prevents a train from being signalled into a section that is already occupied. When operational needs require it, this can be overridden, and provided it is carried out in accordance with the rules this is a safe practice. However, failure to follow protocol can result in a collision: | https://en.wikipedia.org/wiki/Signal_passed_at_danger |
A signal peptide (sometimes referred to as signal sequence , targeting signal , localization signal , localization sequence , transit peptide , leader sequence or leader peptide ) is a short peptide (usually 16–30 amino acids long) [ 1 ] present at the N-terminus (or occasionally nonclassically at the C-terminus [ 2 ] or internally) of most newly synthesized proteins that are destined toward the secretory pathway . [ 3 ] These proteins include those that reside either inside certain organelles (the endoplasmic reticulum , Golgi or endosomes ), secreted from the cell, or inserted into most cellular membranes. Although most type I membrane-bound proteins have signal peptides, most type II and multi-spanning membrane-bound proteins are targeted to the secretory pathway by their first transmembrane domain , which biochemically resembles a signal sequence except that it is not cleaved. They are a kind of target peptide .
Signal peptides function to prompt a cell to translocate the protein, usually to the cellular membrane. In prokaryotes , signal peptides direct the newly synthesized protein to the SecYEG protein-conducting channel, which is present in the plasma membrane . A homologous system exists in eukaryotes , where the signal peptide directs the newly synthesized protein to the Sec61 channel, which shares structural and sequence homology with SecYEG, but is present in the endoplasmic reticulum. [ 4 ] Both the SecYEG and Sec61 channels are commonly referred to as the translocon , and transit through this channel is known as translocation. While secreted proteins are threaded through the channel, transmembrane domains may diffuse across a lateral gate in the translocon to partition into the surrounding membrane.
The core of the signal peptide contains a long stretch of hydrophobic amino acids (about 5–16 residues long) [ 5 ] that has a tendency to form a single alpha-helix and is also referred to as the "h-region". In addition, many signal peptides begin with a short positively charged stretch of amino acids, which may help to enforce proper topology of the polypeptide during translocation by what is known as the positive-inside rule . [ 6 ] Because of its close location to the N-terminus it is called the "n-region". At the end of the signal peptide there is typically a stretch of amino acids that is recognized and cleaved by signal peptidase and therefore named cleavage site. This cleavage site is absent from transmembrane-domains that serve as signal peptides, which are sometimes referred to as signal anchor sequences. Signal peptidase may cleave either during or after completion of translocation to generate a free signal peptide and a mature protein. The free signal peptides are then digested by specific proteases.
Moreover, different target locations are aimed by different types of signal peptides. For example, the structure of a target peptide aiming for the mitochondrial environment differs in terms of length and shows an alternating pattern of small positively charged and hydrophobic stretches. Nucleus aiming signal peptides can be found at both the N-terminus and the C-terminus of a protein and are in most cases retained in the mature protein.
In both prokaryotes and eukaryotes signal sequences may act co-translationally or post-translationally.
The co-translational pathway is initiated when the signal peptide emerges from the ribosome and is recognized by the signal-recognition particle (SRP). [ 7 ] SRP then halts further translation (translational arrest only occurs in Eukaryotes) and directs the signal sequence-ribosome-mRNA complex to the SRP receptor , which is present on the surface of either the plasma membrane (in prokaryotes) or the ER (in eukaryotes). [ 8 ] Once membrane-targeting is completed, the signal sequence is inserted into the translocon. Ribosomes are then physically docked onto the cytoplasmic face of the translocon and protein synthesis resumes. [ 9 ]
The post-translational pathway is initiated after protein synthesis is completed. In prokaryotes, the signal sequence of post-translational substrates is recognized by the SecB chaperone protein that transfers the protein to the SecA ATPase, which in turn pumps the protein through the translocon. Although post-translational translocation is known to occur in eukaryotes, it is poorly understood. It is known that in yeast post-translational translocation requires the translocon and two additional membrane-bound proteins, Sec62 and Sec63 . [ 10 ]
Signal peptides are extremely heterogeneous, many prokaryotic and eukaryotic ones are functionally interchangeable within or between species and all determine protein secretion efficiency. [ 11 ] [ 12 ] [ 13 ]
In vertebrates, the region of the mRNA that codes for the signal peptide (i.e. the signal sequence coding region, or SSCR) can function as an RNA element with specific activities. SSCRs promote nuclear mRNA export and the proper localization to the surface of the endoplasmic reticulum. In addition SSCRs have specific sequence features: they have low adenine -content, are enriched in certain motifs , and tend to be present in the first exon at a frequency that is higher than expected. [ 14 ] [ 15 ]
Proteins without signal peptides can also be secreted by unconventional mechanisms. E.g. Interleukin, Galectin. [ 16 ] The process by which such secretory proteins gain access to the cell exterior is termed unconventional protein secretion (UPS). In plants, even 50% of secreted proteins can be UPS dependent. [ 17 ]
Signal peptides are usually located at the N-terminus of proteins. Some have C-terminal or internal signal peptides (examples: peroxisomal targeting signal and nuclear localisation signal). The structure of these nonclassical signal peptides differs vastly from the N-terminal signal peptides. [ 2 ]
Signal peptides are not to be confused with the leader peptides sometimes encoded by leader mRNA, although both are sometimes ambiguously referred to as "leader peptides." These other leader peptides are short polypeptides that do not function in protein localization, but instead may regulate transcription or translation of the main protein, and are not part of the final protein sequence. This type of leader peptide primarily refers to a form of gene regulation found in bacteria, although a similar mechanism is used to regulate eukaryotic genes, which is referred to as uORFs (upstream open reading frames).
Signal peptide is a potential (therapeutic) antiviral target. Signal peptides with penultimate N-terminus glycine is a target for NMT inhibitors , which inhibit the myristoylation of signal peptides and target the signal peptide for degradation , which affects virus-cellular fusion . [ 18 ] | https://en.wikipedia.org/wiki/Signal_peptide |
SIGNAL is a programming language based on synchronized dataflow (flows + synchronization): a process is a set of equations on elementary flows describing both data and control. [ 1 ]
The SIGNAL formal model provides the capability to describe systems with several clocks [ 2 ] [ 3 ] (polychronous systems) as relational specifications . Relations are useful as partial specifications and as specifications of non-deterministic devices (for instance a non-deterministic bus ) or external processes (for instance an unsafe car driver).
Using SIGNAL allows one to specify [ 4 ] an application, to design an architecture , to refine detailed components down to RTOS [ clarification needed ] or hardware description. The SIGNAL model supports a design methodology which goes from specification to implementation , from abstraction to concretization , from synchrony to asynchrony .
SIGNAL has been mainly developed in INRIA Espresso team since the 1980s, at the same time as similar programming languages, Esterel and Lustre .
The SIGNAL language was first designed for signal processing applications in the beginning of the 1980s. It has been proposed to answer the demand of new domain-specific language for the design of signal processing applications , adopting a dataflow and block-diagram style with array and sliding window operators. P. Le Guernic, A. Benveniste, and T. Gautier have been in charge of the language definition. The first paper on SIGNAL was published in 1982, while the first complete description of SIGNAL appeared in the PhD thesis of T. Gautier. The symbolic representation of SIGNAL via z/3z (over [-1,0,1]) has been introduced in 1986. A full compiler of SIGNAL based on the clock calculus on hierarchy of Boolean clocks, was described by L. Besnard in his PhD thesis in 1992. The clock calculus has been improved later by T. Amagbegnon with the proposition of arborescent canonical forms.
During the 1990s, the application domain of the SIGNAL language has been extended into general embedded and real-time systems. The relation-oriented specification style enabled the increasing construction of the systems, and also led to the design considering multi-clocked systems, compared to the original single-clock-based implementation of Esterel and Lustre. Moreover, the design and implementation of distributed embedded systems were also taken into account in SIGNAL. The corresponding research includes the optimization methods proposed by B. Chéron, the clustering models defined by B. Le Goff, the abstraction and separate compilation formalized by O. Maffeïs, and the implementation of distributed programs developed by P. Aubry.
The Polychrony toolset is an open-source development environment for critical/embedded systems based on SIGNAL, a real-time polychronous dataflow language. It provides a unified model-driven environment to perform design exploration by using top-down and bottom-up design methodologies formally supported by design model transformations from specification to implementation and from synchrony to asynchrony. It can be included in heterogeneous design systems with various input formalisms and output languages.
Polychrony is a set of tools composed of:
The SME (SIGNAL Meta under Eclipse) environment is a front-end of Polychrony in the Eclipse environment based on Model-Driven Engineering (MDE) technologies. It consists of a set of Eclipse plug-ins which rely on the Eclipse Modeling Framework (EMF). The environment is built around SME, a metamodel [ 7 ] of the SIGNAL language extended with mode automata [ 8 ] concepts.
The SME environment is composed of several plug-ins which correspond to: | https://en.wikipedia.org/wiki/Signal_programming |
In telecommunications , signal reflection happens when a signal is transmitted along a transmission medium (such as a copper cable or an optical fiber ) and part of it is reflected back toward the source instead of reaching the end. This reflection is caused by imperfections or physical variations in the cable (such as abrupt changes in its geometry) that lead to impedance mismatches. [ 1 ] These mismatches disrupt the signal and cause some of it to bounce back. In radio frequency (RF) systems, this is typically measured using the voltage standing wave ratio (VSWR), with device called a VSWR bridge. The amount of reflected energy depends on the degree of impedance mismatch and is mathematically describe by the reflection coefficient . [ 2 ]
Because the principles are the same, this concept is perhaps easiest to understand when considering an optical fiber. Imperfections in the glass create mirrors that reflect the light back along the fiber. [ 3 ]
Impedance discontinuities cause attenuation , attenuation distortion , standing waves , ringing and other effects because a portion of a transmitted signal will be reflected back to the transmitting device rather than continuing to the receiver , much like an echo . This effect is compounded if multiple discontinuities cause additional portions of the remaining signal to be reflected back to the transmitter. This is a fundamental problem with the daisy chain method of connecting electronic components. [ 4 ]
When a returning reflection strikes another discontinuity, some of the signal rebounds in the original signal direction, creating multiple echo effects. These forward echoes strike the receiver at different intervals making it difficult for the receiver to accurately detect data values on the signal. The effects can resemble those of jitter .
Because damage to the cable can cause reflections, an instrument called an electrical time-domain reflectometer (ETDR; for electrical cables) or an optical time-domain reflectometer (OTDR; for optical cables) can be used to locate the damaged part of a cable. These instruments work by sending a short pulsed signal into the cable and measuring how long the reflection takes to return. If only reflection magnitudes are desired, however, and exact fault locations are not required, VSWR bridges perform a similar but lesser function for RF cables .
The combination of the effects of signal attenuation and impedance discontinuities on a communications link is called insertion loss . Proper network operation depends on constant characteristic impedance in all cables and connectors, with no impedance discontinuities in the entire cable system. When a sufficient degree of impedance matching is not practical, echo suppressors or echo cancellers , or both, can sometimes reduce the problems.
The Bergeron diagram method, valid for both linear and non-linear models, evaluates the reflection's effects in an electric line. | https://en.wikipedia.org/wiki/Signal_reflection |
In telecommunications , particularly in radio frequency engineering , signal strength is the transmitter power output as received by a reference antenna at a distance from the transmitting antenna. High-powered transmissions, such as those used in broadcasting , are measured in dB - millivolts per metre (dBmV/m). For very low-power systems, such as mobile phones , signal strength is usually expressed in dB - microvolts per metre (dBμV/m) or in decibels above a reference level of one milliwatt ( dBm ). In broadcasting terminology, 1 mV/m is 1000 μV/m or 60 dBμ (often written dBu).
The electric field strength at a specific point can be determined from the power delivered to the transmitting antenna, its geometry and radiation resistance. Consider the case of a center-fed half-wave dipole antenna in free space , where the total length L is equal to one half wavelength (λ/2). If constructed from thin conductors, the current distribution is essentially sinusoidal and the radiating electric field is given by
where θ {\displaystyle \scriptstyle {\theta }} is the angle between the antenna axis and the vector to the observation point, I ∘ {\displaystyle \scriptstyle {I_{\circ }}} is the peak current at the feed-point, ε 0 = 8.85 × 10 − 12 F / m {\displaystyle \scriptstyle {\varepsilon _{0}\,=\,8.85\times 10^{-12}\,F/m}} is the permittivity of free-space, c = 3 × 10 8 m / s {\displaystyle \scriptstyle {c\,=\,3\times 10^{8}\,m/s}} is the speed of light in vacuum, and r {\displaystyle \scriptstyle {r}} is the distance to the antenna in meters. When the antenna is viewed broadside ( θ = π / 2 {\displaystyle \scriptstyle {\theta \,=\,\pi /2}} ) the electric field is maximum and given by
Solving this formula for the peak current yields
The average power to the antenna is
where R a = 73.13 Ω {\displaystyle \scriptstyle {R_{a}=73.13\,\Omega }} is the center-fed half-wave antenna's radiation resistance. Substituting the formula for I ∘ {\displaystyle \scriptstyle {I_{\circ }}} into the one for P a v g {\displaystyle \scriptstyle {P_{avg}}} and solving for the maximum electric field yields
Therefore, if the average power to a half-wave dipole antenna is 1 mW, then the maximum electric field at 313 m (1027 ft) is 1 mV/m (60 dBμ).
For a short dipole ( L ≪ λ / 2 {\displaystyle \scriptstyle {L\ll \lambda /2}} ) the current distribution is nearly triangular. In this case, the electric field and radiation resistance are
Using a procedure similar to that above, the maximum electric field for a center-fed short dipole is
Although there are cell phone base station tower networks across many nations globally, there are still many areas within those nations that do not have good reception. Some rural areas are unlikely to ever be covered effectively since the cost of erecting a cell tower is too high for only a few customers. Even in areas with high signal strength, basements and the interiors of large buildings often have poor reception.
Weak signal strength can also be caused by destructive interference of the signals from local towers in urban areas, or by the construction materials used in some buildings causing significant attenuation of signal strength. Large buildings such as warehouses, hospitals and factories often have no usable signal further than a few metres from the outside walls.
This is particularly true for the networks which operate at higher frequency since these are attenuated more by intervening obstacles, although they are able to use reflection and diffraction to circumvent obstacles.
The estimated received signal strength in an active RFID tag can be estimated as follows:
In general, you can take the path loss exponent into account: [ 1 ]
The effective path loss depends on frequency , topography , and environmental conditions.
Actually, one could use any known signal power dBm 0 at any distance r 0 as a reference:
When we measure cell distance r and received power dBm m pairs,
we can estimate the mean cell radius as follows:
Specialized calculation models exist to plan the location of a new cell tower, taking into account local conditions and radio equipment parameters, as well as consideration that mobile radio signals have line-of-sight propagation , unless reflection occurs. | https://en.wikipedia.org/wiki/Signal_strength_in_telecommunications |
Signal transduction is the process by which a chemical or physical signal is transmitted through a cell as a series of molecular events . Proteins responsible for detecting stimuli are generally termed receptors , although in some cases the term sensor is used. [ 1 ] The changes elicited by ligand binding (or signal sensing) in a receptor give rise to a biochemical cascade , which is a chain of biochemical events known as a signaling pathway .
When signaling pathways interact with one another they form networks, which allow cellular responses to be coordinated, often by combinatorial signaling events. [ 2 ] At the molecular level, such responses include changes in the transcription or translation of genes, and post-translational and conformational changes in proteins, as well as changes in their location. These molecular events are the basic mechanisms controlling cell growth , proliferation, metabolism and many other processes. [ 3 ] In multicellular organisms, signal transduction pathways regulate cell communication in a wide variety of ways.
Each component (or node) of a signaling pathway is classified according to the role it plays with respect to the initial stimulus. Ligands are termed first messengers , while receptors are the signal transducers , which then activate primary effectors . Such effectors are typically proteins and are often linked to second messengers , which can activate secondary effectors , and so on. Depending on the efficiency of the nodes, a signal can be amplified (a concept known as signal gain), so that one signaling molecule can generate a response involving hundreds to millions of molecules. [ 4 ] As with other signals, the transduction of biological signals is characterised by delay, noise, signal feedback and feedforward and interference, which can range from negligible to pathological. [ 5 ] With the advent of computational biology , the analysis of signaling pathways and networks has become an essential tool to understand cellular functions and disease , including signaling rewiring mechanisms underlying responses to acquired drug resistance. [ 6 ]
The basis for signal transduction is the transformation of a certain stimulus into a biochemical signal. The nature of such stimuli can vary widely, ranging from extracellular cues, such as the presence of EGF , to intracellular events, such as the DNA damage resulting from replicative telomere attrition. [ 7 ] Traditionally, signals that reach the central nervous system are classified as senses . These are transmitted from neuron to neuron in a process called synaptic transmission . Many other intercellular signal relay mechanisms exist in multicellular organisms, such as those that govern embryonic development. [ 8 ]
The majority of signal transduction pathways involve the binding of signaling molecules, known as ligands, to receptors that trigger events inside the cell. The binding of a signaling molecule with a receptor causes a change in the conformation of the receptor, known as receptor activation . Most ligands are soluble molecules from the extracellular medium which bind to cell surface receptors . These include growth factors , cytokines and neurotransmitters . Components of the extracellular matrix such as fibronectin and hyaluronan can also bind to such receptors ( integrins and CD44 , respectively). In addition, some molecules such as steroid hormones are lipid-soluble and thus cross the plasma membrane to reach cytoplasmic or nuclear receptors . [ 9 ] In the case of steroid hormone receptors , their stimulation leads to binding to the promoter region of steroid-responsive genes. [ 10 ]
Not all classifications of signaling molecules take into account the molecular nature of each class member. For example, odorants belong to a wide range of molecular classes, [ 11 ] as do neurotransmitters, which range in size from small molecules such as dopamine [ 12 ] to neuropeptides such as endorphins . [ 13 ] Moreover, some molecules may fit into more than one class, e.g. epinephrine is a neurotransmitter when secreted by the central nervous system and a hormone when secreted by the adrenal medulla . [ 14 ]
Some receptors such as HER2 are capable of ligand-independent activation when overexpressed or mutated. This leads to constitutive activation of the pathway, which may or may not be overturned by compensation mechanisms. In the case of HER2, which acts as a dimerization partner of other EGFRs , constitutive activation leads to hyperproliferation and cancer . [ 15 ]
The prevalence of basement membranes in the tissues of Eumetazoans means that most cell types require attachment to survive. This requirement has led to the development of complex mechanotransduction pathways, allowing cells to sense the stiffness of the substratum. Such signaling is mainly orchestrated in focal adhesions , regions where the integrin -bound actin cytoskeleton detects changes and transmits them downstream through YAP1 . [ 16 ] Calcium-dependent cell adhesion molecules such as cadherins and selectins can also mediate mechanotransduction. [ 17 ] Specialised forms of mechanotransduction within the nervous system are responsible for mechanosensation : hearing , touch , proprioception and balance . [ 18 ]
Cellular and systemic control of osmotic pressure (the difference in osmolarity between the cytosol and the extracellular medium) is critical for homeostasis. There are three ways in which cells can detect osmotic stimuli: as changes in macromolecular crowding, ionic strength, and changes in the properties of the plasma membrane or cytoskeleton (the latter being a form of mechanotransduction). [ 19 ] These changes are detected by proteins known as osmosensors or osmoreceptors. In humans, the best characterised osmosensors are transient receptor potential channels present in the primary cilium of human cells. [ 19 ] [ 20 ] In yeast, the HOG pathway has been extensively characterised. [ 21 ]
The sensing of temperature in cells is known as thermoception and is primarily mediated by transient receptor potential channels . [ 22 ] Additionally, animal cells contain a conserved mechanism to prevent high temperatures from causing cellular damage, the heat-shock response . Such response is triggered when high temperatures cause the dissociation of inactive HSF1 from complexes with heat shock proteins Hsp40 / Hsp70 and Hsp90 . With help from the ncRNA hsr1 , HSF1 then trimerizes, becoming active and upregulating the expression of its target genes. [ 23 ] Many other thermosensory mechanisms exist in both prokaryotes and eukaryotes . [ 22 ]
In mammals, light controls the sense of sight and the circadian clock by activating light-sensitive proteins in photoreceptor cells in the eye 's retina . In the case of vision, light is detected by rhodopsin in rod and cone cells . [ 24 ] In the case of the circadian clock, a different photopigment , melanopsin , is responsible for detecting light in intrinsically photosensitive retinal ganglion cells . [ 25 ]
Receptors can be roughly divided into two major classes: intracellular and extracellular receptors.
Extracellular receptors are integral transmembrane proteins and make up most receptors. They span the plasma membrane of the cell, with one part of the receptor on the outside of the cell and the other on the inside. Signal transduction occurs as a result of a ligand binding to the outside region of the receptor (the ligand does not pass through the membrane). Ligand-receptor binding induces a change in the conformation of the inside part of the receptor, a process sometimes called "receptor activation". [ 26 ] This results in either the activation of an enzyme domain of the receptor or the exposure of a binding site for other intracellular signaling proteins within the cell, eventually propagating the signal through the cytoplasm. [ citation needed ]
In eukaryotic cells, most intracellular proteins activated by a ligand/receptor interaction possess an enzymatic activity; examples include tyrosine kinase and phosphatases . Often such enzymes are covalently linked to the receptor. Some of them create second messengers such as cyclic AMP and IP 3 , the latter controlling the release of intracellular calcium stores into the cytoplasm. Other activated proteins interact with adaptor proteins that facilitate signaling protein interactions and coordination of signaling complexes necessary to respond to a particular stimulus. Enzymes and adaptor proteins are both responsive to various second messenger molecules. [ citation needed ]
Many adaptor proteins and enzymes activated as part of signal transduction possess specialized protein domains that bind to specific secondary messenger molecules. For example, calcium ions bind to the EF hand domains of calmodulin , allowing it to bind and activate calmodulin-dependent kinase . PIP 3 and other phosphoinositides do the same thing to the Pleckstrin homology domains of proteins such as the kinase protein AKT .
G protein–coupled receptors (GPCRs) are a family of integral transmembrane proteins that possess seven transmembrane domains and are linked to a heterotrimeric G protein . With nearly 800 members, this is the largest family of membrane proteins and receptors in mammals. Counting all animal species, they add up to over 5000. [ 27 ] Mammalian GPCRs are classified into 5 major families: rhodopsin-like , secretin-like , metabotropic glutamate , adhesion and frizzled / smoothened , with a few GPCR groups being difficult to classify due to low sequence similarity, e.g. vomeronasal receptors . [ 27 ] Other classes exist in eukaryotes, such as the Dictyostelium cyclic AMP receptors and fungal mating pheromone receptors . [ 27 ]
Signal transduction by a GPCR begins with an inactive G protein coupled to the receptor; the G protein exists as a heterotrimer consisting of Gα, Gβ, and Gγ subunits. [ 28 ] Once the GPCR recognizes a ligand, the conformation of the receptor changes to activate the G protein, causing Gα to bind a molecule of GTP and dissociate from the other two G-protein subunits. The dissociation exposes sites on the subunits that can interact with other molecules. [ 29 ] The activated G protein subunits detach from the receptor and initiate signaling from many downstream effector proteins such as phospholipases and ion channels , the latter permitting the release of second messenger molecules. [ 30 ] The total strength of signal amplification by a GPCR is determined by the lifetimes of the ligand-receptor complex and receptor-effector protein complex and the deactivation time of the activated receptor and effectors through intrinsic enzymatic activity; e.g. via protein kinase phosphorylation or b-arrestin-dependent internalization. [ citation needed ]
A study was conducted where a point mutation was inserted into the gene encoding the chemokine receptor CXCR2; mutated cells underwent a malignant transformation due to the expression of CXCR2 in an active conformation despite the absence of chemokine-binding. This meant that chemokine receptors can contribute to cancer development. [ 31 ]
Receptor tyrosine kinases (RTKs) are transmembrane proteins with an intracellular kinase domain and an extracellular domain that binds ligands ; examples include growth factor receptors such as the insulin receptor . [ 32 ] To perform signal transduction, RTKs need to form dimers in the plasma membrane ; [ 33 ] the dimer is stabilized by ligands binding to the receptor. The interaction between the cytoplasmic domains stimulates the auto phosphorylation of tyrosine residues within the intracellular kinase domains of the RTKs, causing conformational changes. Subsequent to this, the receptors' kinase domains are activated, initiating phosphorylation signaling cascades of downstream cytoplasmic molecules that facilitate various cellular processes such as cell differentiation and metabolism . [ 32 ] Many Ser/Thr and dual-specificity protein kinases are important for signal transduction, either acting downstream of [receptor tyrosine kinases], or as membrane-embedded or cell-soluble versions in their own right. The process of signal transduction involves around 560 known protein kinases and pseudokinases , encoded by the human kinome [ 34 ] [ 35 ]
As is the case with GPCRs, proteins that bind GTP play a major role in signal transduction from the activated RTK into the cell. In this case, the G proteins are members of the Ras , Rho , and Raf families, referred to collectively as small G proteins . They act as molecular switches usually tethered to membranes by isoprenyl groups linked to their carboxyl ends. Upon activation, they assign proteins to specific membrane subdomains where they participate in signaling. Activated RTKs in turn activate small G proteins that activate guanine nucleotide exchange factors such as SOS1 . Once activated, these exchange factors can activate more small G proteins, thus amplifying the receptor's initial signal. The mutation of certain RTK genes, as with that of GPCRs, can result in the expression of receptors that exist in a constitutively activated state; such mutated genes may act as oncogenes . [ 36 ]
Histidine-specific protein kinases are structurally distinct from other protein kinases and are found in prokaryotes, fungi, and plants as part of a two-component signal transduction mechanism: a phosphate group from ATP is first added to a histidine residue within the kinase, then transferred to an aspartate residue on a receiver domain on a different protein or the kinase itself, thus activating the aspartate residue. [ 37 ]
Integrins are produced by a wide variety of cells; they play a role in cell attachment to other cells and the extracellular matrix and in the transduction of signals from extracellular matrix components such as fibronectin and collagen . Ligand binding to the extracellular domain of integrins changes the protein's conformation, clustering it at the cell membrane to initiate signal transduction. Integrins lack kinase activity; hence, integrin-mediated signal transduction is achieved through a variety of intracellular protein kinases and adaptor molecules, the main coordinator being integrin-linked kinase . [ 38 ] As shown in the adjacent picture, cooperative integrin-RTK signaling determines the timing of cellular survival, apoptosis , proliferation , and differentiation .
Important differences exist between integrin-signaling in circulating blood cells and non-circulating cells such as epithelial cells ; integrins of circulating cells are normally inactive. For example, cell membrane integrins on circulating leukocytes are maintained in an inactive state to avoid epithelial cell attachment; they are activated only in response to stimuli such as those received at the site of an inflammatory response . In a similar manner, integrins at the cell membrane of circulating platelets are normally kept inactive to avoid thrombosis . Epithelial cells (which are non-circulating) normally have active integrins at their cell membrane, helping maintain their stable adhesion to underlying stromal cells that provide signals to maintain normal functioning. [ 39 ]
In plants, there are no bona fide integrin receptors identified to date; nevertheless, several integrin-like proteins were proposed based on structural homology with the metazoan receptors. [ 40 ] Plants contain integrin-linked kinases that are very similar in their primary structure with the animal ILKs. In the experimental model plant Arabidopsis thaliana , one of the integrin-linked kinase genes, ILK1 , has been shown to be a critical element in the plant immune response to signal molecules from bacterial pathogens and plant sensitivity to salt and osmotic stress. [ 41 ] ILK1 protein interacts with the high-affinity potassium transporter HAK5 and with the calcium sensor CML9. [ 41 ] [ 42 ]
When activated, toll-like receptors (TLRs) take adapter molecules within the cytoplasm of cells in order to propagate a signal. Four adaptor molecules are known to be involved in signaling, which are Myd88 , TIRAP , TRIF , and TRAM . [ 43 ] [ 44 ] [ 45 ] These adapters activate other intracellular molecules such as IRAK1 , IRAK4 , TBK1 , and IKKi that amplify the signal, eventually leading to the induction or suppression of genes that cause certain responses. Thousands of genes are activated by TLR signaling, implying that this method constitutes an important gateway for gene modulation.
A ligand-gated ion channel, upon binding with a ligand, changes conformation to open a channel in the cell membrane through which ions relaying signals can pass. An example of this mechanism is found in the receiving cell of a neural synapse . The influx of ions that occurs in response to the opening of these channels induces action potentials , such as those that travel along nerves, by depolarizing the membrane of post-synaptic cells, resulting in the opening of voltage-gated ion channels.
An example of an ion allowed into the cell during a ligand-gated ion channel opening is Ca 2+ ; it acts as a second messenger initiating signal transduction cascades and altering the physiology of the responding cell. This results in amplification of the synapse response between synaptic cells by remodelling the dendritic spines involved in the synapse.
Intracellular receptors, such as nuclear receptors and cytoplasmic receptors , are soluble proteins localized within their respective areas. The typical ligands for nuclear receptors are non-polar hormones like the steroid hormones testosterone and progesterone and derivatives of vitamins A and D. To initiate signal transduction, the ligand must pass through the plasma membrane by passive diffusion. On binding with the receptor, the ligands pass through the nuclear membrane into the nucleus , altering gene expression.
Activated nuclear receptors attach to the DNA at receptor-specific hormone-responsive element (HRE) sequences, located in the promoter region of the genes activated by the hormone-receptor complex. Due to their enabling gene transcription, they are alternatively called inductors of gene expression . All hormones that act by regulation of gene expression have two consequences in their mechanism of action; their effects are produced after a characteristically long period of time and their effects persist for another long period of time, even after their concentration has been reduced to zero, due to a relatively slow turnover of most enzymes and proteins that would either deactivate or terminate ligand binding onto the receptor.
Nucleic receptors have DNA-binding domains containing zinc fingers and a ligand-binding domain; the zinc fingers stabilize DNA binding by holding its phosphate backbone. DNA sequences that match the receptor are usually hexameric repeats of any kind; the sequences are similar but their orientation and distance differentiate them. The ligand-binding domain is additionally responsible for dimerization of nucleic receptors prior to binding and providing structures for transactivation used for communication with the translational apparatus.
Steroid receptors are a subclass of nuclear receptors located primarily within the cytosol. In the absence of steroids, they associate in an aporeceptor complex containing chaperone or heatshock proteins (HSPs). The HSPs are necessary to activate the receptor by assisting the protein to fold in a way such that the signal sequence enabling its passage into the nucleus is accessible. Steroid receptors, on the other hand, may be repressive on gene expression when their transactivation domain is hidden. Receptor activity can be enhanced by phosphorylation of serine residues at their N-terminal as a result of another signal transduction pathway, a process called crosstalk .
Retinoic acid receptors are another subset of nuclear receptors. They can be activated by an endocrine-synthesized ligand that entered the cell by diffusion, a ligand synthesised from a precursor like retinol brought to the cell through the bloodstream or a completely intracellularly synthesised ligand like prostaglandin . These receptors are located in the nucleus and are not accompanied by HSPs. They repress their gene by binding to their specific DNA sequence when no ligand binds to them, and vice versa.
Certain intracellular receptors of the immune system are cytoplasmic receptors; recently identified NOD-like receptors (NLRs) reside in the cytoplasm of some eukaryotic cells and interact with ligands using a leucine-rich repeat (LRR) motif similar to TLRs. Some of these molecules like NOD2 interact with RIP2 kinase that activates NF-κB signaling, whereas others like NALP3 interact with inflammatory caspases and initiate processing of particular cytokines like interleukin-1 β. [ 46 ] [ 47 ]
First messengers are the signaling molecules (hormones, neurotransmitters, and paracrine/autocrine agents) that reach the cell from the extracellular fluid and bind to their specific receptors. Second messengers are the substances that enter the cytoplasm and act within the cell to trigger a response. In essence, second messengers serve as chemical relays from the plasma membrane to the cytoplasm, thus carrying out intracellular signal transduction.
The release of calcium ions from the endoplasmic reticulum into the cytosol results in its binding to signaling proteins that are then activated; it is then sequestered in the smooth endoplasmic reticulum [ 48 ] and the mitochondria . Two combined receptor/ion channel proteins control the transport of calcium: the InsP 3 -receptor that transports calcium upon interaction with inositol triphosphate on its cytosolic side; and the ryanodine receptor named after the alkaloid ryanodine , similar to the InsP 3 receptor but having a feedback mechanism that releases more calcium upon binding with it. The nature of calcium in the cytosol means that it is active for only a very short time, meaning its free state concentration is very low and is mostly bound to organelle molecules like calreticulin when inactive.
Calcium is used in many processes including muscle contraction, neurotransmitter release from nerve endings, and cell migration . The three main pathways that lead to its activation are GPCR pathways, RTK pathways, and gated ion channels; it regulates proteins either directly or by binding to an enzyme.
Lipophilic second messenger molecules are derived from lipids residing in cellular membranes; enzymes stimulated by activated receptors activate the lipids by modifying them. Examples include diacylglycerol and ceramide , the former required for the activation of protein kinase C .
Nitric oxide (NO) acts as a second messenger because it is a free radical that can diffuse through the plasma membrane and affect nearby cells. It is synthesised from arginine and oxygen by the NO synthase and works through activation of soluble guanylyl cyclase , which when activated produces another second messenger, cGMP. NO can also act through covalent modification of proteins or their metal co-factors; some have a redox mechanism and are reversible. It is toxic in high concentrations and causes damage during stroke , but is the cause of many other functions like the relaxation of blood vessels, apoptosis , and penile erections .
In addition to nitric oxide, other electronically activated species are also signal-transducing agents in a process called redox signaling . Examples include superoxide , hydrogen peroxide , carbon monoxide , and hydrogen sulfide . Redox signaling also includes active modulation of electronic flows in semiconductive biological macromolecules. [ 49 ]
Gene activations [ 50 ] and metabolism alterations [ 51 ] are examples of cellular responses to extracellular stimulation that require signal transduction. Gene activation leads to further cellular effects, since the products of responding genes include instigators of activation; transcription factors produced as a result of a signal transduction cascade can activate even more genes. Hence, an initial stimulus can trigger the expression of a large number of genes, leading to physiological events like the increased uptake of glucose from the blood stream [ 51 ] and the migration of neutrophils to sites of infection. The set of genes and their activation order to certain stimuli is referred to as a genetic program . [ 52 ]
Mammalian cells require stimulation for cell division and survival; in the absence of growth factor , apoptosis ensues. Such requirements for extracellular stimulation are necessary for controlling cell behavior in unicellular and multicellular organisms; signal transduction pathways are perceived to be so central to biological processes that a large number of diseases are attributed to their dysregulation.
Three basic signals determine cellular growth:
The combination of these signals is integrated into altered cytoplasmic machinery which leads to altered cell behaviour.
Following are some major signaling pathways, demonstrating how ligands binding to their receptors can affect second messengers and eventually result in altered cellular responses.
The earliest notion of signal transduction can be traced back to 1855, when Claude Bernard proposed that ductless glands such as the spleen , the thyroid and adrenal glands , were responsible for the release of "internal secretions" with physiological effects. [ 57 ] Bernard's "secretions" were later named " hormones " by Ernest Starling in 1905. [ 58 ] Together with William Bayliss , Starling had discovered secretin in 1902. [ 57 ] Although many other hormones, most notably insulin , were discovered in the following years, the mechanisms remained largely unknown.
The discovery of nerve growth factor by Rita Levi-Montalcini in 1954, and epidermal growth factor by Stanley Cohen in 1962, led to more detailed insights into the molecular basis of cell signaling, in particular growth factors . [ 59 ] Their work, together with Earl Wilbur Sutherland 's discovery of cyclic AMP in 1956, prompted the redefinition of endocrine signaling to include only signaling from glands, while the terms autocrine and paracrine began to be used. [ 60 ] Sutherland was awarded the 1971 Nobel Prize in Physiology or Medicine , while Levi-Montalcini and Cohen shared it in 1986.
In 1970, Martin Rodbell examined the effects of glucagon on a rat's liver cell membrane receptor. He noted that guanosine triphosphate disassociated glucagon from this receptor and stimulated the G-protein , which strongly influenced the cell's metabolism. Thus, he deduced that the G-protein is a transducer that accepts glucagon molecules and affects the cell. [ 61 ] For this, he shared the 1994 Nobel Prize in Physiology or Medicine with Alfred G. Gilman . Thus, the characterization of RTKs and GPCRs led to the formulation of the concept of "signal transduction", a word first used in 1972. [ 62 ] Some early articles used the terms signal transmission and sensory transduction . [ 63 ] [ 64 ] In 2007, a total of 48,377 scientific papers—including 11,211 review papers —were published on the subject. The term first appeared in a paper's title in 1979. [ 65 ] [ 66 ] Widespread use of the term has been traced to a 1980 review article by Rodbell: [ 61 ] [ 67 ] Research papers focusing on signal transduction first appeared in large numbers in the late 1980s and early 1990s. [ 47 ]
The purpose of this section is to briefly describe some developments in immunology in the 1960s and 1970s, relevant to the initial stages of transmembrane signal transduction, and how they impacted our understanding of immunology, and ultimately of other areas of cell biology.
The relevant events begin with the sequencing of myeloma protein light chains, which are found in abundance in the urine of individuals with multiple myeloma . Biochemical experiments revealed that these so-called Bence Jones proteins consisted of 2 discrete domains –one that varied from one molecule to the next (the V domain) and one that did not (the Fc domain or the Fragment crystallizable region ). [ 68 ] An analysis of multiple V region sequences by Wu and Kabat [ 69 ] identified locations within the V region that were hypervariable and which, they hypothesized, combined in the folded protein to form the antigen recognition site. Thus, within a relatively short time a plausible model was developed for the molecular basis of immunological specificity, and for mediation of biological function through the Fc domain. Crystallization of an IgG molecule soon followed [ 70 ] ) confirming the inferences based on sequencing, and providing an understanding of immunological specificity at the highest level of resolution.
The biological significance of these developments was encapsulated in the theory of clonal selection [ 71 ] which holds that a B cell has on its surface immunoglobulin receptors whose antigen-binding site is identical to that of antibodies that are secreted by the cell when it encounters an antigen, and more specifically a particular B cell clone secretes antibodies with identical sequences. The final piece of the story, the Fluid mosaic model of the plasma membrane provided all the ingredients for a new model for the initiation of signal transduction; viz, receptor dimerization.
The first hints of this were obtained by Becker et al [ 72 ] who demonstrated that the extent to which human basophils —for which bivalent Immunoglobulin E (IgE) functions as a surface receptor – degranulate, depends on the concentration of anti IgE antibodies to which they are exposed, and results in a redistribution of surface molecules, which is absent when monovalent ligand is used. The latter observation was consistent with earlier findings by Fanger et al. [ 73 ] These observations tied a biological response to events and structural details of molecules on the cell surface. A preponderance of evidence soon developed that receptor dimerization initiates responses (reviewed in [ 74 ] ) in a variety of cell types, including B cells.
Such observations led to a number of theoretical (mathematical) developments. The first of these was a simple model proposed by Bell [ 75 ] which resolved an apparent paradox: clustering forms stable networks; i.e. binding is essentially irreversible, whereas the affinities of antibodies secreted by B cells increase as the immune response progresses. A theory of the dynamics of cell surface clustering on lymphocyte membranes was developed by DeLisi and Perelson [ 76 ] who found the size distribution of clusters as a function of time, and its dependence on the affinity and valence of the ligand. Subsequent theories for basophils and mast cells were developed by Goldstein and Sobotka and their collaborators, [ 77 ] [ 78 ] all aimed at the analysis of dose-response patterns of immune cells and their biological correlates. [ 79 ] For a recent review of clustering in immunological systems see. [ 80 ]
Ligand binding to cell surface receptors is also critical to motility, a phenomenon that is best understood in single-celled organisms. An example is a detection and response to concentration gradients by bacteria [ 81 ] -–the classic mathematical theory appearing in. [ 82 ] A recent account can be found in [ 83 ] | https://en.wikipedia.org/wiki/Signal_transduction |
In telecommunications , transmission (sometimes abbreviated as "TX") is the process of sending or propagating an analog or digital signal via a medium that is wired , wireless , or fiber-optic . [ 1 ] [ 2 ]
Transmission system technologies typically refer to physical layer protocol duties such as modulation , demodulation , line coding , equalization , error control , bit synchronization and multiplexing , but it may also involve higher-layer protocol duties, for example, digitizing an analog signal, and data compression .
Transmission of a digital message, or of a digitized analog signal, is known as data transmission .
Examples of transmission are the sending of signals with limited duration, for example, a block or packet of data, a phone call, or an email.
This article related to telecommunications is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Signal_transmission |
Signaling Gateway is a web portal dedicated to signaling pathways powered by the San Diego Supercomputer Center at the University of California, San Diego . It was initiated [ 1 ] by a collaboration between the Alliance for Cellular Signaling and Nature . A primary feature is the Molecule Pages database.
Signaling Gateway Molecule Pages is a database containing "essential information on more than 8000 mammalian proteins (Mouse and Human) involved in cellular signaling." [ 2 ] [ 3 ] [ 4 ]
The content of molecule pages is authored by invited experts and is peer-reviewed. The published pages are citable by digital object identifiers (DOIs). All data in the Molecule Pages are freely available to the public.
Data can be exported to PDF , XML , BioPAX / SBPAX and SBML .
MIRIAM Registry Details. [ 5 ] | https://en.wikipedia.org/wiki/Signaling_Gateway_(website) |
For data compression , signaling compression , or SigComp , is a compression method designed especially for compression of text-based communication data as SIP or RTSP . SigComp had originally been defined in RFC 3320 and was later updated with RFC 4896. A Negative Acknowledgement Mechanism for Signaling Compression is defined in RFC 4077. The SigComp work is performed in the ROHC working group in the transport area of the IETF .
SigComp specifications describe a compression schema that is located in between the application layer and the transport layer (e.g. between SIP and UDP). It is implemented upon a virtual machine configuration which executes a specific set of commands that are optimized for decompression purposes (namely UDVM, Universal Decompressor Virtual Machine).
One strong point for SigComp is that the bytecode to decode messages can be sent over SigComp itself, so this allows to use any kind of compression schema given that it is expressed as bytecode for the UDVM. Thus any SigComp compatible device may use compression mechanisms that did not exist when it was released without any firmware change. Additionally, some decoders may be already been standardised, so SigComp may recall that code so it is not needed to be sent over the connection. To assure that a message is decodable the only requirement is that the UDVM code is available, so the compression of messages is executed off the virtual machine, and native code can be used.
As an independent system a mechanism to signal the application conversation (e.g. a given SIP session), a compartment mechanism is used, so a given application may have any given number of different, independent conversations, while persisting all the session status (as needed/specified per compression schema and UDVM code). | https://en.wikipedia.org/wiki/Signaling_compression |
Signalling (or signaling ; see spelling differences ) in contract theory is the idea that one party (the agent ) credibly conveys some information about itself to another party (the principal ).
Signalling was already discussed and mentioned in the seminal Theory of Games and Economic Behavior , which is considered to be the text that created the research field of game theory. [ 1 ]
Although signalling theory was initially developed by Michael Spence based on observed knowledge gaps between organisations and prospective employees, [ 2 ] its intuitive nature led it to be adapted to many other domains, such as Human Resource Management, business, and financial markets. [ 3 ]
In Spence's job-market signaling model, (potential) employees send a signal about their ability level to the employer by acquiring education credentials. The informational value of the credential comes from the fact that the employer believes the credential is positively correlated with having the greater ability and difficult for low-ability employees to obtain. Thus the credential enables the employer to reliably distinguish low-ability workers from high-ability workers. [ 2 ] The concept of signaling is also applicable in competitive altruistic interaction, where the capacity of the receiving party is limited. [ 4 ]
Signalling started with the idea of asymmetric information (a deviation from perfect information ), which relates to the fact that, in some economic transactions, inequalities exist in the normal market for the exchange of goods and services. In his seminal 1973 article, Michael Spence proposed that two parties could get around the problem of asymmetric information by having one party send a signal that would reveal some piece of relevant information to the other party. [ 2 ] That party would then interpret the signal and adjust their purchasing behaviour accordingly—usually by offering a higher price than if they had not received the signal.
There are, of course, many problems that these parties would immediately run into.
In the job market, potential employees seek to sell their services to employers for some wage , or price . Generally, employers are willing to pay higher wages to employ better workers. While the individual may know their own level of ability, the hiring firm is not (usually) able to observe such an intangible trait—thus there is an asymmetry of information between the two parties. Education credentials can be used as a signal to the firm, indicating a certain level of ability that the individual may possess; thereby narrowing the informational gap. This is beneficial to both parties as long as the signal indicates a desirable attribute—a signal such as a criminal record may not be so desirable. Furthermore, signaling can sometimes be detrimental in the educational scenario, when heuristics of education get overvalued such as an academic degree, that is, despite having equivalent amounts of instruction, parties that own a degree get better outcomes—the sheepskin effect .
Michael Spence considers hiring as a type of investment under uncertainty [ 2 ] analogous to buying a lottery ticket and refers to the attributes of an applicant which are observable to the employer as indices. Of these, attributes which the applicant can manipulate are termed signals. [ clarification needed ] Applicant age is thus an index but is not a signal since it does not change at the discretion of the applicant. The employer is supposed to have conditional probability assessments of productive capacity, based on previous experience of the market, for each combination of indices and signals. [ clarification needed ] The employer updates those assessments upon observing each employee's characteristics. The paper is concerned with a risk-neutral employer. The offered wage is the expected marginal product . Signals may be acquired by sustaining signalling costs (monetary and not). If everyone invests in the signal in the exactly the same way, then the signal can't be used as discriminatory, therefore a critical assumption is made: the costs of signalling are negatively correlated with productivity . This situation as described is a feedback loop: the employer updates their beliefs upon new market information and updates the wage schedule , applicants react by signalling, and recruitment takes place. Michael Spence studies the signalling equilibrium that may result from such a situation. He began his 1973 model with a hypothetical example: [ 2 ] suppose that there are two types of employees—good and bad—and that employers are willing to pay a higher wage to the good type than the bad type. Spence assumes that for employers, there's no real way to tell in advance which employees will be of the good or bad type. Bad employees aren't upset about this, because they get a free ride from the hard work of the good employees. But good employees know that they deserve to be paid more for their higher productivity, so they desire to invest in the signal—in this case, some amount of education . But he does make one key assumption: good-type employees pay less for one unit of education than bad-type employees . The cost he refers to is not necessarily the cost of tuition and living expenses, sometimes called out of pocket expenses, as one could make the argument that higher ability persons tend to enroll in "better" (i.e. more expensive) institutions. Rather, the cost Spence is referring to is the opportunity cost . This is a combination of 'costs', monetary and otherwise, including psychological, time, effort and so on. Of key importance to the value of the signal is the differing cost structure between "good" and "bad" workers. The cost of obtaining identical credentials is strictly lower for the "good" employee than it is for the "bad" employee. The differing cost structure need not preclude "bad" workers from obtaining the credential . All that is necessary for the signal to have value (informational or otherwise) is that the group with the signal is positively correlated with the previously unobservable group of "good" workers. In general, the degree to which a signal is thought to be correlated to unknown or unobservable attributes is directly related to its value.
Spence discovered that even if education did not contribute anything to an employee's productivity, it could still have value to both the employer and employee. If the appropriate cost/benefit structure exists (or is created), "good" employees will buy more education in order to signal their higher productivity.
The increase in wages associated with obtaining a higher credential is sometimes referred to as the “ sheepskin effect ”, [ 5 ] since “sheepskin” informally denotes a diploma . It is important to note that this is not the same as the returns from an additional year of education. The "sheepskin" effect is actually the wage increase above what would normally be attributed to the extra year of education. This can be observed empirically in the wage differences between 'drop-outs' vs. 'completers' with an equal number of years of education. It is also important that one does not equate the fact that higher wages are paid to more educated individuals entirely to signalling or the 'sheepskin' effects. In reality, education serves many different purposes for individuals and society as a whole. Only when all of these aspects, as well as all the many factors affecting wages, are controlled for, does the effect of the "sheepskin" approach its true value. Empirical studies of signalling indicate it as a statistically significant determinant of wages, however, it is one of a host of other attributes—age, sex, and geography are examples of other important factors.
To illustrate his argument, Spence imagines, for simplicity, two productively distinct groups in a population facing one employer. The signal under consideration is education, measured by an index y and is subject to individual choice. Education costs are both monetary and psychic. The data can be summarized as:
Suppose that the employer believes that there is a level of education y* below which productivity is 1 and above which productivity is 2. Their offered wage schedule W(y) will be:
Working with these hypotheses Spence shows that:
In conclusion, even if education has no real contribution to the marginal product of the worker, the combination of the beliefs of the employer and the presence of signalling transforms the education level y* in a prerequisite for the higher paying job. It may appear to an external observer that education has raised the marginal product of labor, without this necessarily being true.
For a signal to be effective, certain conditions must be true. In equilibrium, the cost of obtaining the credential must be lower for high productivity workers and act as a signal to the employer such that they will pay a higher wage.
In this model it is optimal for the higher ability person to obtain the credential (the observable signal) but not for the lower ability individual. The table shows the outcome of low ability person l and high ability person h with and without signal S * :
The structure is as follows:
There are two individuals with differing abilities (productivity) levels.
The premise for the model is that a person of high ability ( h ) has a lower cost for obtaining a given level of education than does a person of lower ability ( l ). Cost can be in terms of monetary, such as tuition, or psychological, stress incurred to obtain the credential.
For the individual:
Thus, if both individuals act rationally it is optimal for person h to obtain S * but not for person l so long as the following conditions are satisfied.
Edit: note that this is incorrect with the example as graphed. Both 'l' and 'h' have lower costs than W* at the education level. Also, Person (credential) and Person (no credential) are not clear.
Edit: note that this is ok as for low type "l": W o > W ∗ − C ′ ( l ) {\displaystyle W_{o}>W^{*}-C'(l)} , and thus low type will choose Do not obtain credential.
Edit: For there to be a separating equilibrium the high type 'h' must also check their outside option; do they want to choose the net pay in the separating equilibrium (calculated above) over the net pay in the pooling equilibrium. Thus we also need to test that: W ∗ − C ′ ( h ) > W ∗ q 1 + W o ( 1 − q 1 ) {\displaystyle W^{*}-C'(h)>W^{*}q_{1}+W_{o}(1-q_{1})} Otherwise high type 'h' will choose Do not obtain credential of the pooling equilibrium.
For the employers:
In equilibrium, in order for the signalling model to hold, the employer must recognize the signal and pay the corresponding wage and this will result in the workers self-sorting into the two groups. One can see that the cost/benefit structure for a signal to be effective must fall within certain bounds or else the system will fail. [ 6 ]
Signaling typically occurs in an IPO , where a company issues out shares to the public market to raise equity capital. This arises due to information asymmetry between potential investors and the company raising capital. Given firms are private before an IPO, prospective investors have limited information about the firm's true value or future prospects, which may lead to market inefficiencies and mispricing. To overcome this information asymmetry, firms may use signaling to communicate their true value to potential investors.
Leland and Pyle (1977) analyzed the role of signals within the process of an IPO, finding that companies with good future perspectives and higher possibilities of success ("good companies") should always send clear signals to the market when going public, i.e. the owner should keep control of a significant percentage of the company. In order for this signal to be perceived as reliable, the signal must be too costly to be imitated by "bad companies". By not providing a signal to the market, asymmetric information will result in adverse selection in the IPO market.
Various forms of signaling have also been observed during IPOs, especially when companies underprice the offered share price to prospective investors. Underpricing can be explained by prospect theory , which suggests that investors tend to be more risk-averse when it comes to gains than losses. Hence, when a company offers its shares at a discount to their true value, it creates the perception of a gain for investors, which can increase demand for the shares and lead to a higher aftermarket price. This excess demand also sends a positive signal to the market that the firm is undervalued, as the issuer signals to the market that they are leaving money on the table - defined as number of shares sold times the difference between the first-day closing market price and the offer price. This represents a substantial indirect cost to the issuing firm, but allows initial investors to achieve sizeable financial returns at the very first day of trading. [ 7 ]
In spite of leaving money on the table, underpricing is still beneficial to the firm because it allows them to raise more capital than they would have if they had priced the shares at their true value, assuming a higher price at market close. This also helps to generate positive publicity and media attention for the issuer, providing further signaling for a company's positive growth prospects.
Additionally, firms can also signal their quality to the market through their choice of an underwriter . A reputable underwriter, such as a well-known investment bank , can signal that the issuing firm is of high quality and has a strong likelihood of future success. Considering the underwriter's role in providing due diligence and expertise in the IPO process, it is unlikely for an underwriter to associate themselves with firms that have a high likelihood of failure. This helps increase the credibility of the issuing firm, and hence the share capital on offer. Additionally, the underwriter's compensation structure, which is typically based on the success of the IPO, provides an incentive for the underwriter to ensure the success of the IPO. Therefore, by choosing a reputable underwriter, the issuing firm can signal its quality to potential investors, which increases the demand for its shares and can potentially lead to a higher aftermarket price. [ 8 ]
However, while signaling mechanisms can benefit issuers, they can also impose costs on investors. Information asymmetry can make it difficult for investors to distinguish between true signals of quality and mere attempts to manipulate the market. Moreover, the use of signals can lead to a "winner's curse" where investors overpay for shares that are not worth the price paid. [ 9 ] Thus, understanding the costs and benefits of different signaling mechanisms is crucial in improving market efficiency and reducing information asymmetry problems.
The development of brand capital is an important strategy firms use to signal quality and reliability to consumers. Waldfogel and Chen (2006) studied the impact of retailers providing information on internet retail sites to the importance of branding as a signalling mechanism. [ 10 ] Their study used web visits to branded vendors, unbranded vendors and third party sites which took data and collated it for consumers labelled information intermediaries. [ 11 ] The paper did not directly measure the outcome on consumer spending because it did not include actual consumer expenditure on branded or unbranded products. [ 12 ] It further acknowledged there is the potential consumer spending deviates from visiting behaviour. [ 13 ] Nonetheless, it found using information intermediaries increases the number of consumer visits to unbranded vendors while it also depresses visits to branded vendors. [ 14 ] The authors concluded by observing that while branding is a market concentrating mechanism, the internet has the potential to result in reducing market concentration as information provision undermines the effectiveness of brand spending. [ 13 ] The extent of its effectiveness depends on the ease and cost effectiveness by which information can be provided. [ 15 ]
Various studies and experiments have analysed signalling in the context of altruism. Historically, due to the nature of small communities, cooperation was particularly important to ensure human flourishing. [ 16 ] Signalling altruism is critical in human societies because altruism is a method of signalling willingness to cooperate. [ 17 ] Studies indicate that altruism boosts an individual’s reputation in the community, which in turn enables the individual to reap greater benefits from reputation including increased assistance if they are in need. [ 17 ] There is often difficulty in distinguishing between pure altruists who do altruistic acts expecting no benefit to themselves whatsoever and impure altruists who do altruistic acts expecting some form of benefit. Pure altruists will be altruistic irrespective of whether there is anyone observing their conduct, whereas impure altruists will give where their altruism is observed and can be reciprocated.
Laboratory experiments conducted by behavioural economists has found that pure altruism is relatively rare. A study conducted by Dana, Weber and Xi Kuang found that in dictator games, the level of proposing 5:5 distributions were much higher when proposers could not excuse their choice by reference to moral considerations. [ 18 ] In games where voters were provided by the testers with a mitigating reason they could cite to the other person to explain their decision, 6:1 splits were much more common than fair 50:50 split. [ 19 ]
Empirical research in real world scenarios shows charitable giving diminishes with anonymity. [ 20 ] Anonymous donations are much less common than non-anonymous donations. [ 20 ] In respect to donations to a national park, researchers found participants were 25% less generous when their identities were not revealed relative to when they were. [ 21 ] They also found donations were subject to reference effects. [ 21 ] Participants on average gave less money where researchers told them the average donation was lower than in other instances where the researchers told participants the amount of the average donation was higher. [ 21 ]
A study on charity runs where donors could reveal only their name, only the amount, their name and amount or remain completely anonymous with no reference to donation amount had three main findings. First, donors that gave a significant amount of money revealed the amounts donated but were more likely to not reveal their names. [ 22 ] Second, those who gave small donations were more likely to reveal their names but hide their donations. [ 22 ] Third, average donors were most likely to reveal both name and amount information. [ 22 ] The researchers noted small donor donations were consistent with free riding behaviour where participants would try and obtain reputation enhancement by noting their donation, without having to donate at levels that would otherwise be necessary to get the same boost if amount information was published. [ 23 ] Average donors revealed name and amount to also gain reputation. [ 23 ] With respect to high donors, the researchers thought two alternatives were possible. Either, donors did not reveal names because despite high donations signalling high cost altruism there were larger reputational drawbacks to what is perceived to be showboating, [ 23 ] or large contributors were genuinely altruistic and wanted to signal the importance of the cause. [ 24 ] Revealing amount values the authors thought is more consistent with the latter hypothesis. [ 24 ]
Signalling has been studied and proposed as a means to address asymmetric information in markets for "lemons". [ 25 ] Recently, signalling theory has been applied in used cars market such as eBay Motors . Lewis (2011) [ 26 ] examines the role of information access and shows that the voluntary disclosure of private information increases the prices of used cars on eBay. Dimoka et al. (2012) [ 27 ] analyzed data from eBay Motors on the role of signals to mitigate product uncertainty. Extending the information asymmetry literature in consumer behavior literature from the agent (seller) to the product, authors theorized and validated the nature and dimensions of product uncertainty, which is distinct from, yet shaped by, seller uncertainty. Authors also found information signals (diagnostic product descriptions and third-party product assurances) to reduce product uncertainty, which negatively affect price premiums (relative to the book values) of the used cars in online used cars markets.
In internet-based hospitality exchange networks such as BeWelcome and Warm Showers , hosts do not expect to receive payments from travelers. The relation between traveler and host is rather shaped by mutual altruism . Travelers send homestay requests to the hosts, which the hosts are not obligated to accept. Both networks as non-profit organizations grant trustworthy teams of scientists access to their anonymized data for publication of insights to the benefit of humanity. In 2015, datasets from BeWelcome and Warm Showers were analyzed. [ 28 ] Analysis of 97,915 homestay requests from BeWelcome and 285,444 homestay requests from Warm Showers showed general regularity — the less time is spent on writing a homestay request, the less is the probability of being accepted by a host. Low-effort communication aka 'copy and paste requests' obviously sends the wrong signal. [ 28 ]
Most signalling models are plagued by a multiplicity of possible equilibrium outcomes. [ 29 ] In a study published in the Journal of Economic Theory , a signalling model has been proposed that has a unique equilibrium outcome. [ 30 ] In the principal-agent model it is argued that an agent will choose a large (observable) investment level when he has a strong outside option. Yet, an agent with a weak outside option might try to bluff by also choosing a large investment, in order to make the principal believe that the agent has a strong outside option (so that the principal will make a better contract offer to the agent). Hence, when an agent has private information about his outside option, signalling may mitigate the hold-up problem .
Due to the nature of international relations and foreign policy, signaling has long been a topic of interest when analyzing the actions of the agents involved. This study of signaling regarding foreign policy has further allowed economists and academics to understand the actions and reactions of foreign bodies when presented with varying information. Typically when interacting with one another, the actions of these foreign parties are heavily dependent on the proposed actions and reactions of each other. [ 31 ] In many cases however, there is an asymmetry of information between the two parties with both looking to aid their own non-mutually beneficial interests.
In foreign policy, it is common to see game theory problems such as the prisoner’s dilemma and chicken game occur as the different parties both have a dominating strategy regardless of the actions of the other party. In order to signal to the other parties, and furthermore for the signal to be credible, strategies such as tying hands and sinking costs are often implemented. These are examples of costly signals which typically present some form of assurance and commitment in order to show that the signal is credible and the party receiving the signal should act on the information given. [ 31 ] Despite this however, there is still much contention as to whether, in practice, costly signaling is effective. In studies by Quek (2016) it was suggested that decision makers such as politicians and leaders don't seem to interpret and understand signals the way that models suggest they should. [ 32 ]
A costly signal in which the cost of an action is incurred upfront ("ex ante") is a sunk cost. An example of this would be the mobilization of an army as this sends a clear signal of intentions and the costs are incurred immediately.
When the cost of the action is incurred after the decision is made ("ex post") it is considered to be tying hands. A common example is an alliance which does not have a large initial monetary cost yet ties the hands of the parties, as either party would incur significant costs if they abandoned the other party, especially in crises.
Theoretically both sinking costs and tying hands are valid forms of costly signaling however they have garnered much criticism due to differing beliefs regarding the overall effectiveness of the methods in altering the likelihood of war. Recent studies such as the Journal of Conflict Resolution suggest that sinking costs and tying hands are both effective in increasing credibility. This was done by finding how the change in the costs of costly signals vary their credibility. Prior to this research studies conducted were binary and static by nature, limiting the capability of the model. [ 33 ] This increased the validity of the use of these signaling mechanisms in foreign diplomacy.
The initial research into signaling suggested that it was an effective tool in order to manage foreign economic and military affairs however, with time and more thorough analysis problems began to present themselves, these being:
In Fearon’s original models ( Bargaining model of war ) the model was simple in that a party would display their intentions, their intended audience would then interpret the signals and act upon them. Thus, creating a perfect scenario which validates the use of signaling. Later in works by Slantchev (2005), it was suggested that due to the nature of using military mobilization as a signal, despite having intentions to avoid war can increase tensions and thus both be a sunk cost and can tie the party’s hands. Furthermore Yarhi-Milo, Kertzer and Renshon (2017) were able to use a more dynamic model to assess the effectiveness of these signals given varying cost levels and reaction levels. [ 32 ] | https://en.wikipedia.org/wiki/Signalling_(economics) |
Signature-tagged mutagenesis ( STM ) is a genetic technique used to study gene function. Recent advances in genome sequencing have allowed us to catalogue a large variety of organisms' genomes, but the function of the genes they contain is still largely unknown. Using STM, the function of the product of a particular gene can be inferred by disabling it and observing the effect on the organism. The original and most common use of STM is to discover which genes in a pathogen are involved in virulence in its host , to aid the development of new medical therapies/drugs.
The gene in question is inactivated by insertional mutation ; a transposon is used which inserts itself into the gene sequence. When that gene is transcribed and translated into a protein, the insertion of the transposon affects the protein structure and (in theory) prevents it from functioning. In STM, mutants are created by random transposon insertion and each transposon contains a different 'tag' sequence that uniquely identifies it. If an insertional mutant bacterium exhibits a phenotype of interest, such as susceptibility to an antibiotic it was previously resistant to, its genome can be sequenced and searched (using a computer) for any of the tags used in the experiment. When a tag is located, the gene that it disrupts is also thus located (it will reside somewhere between a start and stop codon which mark the boundaries of the gene).
STM can be used to discover which genes are critical to a pathogen's virulence by injecting a 'pool' of different random mutants into an animal model (e.g. a mouse infection model) and observing which of the mutants survive and proliferate in the host. Those mutant pathogens that don't survive in the host must have an inactivated gene, required for virulence. Hence, this is an example of a negative selection method.
This genetics article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Signature-tagged_mutagenesis |
In logic , especially mathematical logic , a signature lists and describes the non-logical symbols of a formal language . In universal algebra , a signature lists the operations that characterize an algebraic structure . In model theory , signatures are used for both purposes. They are rarely made explicit in more philosophical treatments of logic.
Formally, a (single-sorted) signature can be defined as a 4-tuple σ = ( S func , S rel , S const , ar ) , {\displaystyle \sigma =\left(S_{\operatorname {func} },S_{\operatorname {rel} },S_{\operatorname {const} },\operatorname {ar} \right),} where S func {\displaystyle S_{\operatorname {func} }} and S rel {\displaystyle S_{\operatorname {rel} }} are disjoint sets not containing any other basic logical symbols, called respectively
and a function ar : S func ∪ S rel → N {\displaystyle \operatorname {ar} :S_{\operatorname {func} }\cup S_{\operatorname {rel} }\to \mathbb {N} } which assigns a natural number called arity to every function or relation symbol. A function or relation symbol is called n {\displaystyle n} -ary if its arity is n . {\displaystyle n.} Some authors define a nullary ( 0 {\displaystyle 0} -ary) function symbol as constant symbol , otherwise constant symbols are defined separately.
A signature with no function symbols is called a relational signature , and a signature with no relation symbols is called an algebraic signature . [ 1 ] A finite signature is a signature such that S func {\displaystyle S_{\operatorname {func} }} and S rel {\displaystyle S_{\operatorname {rel} }} are finite . More generally, the cardinality of a signature σ = ( S func , S rel , S const , ar ) {\displaystyle \sigma =\left(S_{\operatorname {func} },S_{\operatorname {rel} },S_{\operatorname {const} },\operatorname {ar} \right)} is defined as | σ | = | S func | + | S rel | + | S const | . {\displaystyle |\sigma |=\left|S_{\operatorname {func} }\right|+\left|S_{\operatorname {rel} }\right|+\left|S_{\operatorname {const} }\right|.}
The language of a signature is the set of all well formed sentences built from the symbols in that signature together with the symbols in the logical system.
In universal algebra the word type or similarity type is often used as a synonym for "signature". In model theory, a signature σ {\displaystyle \sigma } is often called a vocabulary , or identified with the (first-order) language L {\displaystyle L} to which it provides the non-logical symbols . However, the cardinality of the language L {\displaystyle L} will always be infinite; if σ {\displaystyle \sigma } is finite then | L | {\displaystyle |L|} will be ℵ 0 {\displaystyle \aleph _{0}} .
As the formal definition is inconvenient for everyday use, the definition of a specific signature is often abbreviated in an informal way, as in:
Sometimes an algebraic signature is regarded as just a list of arities, as in:
Formally this would define the function symbols of the signature as something like f 0 {\displaystyle f_{0}} (which is binary), f 1 {\displaystyle f_{1}} (which is unary) and f 2 {\displaystyle f_{2}} (which is nullary), but in reality the usual names are used even in connection with this convention.
In mathematical logic , very often symbols are not allowed to be nullary, [ citation needed ] so that constant symbols must be treated separately rather than as nullary function symbols. They form a set S const {\displaystyle S_{\operatorname {const} }} disjoint from S func , {\displaystyle S_{\operatorname {func} },} on which the arity function ar {\displaystyle \operatorname {ar} } is not defined. However, this only serves to complicate matters, especially in proofs by induction over the structure of a formula, where an additional case must be considered. Any nullary relation symbol, which is also not allowed under such a definition, can be emulated by a unary relation symbol together with a sentence expressing that its value is the same for all elements. This translation fails only for empty structures (which are often excluded by convention). If nullary symbols are allowed, then every formula of propositional logic is also a formula of first-order logic .
An example for an infinite signature uses S func = { + } ∪ { f a : a ∈ F } {\displaystyle S_{\operatorname {func} }=\{+\}\cup \left\{f_{a}:a\in F\right\}} and S rel = { = } {\displaystyle S_{\operatorname {rel} }=\{=\}} to formalize expressions and equations about a vector space over an infinite scalar field F , {\displaystyle F,} where each f a {\displaystyle f_{a}} denotes the unary operation of scalar multiplication by a . {\displaystyle a.} This way, the signature and the logic can be kept single-sorted, with vectors being the only sort. [ 2 ]
In the context of first-order logic , the symbols in a signature are also known as the non-logical symbols , because together with the logical symbols they form the underlying alphabet over which two formal languages are inductively defined: The set of terms over the signature and the set of (well-formed) formulas over the signature.
In a structure , an interpretation ties the function and relation symbols to mathematical objects that justify their names: The interpretation of an n {\displaystyle n} -ary function symbol f {\displaystyle f} in a structure A {\displaystyle \mathbf {A} } with domain A {\displaystyle A} is a function f A : A n → A , {\displaystyle f^{\mathbf {A} }:A^{n}\to A,} and the interpretation of an n {\displaystyle n} -ary relation symbol is a relation R A ⊆ A n . {\displaystyle R^{\mathbf {A} }\subseteq A^{n}.} Here A n = A × A × ⋯ × A {\displaystyle A^{n}=A\times A\times \cdots \times A} denotes the n {\displaystyle n} -fold cartesian product of the domain A {\displaystyle A} with itself, and so f {\displaystyle f} is in fact an n {\displaystyle n} -ary function, and R {\displaystyle R} an n {\displaystyle n} -ary relation.
For many-sorted logic and for many-sorted structures , signatures must encode information about the sorts. The most straightforward way of doing this is via symbol types that play the role of generalized arities. [ 3 ]
Let S {\displaystyle S} be a set (of sorts) not containing the symbols × {\displaystyle \times } or → . {\displaystyle \to .}
The symbol types over S {\displaystyle S} are certain words over the alphabet S ∪ { × , → } {\displaystyle S\cup \{\times ,\to \}} : the relational symbol types s 1 × ⋯ × s n , {\displaystyle s_{1}\times \cdots \times s_{n},} and the functional symbol types s 1 × ⋯ × s n → s ′ , {\displaystyle s_{1}\times \cdots \times s_{n}\to s^{\prime },} for non-negative integers n {\displaystyle n} and s 1 , s 2 , … , s n , s ′ ∈ S . {\displaystyle s_{1},s_{2},\ldots ,s_{n},s^{\prime }\in S.} (For n = 0 , {\displaystyle n=0,} the expression s 1 × ⋯ × s n {\displaystyle s_{1}\times \cdots \times s_{n}} denotes the empty word.)
A (many-sorted) signature is a triple ( S , P , type ) {\displaystyle (S,P,\operatorname {type} )} consisting of | https://en.wikipedia.org/wiki/Signature_(logic) |
In mathematical notation for numbers , a signed-digit representation is a positional numeral system with a set of signed digits used to encode the integers .
Signed-digit representation can be used to accomplish fast addition of integers because it can eliminate chains of dependent carries. [ 1 ] In the binary numeral system , a special case signed-digit representation is the non-adjacent form , which can offer speed benefits with minimal space overhead.
Challenges in calculation stimulated early authors Colson (1726) and Cauchy (1840) to use signed-digit representation. The further step of replacing negated digits with new ones was suggested by Selling (1887) and Cajori (1928).
In 1928, Florian Cajori noted the recurring theme of signed digits, starting with Colson (1726) and Cauchy (1840). [ 2 ] In his book History of Mathematical Notations , Cajori titled the section "Negative numerals". [ 3 ] For completeness, Colson [ 4 ] uses examples and describes addition (pp. 163–4), multiplication (pp. 165–6) and division (pp. 170–1) using a table of multiples of the divisor. He explains the convenience of approximation by truncation in multiplication. Colson also devised an instrument (Counting Table) that calculated using signed digits.
Eduard Selling [ 5 ] advocated inverting the digits 1, 2, 3, 4, and 5 to indicate the negative sign. He also suggested snie , jes , jerd , reff , and niff as names to use vocally. Most of the other early sources used a bar over a digit to indicate a negative sign for it. Another German usage of signed-digits was described in 1902 in Klein's encyclopedia . [ 6 ]
Let D {\displaystyle {\mathcal {D}}} be a finite set of numerical digits with cardinality b > 1 {\displaystyle b>1} (If b ≤ 1 {\displaystyle b\leq 1} , then the positional number system is trivial and only represents the trivial ring ), with each digit denoted as d i {\displaystyle d_{i}} for 0 ≤ i < b . {\displaystyle 0\leq i<b.} b {\displaystyle b} is known as the radix or number base . D {\displaystyle {\mathcal {D}}} can be used for a signed-digit representation if it's associated with a unique function f D : D → Z {\displaystyle f_{\mathcal {D}}:{\mathcal {D}}\rightarrow \mathbb {Z} } such that f D ( d i ) ≡ i mod b {\displaystyle f_{\mathcal {D}}(d_{i})\equiv i{\bmod {b}}} for all 0 ≤ i < b . {\displaystyle 0\leq i<b.} This function, f D , {\displaystyle f_{\mathcal {D}},} is what rigorously and formally establishes how integer values are assigned to the symbols/glyphs in D . {\displaystyle {\mathcal {D}}.} One benefit of this formalism is that the definition of "the integers" (however they may be defined) is not conflated with any particular system for writing/representing them; in this way, these two distinct (albeit closely related) concepts are kept separate.
D {\displaystyle {\mathcal {D}}} can be partitioned into three distinct sets D + {\displaystyle {\mathcal {D}}_{+}} , D 0 {\displaystyle {\mathcal {D}}_{0}} , and D − {\displaystyle {\mathcal {D}}_{-}} , representing the positive, zero, and negative digits respectively, such that all digits d + ∈ D + {\displaystyle d_{+}\in {\mathcal {D}}_{+}} satisfy f D ( d + ) > 0 {\displaystyle f_{\mathcal {D}}(d_{+})>0} , all digits d 0 ∈ D 0 {\displaystyle d_{0}\in {\mathcal {D}}_{0}} satisfy f D ( d 0 ) = 0 {\displaystyle f_{\mathcal {D}}(d_{0})=0} and all digits d − ∈ D − {\displaystyle d_{-}\in {\mathcal {D}}_{-}} satisfy f D ( d − ) < 0 {\displaystyle f_{\mathcal {D}}(d_{-})<0} . The cardinality of D + {\displaystyle {\mathcal {D}}_{+}} is b + {\displaystyle b_{+}} , the cardinality of D 0 {\displaystyle {\mathcal {D}}_{0}} is b 0 {\displaystyle b_{0}} , and the cardinality of D − {\displaystyle {\mathcal {D}}_{-}} is b − {\displaystyle b_{-}} , giving the number of positive and negative digits respectively, such that b = b + + b 0 + b − {\displaystyle b=b_{+}+b_{0}+b_{-}} .
Balanced form representations are representations where for every positive digit d + {\displaystyle d_{+}} , there exist a corresponding negative digit d − {\displaystyle d_{-}} such that f D ( d + ) = − f D ( d − ) {\displaystyle f_{\mathcal {D}}(d_{+})=-f_{\mathcal {D}}(d_{-})} . It follows that b + = b − {\displaystyle b_{+}=b_{-}} . Only odd bases can have balanced form representations, as otherwise d b / 2 {\displaystyle d_{b/2}} has to be the opposite of itself and hence 0, but 0 ≠ b 2 {\displaystyle 0\neq {\frac {b}{2}}} . In balanced form, the negative digits d − ∈ D − {\displaystyle d_{-}\in {\mathcal {D}}_{-}} are usually denoted as positive digits with a bar over the digit, as d − = d ¯ + {\displaystyle d_{-}={\bar {d}}_{+}} for d + ∈ D + {\displaystyle d_{+}\in {\mathcal {D}}_{+}} . For example, the digit set of balanced ternary would be D 3 = { 1 ¯ , 0 , 1 } {\displaystyle {\mathcal {D}}_{3}=\lbrace {\bar {1}},0,1\rbrace } with f D 3 ( 1 ¯ ) = − 1 {\displaystyle f_{{\mathcal {D}}_{3}}({\bar {1}})=-1} , f D 3 ( 0 ) = 0 {\displaystyle f_{{\mathcal {D}}_{3}}(0)=0} , and f D 3 ( 1 ) = 1 {\displaystyle f_{{\mathcal {D}}_{3}}(1)=1} . This convention is adopted in finite fields of odd prime order q {\displaystyle q} : [ 7 ]
Every digit set D {\displaystyle {\mathcal {D}}} has a dual digit set D op {\displaystyle {\mathcal {D}}^{\operatorname {op} }} given by the inverse order of the digits with an isomorphism g : D → D op {\displaystyle g:{\mathcal {D}}\rightarrow {\mathcal {D}}^{\operatorname {op} }} defined by − f D = g ∘ f D op {\displaystyle -f_{\mathcal {D}}=g\circ f_{{\mathcal {D}}^{\operatorname {op} }}} . As a result, for any signed-digit representations N {\displaystyle {\mathcal {N}}} of a number system ring N {\displaystyle N} constructed from D {\displaystyle {\mathcal {D}}} with valuation v D : N → N {\displaystyle v_{\mathcal {D}}:{\mathcal {N}}\rightarrow N} , there exists a dual signed-digit representations of N {\displaystyle N} , N op {\displaystyle {\mathcal {N}}^{\operatorname {op} }} , constructed from D op {\displaystyle {\mathcal {D}}^{\operatorname {op} }} with valuation v D op : N op → N {\displaystyle v_{{\mathcal {D}}^{\operatorname {op} }}:{\mathcal {N}}^{\operatorname {op} }\rightarrow N} , and an isomorphism h : N → N op {\displaystyle h:{\mathcal {N}}\rightarrow {\mathcal {N}}^{\operatorname {op} }} defined by − v D = h ∘ v D op {\displaystyle -v_{\mathcal {D}}=h\circ v_{{\mathcal {D}}^{\operatorname {op} }}} , where − {\displaystyle -} is the additive inverse operator of N {\displaystyle N} . The digit set for balanced form representations is self-dual .
Given the digit set D {\displaystyle {\mathcal {D}}} and function f : D → Z {\displaystyle f:{\mathcal {D}}\rightarrow \mathbb {Z} } as defined above, let us define an integer endofunction T : Z → Z {\displaystyle T:\mathbb {Z} \rightarrow \mathbb {Z} } as the following:
If the only periodic point of T {\displaystyle T} is the fixed point 0 {\displaystyle 0} , then the set of all signed-digit representations of the integers Z {\displaystyle \mathbb {Z} } using D {\displaystyle {\mathcal {D}}} is given by the Kleene plus D + {\displaystyle {\mathcal {D}}^{+}} , the set of all finite concatenated strings of digits d n … d 0 {\displaystyle d_{n}\ldots d_{0}} with at least one digit, with n ∈ N {\displaystyle n\in \mathbb {N} } . Each signed-digit representation m ∈ D + {\displaystyle m\in {\mathcal {D}}^{+}} has a valuation v D : D + → Z {\displaystyle v_{\mathcal {D}}:{\mathcal {D}}^{+}\rightarrow \mathbb {Z} }
Examples include balanced ternary with digits D = { 1 ¯ , 0 , 1 } {\displaystyle {\mathcal {D}}=\lbrace {\bar {1}},0,1\rbrace } .
Otherwise, if there exist a non-zero periodic point of T {\displaystyle T} , then there exist integers that are represented by an infinite number of non-zero digits in D {\displaystyle {\mathcal {D}}} . Examples include the standard decimal numeral system with the digit set dec = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } {\displaystyle \operatorname {dec} =\lbrace 0,1,2,3,4,5,6,7,8,9\rbrace } , which requires an infinite number of the digit 9 {\displaystyle 9} to represent the additive inverse − 1 {\displaystyle -1} , as T dec ( − 1 ) = − 1 − 9 10 = − 1 {\displaystyle T_{\operatorname {dec} }(-1)={\frac {-1-9}{10}}=-1} , and the positional numeral system with the digit set D = { A , 0 , 1 } {\displaystyle {\mathcal {D}}=\lbrace {\text{A}},0,1\rbrace } with f ( A ) = − 4 {\displaystyle f({\text{A}})=-4} , which requires an infinite number of the digit A {\displaystyle {\text{A}}} to represent the number 2 {\displaystyle 2} , as T D ( 2 ) = 2 − ( − 4 ) 3 = 2 {\displaystyle T_{\mathcal {D}}(2)={\frac {2-(-4)}{3}}=2} .
If the integers can be represented by the Kleene plus D + {\displaystyle {\mathcal {D}}^{+}} , then the set of all signed-digit representations of the decimal fractions , or b {\displaystyle b} -adic rationals Z [ 1 ∖ b ] {\displaystyle \mathbb {Z} [1\backslash b]} , is given by Q = D + × P × D ∗ {\displaystyle {\mathcal {Q}}={\mathcal {D}}^{+}\times {\mathcal {P}}\times {\mathcal {D}}^{*}} , the Cartesian product of the Kleene plus D + {\displaystyle {\mathcal {D}}^{+}} , the set of all finite concatenated strings of digits d n … d 0 {\displaystyle d_{n}\ldots d_{0}} with at least one digit, the singleton P {\displaystyle {\mathcal {P}}} consisting of the radix point ( . {\displaystyle .} or , {\displaystyle ,} ), and the Kleene star D ∗ {\displaystyle {\mathcal {D}}^{*}} , the set of all finite concatenated strings of digits d − 1 … d − m {\displaystyle d_{-1}\ldots d_{-m}} , with m , n ∈ N {\displaystyle m,n\in \mathbb {N} } . Each signed-digit representation q ∈ Q {\displaystyle q\in {\mathcal {Q}}} has a valuation v D : Q → Z [ 1 ∖ b ] {\displaystyle v_{\mathcal {D}}:{\mathcal {Q}}\rightarrow \mathbb {Z} [1\backslash b]}
If the integers can be represented by the Kleene plus D + {\displaystyle {\mathcal {D}}^{+}} , then the set of all signed-digit representations of the real numbers R {\displaystyle \mathbb {R} } is given by R = D + × P × D N {\displaystyle {\mathcal {R}}={\mathcal {D}}^{+}\times {\mathcal {P}}\times {\mathcal {D}}^{\mathbb {N} }} , the Cartesian product of the Kleene plus D + {\displaystyle {\mathcal {D}}^{+}} , the set of all finite concatenated strings of digits d n … d 0 {\displaystyle d_{n}\ldots d_{0}} with at least one digit, the singleton P {\displaystyle {\mathcal {P}}} consisting of the radix point ( . {\displaystyle .} or , {\displaystyle ,} ), and the Cantor space D N {\displaystyle {\mathcal {D}}^{\mathbb {N} }} , the set of all infinite concatenated strings of digits d − 1 d − 2 … {\displaystyle d_{-1}d_{-2}\ldots } , with n ∈ N {\displaystyle n\in \mathbb {N} } . Each signed-digit representation r ∈ R {\displaystyle r\in {\mathcal {R}}} has a valuation v D : R → R {\displaystyle v_{\mathcal {D}}:{\mathcal {R}}\rightarrow \mathbb {R} }
The infinite series always converges to a finite real number.
All base- b {\displaystyle b} numerals can be represented as a subset of D Z {\displaystyle {\mathcal {D}}^{\mathbb {Z} }} , the set of all doubly infinite sequences of digits in D {\displaystyle {\mathcal {D}}} , where Z {\displaystyle \mathbb {Z} } is the set of integers , and the ring of base- b {\displaystyle b} numerals is represented by the formal power series ring Z [ [ b , b − 1 ] ] {\displaystyle \mathbb {Z} [[b,b^{-1}]]} , the doubly infinite series
where a i ∈ Z {\displaystyle a_{i}\in \mathbb {Z} } for i ∈ Z {\displaystyle i\in \mathbb {Z} } .
The set of all signed-digit representations of the integers modulo b n {\displaystyle b^{n}} , Z ∖ b n Z {\displaystyle \mathbb {Z} \backslash b^{n}\mathbb {Z} } is given by the set D n {\displaystyle {\mathcal {D}}^{n}} , the set of all finite concatenated strings of digits d n − 1 … d 0 {\displaystyle d_{n-1}\ldots d_{0}} of length n {\displaystyle n} , with n ∈ N {\displaystyle n\in \mathbb {N} } . Each signed-digit representation m ∈ D n {\displaystyle m\in {\mathcal {D}}^{n}} has a valuation v D : D n → Z / b n Z {\displaystyle v_{\mathcal {D}}:{\mathcal {D}}^{n}\rightarrow \mathbb {Z} /b^{n}\mathbb {Z} }
A Prüfer group is the quotient group Z ( b ∞ ) = Z [ 1 ∖ b ] / Z {\displaystyle \mathbb {Z} (b^{\infty })=\mathbb {Z} [1\backslash b]/\mathbb {Z} } of the integers and the b {\displaystyle b} -adic rationals. The set of all signed-digit representations of the Prüfer group is given by the Kleene star D ∗ {\displaystyle {\mathcal {D}}^{*}} , the set of all finite concatenated strings of digits d 1 … d n {\displaystyle d_{1}\ldots d_{n}} , with n ∈ N {\displaystyle n\in \mathbb {N} } . Each signed-digit representation p ∈ D ∗ {\displaystyle p\in {\mathcal {D}}^{*}} has a valuation v D : D ∗ → Z ( b ∞ ) {\displaystyle v_{\mathcal {D}}:{\mathcal {D}}^{*}\rightarrow \mathbb {Z} (b^{\infty })}
The circle group is the quotient group T = R / Z {\displaystyle \mathbb {T} =\mathbb {R} /\mathbb {Z} } of the integers and the real numbers. The set of all signed-digit representations of the circle group is given by the Cantor space D N {\displaystyle {\mathcal {D}}^{\mathbb {N} }} , the set of all right-infinite concatenated strings of digits d 1 d 2 … {\displaystyle d_{1}d_{2}\ldots } . Each signed-digit representation m ∈ D n {\displaystyle m\in {\mathcal {D}}^{n}} has a valuation v D : D N → T {\displaystyle v_{\mathcal {D}}:{\mathcal {D}}^{\mathbb {N} }\rightarrow \mathbb {T} }
The infinite series always converges .
The set of all signed-digit representations of the b {\displaystyle b} -adic integers , Z b {\displaystyle \mathbb {Z} _{b}} is given by the Cantor space D N {\displaystyle {\mathcal {D}}^{\mathbb {N} }} , the set of all left-infinite concatenated strings of digits … d 1 d 0 {\displaystyle \ldots d_{1}d_{0}} . Each signed-digit representation m ∈ D n {\displaystyle m\in {\mathcal {D}}^{n}} has a valuation v D : D N → Z b {\displaystyle v_{\mathcal {D}}:{\mathcal {D}}^{\mathbb {N} }\rightarrow \mathbb {Z} _{b}}
The set of all signed-digit representations of the b {\displaystyle b} -adic solenoids , T b {\displaystyle \mathbb {T} _{b}} is given by the Cantor space D Z {\displaystyle {\mathcal {D}}^{\mathbb {Z} }} , the set of all doubly infinite concatenated strings of digits … d 1 d 0 d − 1 … {\displaystyle \ldots d_{1}d_{0}d_{-1}\ldots } . Each signed-digit representation m ∈ D n {\displaystyle m\in {\mathcal {D}}^{n}} has a valuation v D : D Z → T b {\displaystyle v_{\mathcal {D}}:{\mathcal {D}}^{\mathbb {Z} }\rightarrow \mathbb {T} _{b}}
The oral and written forms of numbers in the Indo-Aryan languages use a negative numeral (e.g., "un" in Hindi and Bengali , "un" or "unna" in Punjabi , "ekon" in Marathi ) for the numbers between 11 and 90 that end with a nine. The numbers followed by their names are shown for Punjabi below (the prefix "ik" means "one"): [ 8 ]
Similarly, the Sesotho language utilizes negative numerals to form 8's and 9's.
In Classical Latin , [ 9 ] integers 18 and 19 did not even have a spoken, nor written form including corresponding parts for "eight" or "nine" in practice - despite them being in existence. Instead, in Classic Latin,
For upcoming integer numerals [28, 29, 38, 39, ..., 88, 89] the additive form in the language had been much more common, however, for the listed numbers, the above form was still preferred. Hence, approaching thirty, numerals were expressed as: [ 10 ]
This is one of the main foundations of contemporary historians' reasoning, explaining why the subtractive I- and II- was so common in this range of cardinals compared to other ranges. Numerals 98 and 99 could also be expressed in both forms, yet "two to hundred" might have sounded a bit odd - clear evidence is the scarce occurrence of these numbers written down in a subtractive fashion in authentic sources.
There is yet another language having this feature (by now, only in traces), however, still in active use today. This is the Finnish Language , where the (spelled out) numerals are used this way should a digit of 8 or 9 occur. The scheme is like this: [ 11 ]
...
Above list is no special case, it consequently appears in larger cardinals as well, e.g.:
Emphasizing of these attributes stay present even in the shortest colloquial forms of numerals:
...
However, this phenomenon has no influence on written numerals, the Finnish use the standard Western-Arabic decimal notation.
In the English language it is common to refer to times as, for example, 'seven to three', 'to' performing the negation.
There exist other signed-digit bases such that the base b ≠ b + + b − + 1 {\displaystyle b\neq b_{+}+b_{-}+1} . A notable examples of this is Booth encoding , which has a digit set D = { 1 ¯ , 0 , 1 } {\displaystyle {\mathcal {D}}=\lbrace {\bar {1}},0,1\rbrace } with b + = 1 {\displaystyle b_{+}=1} and b − = 1 {\displaystyle b_{-}=1} , but which uses a base b = 2 < 3 = b + + b − + 1 {\displaystyle b=2<3=b_{+}+b_{-}+1} . The standard binary numeral system would only use digits of value { 0 , 1 } {\displaystyle \lbrace 0,1\rbrace } .
Note that non-standard signed-digit representations are not unique. For instance:
The non-adjacent form (NAF) of Booth encoding does guarantee a unique representation for every integer value. However, this only applies for integer values. For example, consider the following repeating binary numbers in NAF, | https://en.wikipedia.org/wiki/Signed-digit_representation |
In mathematics , the sign of a real number is its property of being either positive, negative , or 0 . Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. In some contexts, it makes sense to distinguish between a positive and a negative zero .
In mathematics and physics, the phrase "change of sign" is associated with exchanging an object for its additive inverse (multiplication with −1 , negation), an operation which is not restricted to real numbers. It applies among other objects to vectors, matrices, and complex numbers, which are not prescribed to be only either positive, negative, or zero.
The word "sign" is also often used to indicate binary aspects of mathematical or scientific objects, such as odd and even ( sign of a permutation ), sense of orientation or rotation ( cw/ccw ), one sided limits , and other concepts described in § Other meanings below.
Numbers from various number systems, like integers , rationals , complex numbers , quaternions , octonions , ... may have multiple attributes, that fix certain properties of a number. A number system that bears the structure of an ordered ring contains a unique number that when added with any number leaves the latter unchanged. This unique number is known as the system's additive identity element . For example, the integers has the structure of an ordered ring. This number is generally denoted as 0. Because of the total order in this ring, there are numbers greater than zero, called the positive numbers. Another property required for a ring to be ordered is that, for each positive number, there exists a unique corresponding number less than 0 whose sum with the original positive number is 0. These numbers less than 0 are called the negative numbers. The numbers in each such pair are their respective additive inverses . This attribute of a number, being exclusively either zero (0) , positive (+) , or negative (−) , is called its sign , and is often encoded to the real numbers 0 , 1 , and −1 , respectively (similar to the way the sign function is defined). [ 1 ] Since rational and real numbers are also ordered rings (in fact ordered fields ), the sign attribute also applies to these number systems.
When a minus sign is used in between two numbers, it represents the binary operation of subtraction. When a minus sign is written before a single number, it represents the unary operation of yielding the additive inverse (sometimes called negation ) of the operand. Abstractly then, the difference of two number is the sum of the minuend with the additive inverse of the subtrahend. While 0 is its own additive inverse ( −0 = 0 ), the additive inverse of a positive number is negative, and the additive inverse of a negative number is positive. A double application of this operation is written as −(−3) = 3 . The plus sign is predominantly used in algebra to denote the binary operation of addition, and only rarely to emphasize the positivity of an expression.
In common numeral notation (used in arithmetic and elsewhere), the sign of a number is often made explicit by placing a plus or a minus sign before the number. For example, +3 denotes "positive three", and −3 denotes "negative three" (algebraically: the additive inverse of 3 ). Without specific context (or when no explicit sign is given), a number is interpreted per default as positive. This notation establishes a strong association of the minus sign " − " with negative numbers, and the plus sign "+" with positive numbers.
Within the convention of zero being neither positive nor negative, a specific sign-value 0 may be assigned to the number value 0 . This is exploited in the sgn {\displaystyle \operatorname {sgn} } -function , as defined for real numbers. [ 1 ] In arithmetic, +0 and −0 both denote the same number 0 . There is generally no danger of confusing the value with its sign, although the convention of assigning both signs to 0 does not immediately allow for this discrimination.
In certain European countries, e.g. in Belgium and France, 0 is considered to be both positive and negative following the convention set forth by Nicolas Bourbaki . [ 2 ]
In some contexts, such as floating-point representations of real numbers within computers, it is useful to consider signed versions of zero, with signed zeros referring to different, discrete number representations (see signed number representations for more).
The symbols +0 and −0 rarely appear as substitutes for 0 + and 0 − , used in calculus and mathematical analysis for one-sided limits (right-sided limit and left-sided limit, respectively). This notation refers to the behaviour of a function as its real input variable approaches 0 along positive (resp., negative) values; the two limits need not exist or agree.
When 0 is said to be neither positive nor negative, the following phrases may refer to the sign of a number:
When 0 is said to be both positive and negative, [ citation needed ] modified phrases are used to refer to the sign of a number:
For example, the absolute value of a real number is always "non-negative", but is not necessarily "positive" in the first interpretation, whereas in the second interpretation, it is called "positive"—though not necessarily "strictly positive".
The same terminology is sometimes used for functions that yield real or other signed values. For example, a function would be called a positive function if its values are positive for all arguments of its domain, or a non-negative function if all of its values are non-negative.
Complex numbers are impossible to order, so they cannot carry the structure of an ordered ring, and, accordingly, cannot be partitioned into positive and negative complex numbers. They do, however, share an attribute with the reals, which is called absolute value or magnitude . Magnitudes are always non-negative real numbers, and to any non-zero number there belongs a positive real number, its absolute value .
For example, the absolute value of −3 and the absolute value of 3 are both equal to 3 . This is written in symbols as | −3 | = 3 and | 3 | = 3 .
In general, any arbitrary real value can be specified by its magnitude and its sign. Using the standard encoding, any real value is given by the product of the magnitude and the sign in standard encoding. This relation can be generalized to define a sign for complex numbers.
Since the real and complex numbers both form a field and contain the positive reals, they also contain the reciprocals of the magnitudes of all non-zero numbers. This means that any non-zero number may be multiplied with the reciprocal of its magnitude, that is, divided by its magnitude. It is immediate that the quotient of any non-zero real number by its magnitude yields exactly its sign. By analogy, the sign of a complex number z can be defined as the quotient of z and its magnitude | z | . The sign of a complex number is the exponential of the product of its argument with the imaginary unit. represents in some sense its complex argument. This is to be compared to the sign of real numbers, except with e i π = − 1. {\displaystyle e^{i\pi }=-1.} For the definition of a complex sign-function. see § Complex sign function below.
When dealing with numbers, it is often convenient to have their sign available as a number. This is accomplished by functions that extract the sign of any number, and map it to a predefined value before making it available for further calculations. For example, it might be advantageous to formulate an intricate algorithm for positive values only, and take care of the sign only afterwards.
The sign function or signum function extracts the sign of a real number, by mapping the set of real numbers to the set of the three reals { − 1 , 0 , 1 } . {\displaystyle \{-1,\;0,\;1\}.} It can be defined as follows: [ 1 ] sgn : R → { − 1 , 0 , 1 } x ↦ sgn ( x ) = { − 1 if x < 0 , 0 if x = 0 , 1 if x > 0. {\displaystyle {\begin{aligned}\operatorname {sgn} :{}&\mathbb {R} \to \{-1,0,1\}\\&x\mapsto \operatorname {sgn}(x)={\begin{cases}-1&{\text{if }}x<0,\\~~\,0&{\text{if }}x=0,\\~~\,1&{\text{if }}x>0.\end{cases}}\end{aligned}}} Thus sgn( x ) is 1 when x is positive, and sgn( x ) is −1 when x is negative. For non-zero values of x , this function can also be defined by the formula sgn ( x ) = x | x | = | x | x , {\displaystyle \operatorname {sgn}(x)={\frac {x}{|x|}}={\frac {|x|}{x}},} where | x | is the absolute value of x .
While a real number has a 1-dimensional direction, a complex number has a 2-dimensional direction. The complex sign function requires the magnitude of its argument z = x + iy , which can be calculated as | z | = z z ¯ = x 2 + y 2 . {\displaystyle |z|={\sqrt {z{\bar {z}}}}={\sqrt {x^{2}+y^{2}}}.}
Analogous to above, the complex sign function extracts the complex sign of a complex number by mapping the set of non-zero complex numbers to the set of unimodular complex numbers, and 0 to 0 : { z ∈ C : | z | = 1 } ∪ { 0 } . {\displaystyle \{z\in \mathbb {C} :|z|=1\}\cup \{0\}.} It may be defined as follows:
Let z be also expressed by its magnitude and one of its arguments φ as z = | z |⋅ e iφ , then [ 3 ] sgn ( z ) = { 0 for z = 0 z | z | = e i φ otherwise . {\displaystyle \operatorname {sgn}(z)={\begin{cases}0&{\text{for }}z=0\\{\dfrac {z}{|z|}}=e^{i\varphi }&{\text{otherwise}}.\end{cases}}}
This definition may also be recognized as a normalized vector, that is, a vector whose direction is unchanged, and whose length is fixed to unity . If the original value was R,θ in polar form, then sign(R, θ) is 1 θ. Extension of sign() or signum() to any number of dimensions is obvious, but this has already been defined as normalizing a vector.
In situations where there are exactly two possibilities on equal footing for an attribute, these are often labelled by convention as plus and minus , respectively. In some contexts, the choice of this assignment (i.e., which range of values is considered positive and which negative) is natural, whereas in other contexts, the choice is arbitrary, making an explicit sign convention necessary, the only requirement being consistent use of the convention.
In many contexts, it is common to associate a sign with the measure of an angle , particularly an oriented angle or an angle of rotation . In such a situation, the sign indicates whether the angle is in the clockwise or counterclockwise direction. Though different conventions can be used, it is common in mathematics to have counterclockwise angles count as positive, and clockwise angles count as negative. [ 4 ]
It is also possible to associate a sign to an angle of rotation in three dimensions, assuming that the axis of rotation has been oriented. Specifically, a right-handed rotation around an oriented axis typically counts as positive, while a left-handed rotation counts as negative.
An angle which is the negative of a given angle has an equal arc, but the opposite axis . [ 5 ]
When a quantity x changes over time, the change in the value of x is typically defined by the equation Δ x = x final − x initial . {\displaystyle \Delta x=x_{\text{final}}-x_{\text{initial}}.}
Using this convention, an increase in x counts as positive change, while a decrease of x counts as negative change. In calculus , this same convention is used in the definition of the derivative . As a result, any increasing function has positive derivative, while any decreasing function has negative derivative.
When studying one-dimensional displacements and motions in analytic geometry and physics , it is common to label the two possible directions as positive and negative. Because the number line is usually drawn with positive numbers to the right, and negative numbers to the left, a common convention is for motions to the right to be given a positive sign, and for motions to the left to be given a negative sign.
On the Cartesian plane , the rightward and upward directions are usually thought of as positive, with rightward being the positive x -direction, and upward being the positive y -direction. If a displacement vector is separated into its vector components , then the horizontal part will be positive for motion to the right and negative for motion to the left, while the vertical part will be positive for motion upward and negative for motion downward.
Likewise, a negative speed (rate of change of displacement) implies a velocity in the opposite direction , i.e., receding instead of advancing; a special case is the radial speed .
In 3D space , notions related to sign can be found in the two normal orientations and orientability in general.
In computing , an integer value may be either signed or unsigned, depending on whether the computer is keeping track of a sign for the number. By restricting an integer variable to non-negative values only, one more bit can be used for storing the value of a number. Because of the way integer arithmetic is done within computers, signed number representations usually do not store the sign as a single independent bit, instead using e.g. two's complement .
In contrast, real numbers are stored and manipulated as floating point values. The floating point values are represented using three separate values, mantissa, exponent, and sign. Given this separate sign bit, it is possible to represent both positive and negative zero. Most programming languages normally treat positive zero and negative zero as equivalent values, albeit, they provide means by which the distinction can be detected.
In addition to the sign of a real number, the word sign is also used in various related ways throughout mathematics and other sciences: | https://en.wikipedia.org/wiki/Signed_direction |
In the area of graph theory in mathematics , a signed graph is a graph in which each edge has a positive or negative sign.
A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. [ 1 ] Dénes Kőnig had already studied equivalent notions in 1936 under a different terminology but without recognizing the relevance of the sign group. [ 2 ] At the Center for Group Dynamics at the University of Michigan , Dorwin Cartwright and Harary generalized Fritz Heider 's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs. [ 3 ] [ 4 ]
Signed graphs have been rediscovered many times because they come up naturally in many unrelated areas. [ 5 ] For instance, they enable one to describe and analyze the geometry of subsets of the classical root systems . They appear in topological graph theory and group theory . They are a natural context for questions about odd and even cycles in graphs. They appear in computing the ground state energy in the non-ferromagnetic Ising model ; for this one needs to find a largest balanced edge set in Σ. They have been applied to data classification in correlation clustering .
The sign of a path is the product of the signs of its edges. Thus a path is positive only if there are an even number of negative edges in it (where zero is even). In the mathematical balance theory of Frank Harary , a signed graph is balanced when every cycle is positive. Harary proves that a signed graph is balanced when (1) for every pair of nodes, all paths between them have the same sign, or (2) the vertices partition into a pair of subsets (possibly empty), each containing only positive edges, but connected by negative edges. [ 1 ] It generalizes the theorem that an ordinary (unsigned) graph is bipartite if and only if every cycle has even length.
A simple proof uses the method of switching. Switching a signed graph means reversing the signs of all edges between a vertex subset and its complement. To prove Harary's theorem, one shows by induction that Σ can be switched to be all positive if and only if it is balanced.
A weaker theorem, but with a simpler proof, is that if every 3-cycle in a signed complete graph is positive, then the graph is balanced. For the proof, pick an arbitrary node n and place it and all those nodes that are linked to n by a positive edge in one group, called A , and all those linked to n by a negative edge in the other, called B . Since this is a complete graph, every two nodes in A must be friends and every two nodes in B must be friends, otherwise there would be a 3-cycle which was unbalanced. (Since this is a complete graph, any one negative edge would cause an unbalanced 3-cycle.) Likewise, all negative edges must go between the two groups. [ 6 ]
The frustration index (early called the line index of balance [ 7 ] ) of Σ is the smallest number of edges whose deletion, or equivalently whose sign reversal (a theorem of Harary [ 7 ] ), makes Σ balanced. The reason for the equivalence is that the frustration index equals the smallest number of edges whose negation (or, equivalently, deletion) makes Σ balanced.
A second way of describing the frustration index is that it is the smallest number of edges that cover all negative cycles. This quantity has been called the negative cycle cover number .
There is another equivalent definition (which can be proved easily by switching). Give each vertex a value of +1 or −1; we call this a state of Σ. An edge is called satisfied if it is positive and both endpoints have the same value, or it is negative and the endpoints have opposite values. An edge that is not satisfied is called frustrated . The smallest number of frustrated edges over all states is the frustration index. This definition was first introduced in a different notation by Abelson and Rosenberg under the (obsolete) name complexity . [ 8 ] The complement of such a set is a balanced subgraph of Σ with the most possible edges.
Finding the frustration index is an NP-hard problem.
One can see the NP-hard complexity by observing that the frustration index of an all-negative signed graph is the same as the maximum cut problem in graph theory, which is NP-hard.
The frustration index is important in a model of spin glasses , the mixed Ising model . In this model, the signed graph is fixed. A state consists of giving a "spin", either "up" or "down", to each vertex. We think of spin up as +1 and spin down as −1. Thus, each state has a number of frustrated edges. The energy of a state is larger when it has more frustrated edges, so a ground state is a state with the fewest frustrated energy. Thus, to find the ground state energy of Σ one has to find the frustration index.
The analogous vertex number is the frustration number , defined as the smallest number of vertices whose deletion from Σ results in balance. Equivalently, one wants the largest order of a balanced induced subgraph of Σ.
Three fundamental questions about a signed graph are: Is it balanced? What is the largest size of a balanced edge set in it? What is the smallest number of vertices that must be deleted to make it balanced? The first question is easy to solve in polynomial time. The second question is called the Frustration Index or Maximum Balanced Subgraph problem. It is NP-hard because its special case (when all edges of the graph are negative) is the NP-hard problem Maximum Cut . The third question is called the Frustration Number or Maximum Balanced Induced Subgraph problem, is also NP-hard ; see e.g. [ 9 ]
There are two matroids associated with a signed graph, called the signed-graphic matroid (also called the frame matroid or sometimes bias matroid ) and the lift matroid , both of which generalize the cycle matroid of a graph. They are special cases of the same matroids of a biased graph .
The frame matroid (or signed-graphic matroid ) M ( G ) has for its ground set the edge set E . [ 10 ] An edge set is independent if each component contains either no circles or just one circle, which is negative. (In matroid theory a half-edge acts exactly like a negative loop.) A circuit of the matroid is either a positive circle, or a pair of negative circles together with a connecting simple path, such that the two circles are either disjoint (then the connecting path has one end in common with each circle and is otherwise disjoint from both) or share just a single common vertex (in this case the connecting path is that single vertex). The rank of an edge set S is n − b , where n is the number of vertices of G and b is the number of balanced components of S , counting isolated vertices as balanced components.
This matroid is the column matroid of the incidence matrix of the signed graph.
That is why it describes the linear dependencies of the roots of a classical root system.
The extended lift matroid L 0 ( G ) has for its ground set the set E 0 the union of edge set E with an extra point , which we denote e 0 . The lift matroid L ( G ) is the extended lift matroid restricted to E . The extra point acts exactly like a negative loop, so we describe only the lift matroid. An edge set is independent if it contains either no circles or just one circle, which is negative. (This is the same rule that is applied separately to each component in the signed-graphic matroid.) A matroid circuit is either a positive circle or a pair of negative circles that are either disjoint or have just a common vertex. The rank of an edge set S is n − c + ε, where c is the number of components of S , counting isolated vertices, and ε is 0 if S is balanced and 1 if it is not.
Sometimes the signs are taken to be +1 and −1. This is only a difference of notation, if the signs are still multiplied around a circle and the sign of the product is the important thing. However, there are two other ways of treating the edge labels that do not fit into signed graph theory.
The term signed graph is applied occasionally to graphs in which each edge has a weight, w ( e ) = +1 or −1. These are not the same kind of signed graph; they are weighted graphs with a restricted weight set. The difference is that weights are added, not multiplied. The problems and methods are completely different.
The name is also applied to graphs in which the signs function as colors on the edges. The significance of the color is that it determines various weights applied to the edge, and not that its sign is intrinsically significant. This is the case in knot theory , where the only significance of the signs is that they can be interchanged by the two-element group, but there is no intrinsic difference between positive and negative. The matroid of a sign-colored graph is the cycle matroid of the underlying graph; it is not the frame or lift matroid of the signed graph. The sign labels, instead of changing the matroid, become signs on the elements of the matroid.
In this article we discuss only signed graph theory in the strict sense. For sign-colored graphs see colored matroids .
A signed digraph is a directed graph with signed arcs. Signed digraphs are far more complicated than signed graphs, because only the signs of directed cycles are significant. For instance, there are several definitions of balance, each of which is hard to characterize, in strong contrast with the situation for signed undirected graphs.
Signed digraphs should not be confused with oriented signed graphs . The latter are bidirected graphs , not directed graphs (except in the trivial case of all positive signs).
A vertex-signed graph , sometimes called a marked graph , is a graph whose vertices are given signs. A circle is called consistent (but this is unrelated to logical consistency) or harmonious if the product of its vertex signs is positive, and inconsistent or inharmonious if the product is negative. There is no simple characterization of harmonious vertex-signed graphs analogous to Harary's balance theorem; instead, the characterization has been a difficult problem, best solved (even more generally) by Joglekar, Shah, and Diwan (2012). [ 11 ]
It is often easy to add edge signs to the theory of vertex signs without major change; thus, many results for vertex-signed graphs (or "marked signed graphs") extend naturally to vertex-and-edge-signed graphs. This is notably true for the characterization of harmony by Joglekar, Shah, and Diwan (2012).
The difference between a marked signed graph and a signed graph with a state function (as in § Frustration ) is that the vertex signs in the former are part of the essential structure, while a state function is a variable function on the signed graph.
Note that the term "marked graph" is widely used in Petri nets in a completely different meaning; see the article on marked graphs .
As with unsigned graphs , there is a notion of signed graph coloring. Where a coloring of a graph is a mapping from the vertex set to the natural numbers, a coloring of a signed graph is a mapping from the vertex set to the integers.
The constraints on proper colorings come from the edges of the signed graph. The integers assigned to two vertices must be distinct if they are connected by a positive edge. The labels on adjacent vertices must not be additive inverses if the vertices are connected by a negative edge. There can be no proper coloring of a signed graph with a positive loop.
When restricting the vertex labels to the set of integers with magnitude at most a natural number k , the set of proper colorings of a signed graph is finite. The relation between the number of such proper colorings and k is a polynomial in k ; when expressed in terms of 2 k + 1 {\displaystyle 2k+1} it is called the chromatic polynomial of the signed graph. It is analogous to the chromatic polynomial of an unsigned graph.
In social psychology , signed graphs have been used to model social situations, with positive edges representing friendships and negative edges enmities between nodes, which represent people. [ 3 ] Then, for example, a positive 3-cycle is either three mutual friends, or two friends with a common enemy; while a negative 3-cycle is either three mutual enemies, or two enemies who share a mutual friend. According to balance theory , positive cycles are balanced and supposed to be stable social situations, whereas negative cycles are unbalanced and supposed to be unstable. According to the theory, in the case of three mutual enemies, this is because sharing a common enemy is likely to cause two of the enemies to become friends . In the case of two enemies sharing a friend, the shared friend is likely to choose one over the other and turn one of his or her friendships into an enemy.
Antal, Krapivsky and Reder consider social dynamics as the change in sign on an edge of a signed graph. [ 12 ] The social relations with previous friends of a divorcing couple are used to illustrate the evolution of a signed graph in society. Another illustration describes the changing international alliances between European powers in the decades before the First World War . They consider local triad dynamics and constrained triad dynamics, where in the latter case a relationship change is made only when the total number of unbalanced triads is reduced. The simulation presumed a complete graph with random relations having a random unbalanced triad selected for transformation. The evolution of the signed graph with N nodes under this process is studied and simulated to describe the stationary density of friendly links.
Balance theory has been severely challenged, especially in its application to large systems, on the theoretical ground that friendly relations tie a society together, while a society divided into two camps of enemies would be highly unstable. [ 13 ] Experimental studies have also provided only weak confirmation of the predictions of structural balance theory. [ 14 ]
In physics, signed graphs are a natural context for the nonferromagnetic Ising model , which is applied to the study of spin glasses .
Using an analytic method initially developed in population biology and ecology, but now used in many scientific disciplines, signed digraphs have found application in reasoning about the behavior of complex causal systems. [ 15 ] [ 16 ] Such analyses answer questions about feedback at given levels of the system, and about the direction of variable responses given a perturbation to a system at one or more points, variable correlations given such perturbations, the distribution of variance across the system, and the sensitivity or insensitivity of particular variables to system perturbations.
Correlation clustering looks for natural clustering of data by similarity. The data points are represented as the vertices of a graph, with a positive edge joining similar items and a negative edge joining dissimilar items.
Brain can be considered as a signed graph where synchrony and anti-synchrony between activity patterns of brain regions determine positive and negative edges. In this regard, stability and energy of the brain network can be explored. [ 17 ] Also, recently, the concept of frustration has been used in brain network analysis to identify the non-trivial assemblage of neural connections and highlight the adjustable elements of the brain. [ 18 ]
A signed graph is the special kind of gain graph in which the gain group has order 2. The pair ( G , B (Σ)) determined by a signed graph Σ is a special kind of biased graph . The sign group has the special property, not shared by larger gain groups, that the edge signs are determined up to switching by the set B (Σ) of balanced cycles. [ 19 ] | https://en.wikipedia.org/wiki/Signed_graph |
In computing, a signed overpunch is a coding scheme which stores the sign of a number by changing (usually) the last digit. It is used in character data on IBM mainframes by languages such as COBOL , PL/I , and RPG . [ 1 ] Its purpose is to save a character that would otherwise be used by the sign digit. [ 2 ] The code is derived from the Hollerith Punched Card Code , where both a digit and a sign can be entered in the same card column. It is called an overpunch because the digit in that column has a 12-punch or an 11-punch above it to indicate the sign. The top three rows of the card are called zone punches , [ 3 ] and so numeric character data which may contain overpunches is called zoned decimal .
In IBM terminology, the low-order four bits of a byte in storage are called the digit , and the high-order four bits are the zone . [ 4 ] The digit bits contain the numeric value 0–9. The zone bits contain either 'F'x, forming the characters 0–9, or the character position containing the overpunch contains a hexadecimal value indicating a positive or negative value, forming a different set of characters. (A, C, E, and F zones indicate positive values, B and D negative).
The PACK instruction on IBM System/360 architecture machines converts the sign of a zoned decimal number when converting to packed decimal ,
and the corresponding UNPK instruction will set the correct overpunched sign of its zoned decimal output. [ 5 ]
PL/I uses the PICTURE attribute to declare zoned decimal data with a signed overpunch. Each character in a numeric picture except V , which indicates the position of the assumed decimal point, represents a digit. A picture character of T , I , or R indicates a digit position which may contain an overpunch. T indicates that the position will contain {–I if positive and {–R if negative. I indicates that the position will contain {–I if positive and 0-9 if negative. R indicates that the position will contain 0–9 if positive and {–R if negative.
For example PICTURE 'Z99R' describes a four-character numeric field. The first position may be blank or will contain a digit 0–9. The next two positions will contain digits, and the fourth position will contain 0–9 for a positive number and {–R for negative. [ 6 ]
Assigning the value 1021 to the above picture will store the characters "1021" in memory; assigning -1021 will store "102J".
COBOL uses the picture character 'S' for USAGE IS DISPLAY data without SIGN IS SEPARATE CHARACTER to indicate an overpunch. SIGN IS LEADING indicates that the overpunch is over the first character of the field. SIGN IS TRAILING , locates it over the last character. SIGN IS TRAILING is the default. [ 7 ]
The C language has no provision for zoned decimal. The IBM ILE C/C++ compiler for System i provides functions for conversion between int or double and zoned decimal: [ 8 ]
10} is -100 45A is 451
Representation of signed overpunch characters "is not standardized in ASCII, and different compilers use different overpunch codes." In some cases, "the representation is not the same as the result of converting an EBCDIC Signed field to ASCII with a translation table." [ 10 ] In other cases they are the same, to maintain source-data compatibility at the loss of the connection between the character code and the corresponding digit.
An EBCDIC negative field ending with the digit '1' will encode that digit as 'D1'x, upper-case 'J', where the digit is '1' and the zone is 'D' to indicate a negative field. ASCII upper-case 'J' is '4A'x, where the hexadecimal value bears no relationship to the numeric value. An alternative encoding uses lower-case 'q', '71'x, for this representation, where the digit is '1' and the zone is '7'. This preserves the digit and the collating sequence at the cost of having to recognize and translate fields with overpunches individually.
Gnu COBOL and MicroFocus COBOL use lower-case 'p' thru 'y' to represent negative '0' thru '9'. [ 11 ] [ 12 ]
PL/I compilers on ASCII systems use the same set of characters ({, J–R) as EBCDIC to represent overpunches. [ 13 ] | https://en.wikipedia.org/wiki/Signed_overpunch |
In computing, signedness is a property of data types representing numbers in computer programs. A numeric variable is signed if it can represent both positive and negative numbers, and unsigned if it can only represent non-negative numbers (zero or positive numbers).
As signed numbers can represent negative numbers, they lose a range of positive numbers that can only be represented with unsigned numbers of the same size (in bits) because roughly half the possible values are non-positive values, whereas the respective unsigned type can dedicate all the possible values to the positive number range.
For example, a two's complement signed 16-bit integer can hold the values −32768 to 32767 inclusively, while an unsigned 16 bit integer can hold the values 0 to 65535 . For this sign representation method, the leftmost bit ( most significant bit ) denotes whether the value is negative (0 for positive or zero, 1 for negative).
For most architectures, there is no signed–unsigned type distinction in the machine language . Nevertheless, arithmetic instructions usually set different CPU flags such as the carry flag for unsigned arithmetic and the overflow flag for signed. Those values can be taken into account by subsequent branch or arithmetic commands.
The C programming language , along with its derivatives, implements a signedness for all integer data types , as well as for "character" . For Integers, the unsigned modifier defines the type to be unsigned. The default integer signedness outside bit-fields is signed, but can be set explicitly with signed modifier. By contrast, the C standard declares signed char , unsigned char , and char , to be three distinct types, but specifies that all three must have the same size and alignment. Further, char must have the same numeric range as either signed char or unsigned char , but the choice of which depends on the platform. Integer literals can be made unsigned with U suffix.
Compilers often issue a warning when comparisons are made between signed and unsigned numbers or when one is cast to the other. These are potentially dangerous operations as the ranges of the signed and unsigned types are different. | https://en.wikipedia.org/wiki/Signedness |
Microarray analysis techniques are used in interpreting the data generated from experiments on DNA ( Gene chip analysis ), RNA, and protein microarrays , which allow researchers to investigate the expression state of a large number of genes – in many cases, an organism's entire genome – in a single experiment. [ 1 ] Such experiments can generate very large amounts of data, allowing researchers to assess the overall state of a cell or organism. Data in such large quantities is difficult – if not impossible – to analyze without the help of computer programs.
Microarray data analysis is the final step in reading and processing data produced by a microarray chip. Samples undergo various processes including purification and scanning using the microchip, which then produces a large amount of data that requires processing via computer software. It involves several distinct steps, as outlined in the image below. Changing any one of the steps will change the outcome of the analysis, so the MAQC Project [ 2 ] was created to identify a set of standard strategies. Companies exist that use the MAQC protocols to perform a complete analysis. [ 3 ]
Most microarray manufacturers, such as Affymetrix and Agilent , [ 4 ] provide commercial data analysis software alongside their microarray products. There are also open source options that utilize a variety of methods for analyzing microarray data.
Comparing two different arrays or two different samples hybridized to the same array generally involves making adjustments for systematic errors introduced by differences in procedures and dye intensity effects. Dye normalization for two color arrays is often achieved by local regression . LIMMA provides a set of tools for background correction and scaling, as well as an option to average on-slide duplicate spots. [ 5 ] A common method for evaluating how well normalized an array is, is to plot an MA plot of the data. MA plots can be produced using programs and languages such as R and MATLAB. [ 6 ] [ 7 ]
Raw Affy data contains about twenty probes for the same RNA target. Half of these are "mismatch spots", which do not precisely match the target sequence. These can theoretically measure the amount of nonspecific binding for a given target. Robust Multi-array Average (RMA) [ 8 ] is a normalization approach that does not take advantage of these mismatch spots but still must summarize the perfect matches through median polish . [ 9 ] The median polish algorithm, although robust, behaves differently depending on the number of samples analyzed. [ 10 ] Quantile normalization , also part of RMA, is one sensible approach to normalize a batch of arrays in order to make further comparisons meaningful.
The current Affymetrix MAS5 algorithm, which uses both perfect match and mismatch probes, continues to enjoy popularity and do well in head to head tests. [ 11 ]
Factor analysis for Robust Microarray Summarization (FARMS) [ 12 ] is a model-based technique for summarizing array data at perfect match probe level. It is based on a factor analysis model for which a Bayesian maximum a posteriori method optimizes the model parameters under the assumption of Gaussian measurement noise. According to the Affycomp benchmark [ 13 ] FARMS outperformed all other summarizations methods with respect to sensitivity and specificity.
Many strategies exist to identify array probes that show an unusual level of over-expression or under-expression. The simplest one is to call "significant" any probe that differs by an average of at least twofold between treatment groups. More sophisticated approaches are often related to t-tests or other mechanisms that take both effect size and variability into account. Curiously, the p-values associated with particular genes do not reproduce well between replicate experiments, and lists generated by straight fold change perform much better. [ 14 ] [ 15 ] This represents an extremely important observation, since the point of performing experiments has to do with predicting general behavior. The MAQC group recommends using a fold change assessment plus a non-stringent p-value cutoff, further pointing out that changes in the background correction and scaling process have only a minimal impact on the rank order of fold change differences, but a substantial impact on p-values. [ 14 ]
Clustering is a data mining technique used to group genes having similar expression patterns. Hierarchical clustering , and k-means clustering are widely used techniques in microarray analysis.
Hierarchical clustering is a statistical method for finding relatively homogeneous clusters. Hierarchical clustering consists of two separate phases. Initially, a distance matrix containing all the pairwise distances between the genes is calculated. Pearson's correlation and Spearman's correlation are often used as dissimilarity estimates, but other methods, like Manhattan distance or Euclidean distance , can also be applied. Given the number of distance measures available and their influence in the clustering algorithm results, several studies have compared and evaluated different distance measures for the clustering of microarray data, considering their intrinsic properties and robustness to noise. [ 16 ] [ 17 ] [ 18 ] After calculation of the initial distance matrix, the hierarchical clustering algorithm either (A) joins iteratively the two closest clusters starting from single data points (agglomerative, bottom-up approach, which is fairly more commonly used), or (B) partitions clusters iteratively starting from the complete set (divisive, top-down approach). After each step, a new distance matrix between the newly formed clusters and the other clusters is recalculated. Hierarchical cluster analysis methods include:
Different studies have already shown empirically that the Single linkage clustering algorithm produces poor results when employed to gene expression microarray data and thus should be avoided. [ 18 ] [ 19 ]
K-means clustering is an algorithm for grouping genes or samples based on pattern into K groups. Grouping is done by minimizing the sum of the squares of distances between the data and the corresponding cluster centroid . Thus the purpose of K-means clustering is to classify data based on similar expression. [ 20 ] K-means clustering algorithm and some of its variants (including k-medoids ) have been shown to produce good results for gene expression data (at least better than hierarchical clustering methods). Empirical comparisons of k-means , k-medoids , hierarchical methods and, different distance measures can be found in the literature. [ 18 ] [ 19 ]
Commercial systems for gene network analysis such as Ingenuity [ 21 ] and Pathway studio [ 22 ] create visual representations of differentially expressed genes based on current scientific literature. Non-commercial tools such as FunRich, [ 23 ] GenMAPP and Moksiskaan also aid in organizing and visualizing gene network data procured from one or several microarray experiments. A wide variety of microarray analysis tools are available through Bioconductor written in the R programming language . The frequently cited SAM module and other microarray tools [ 24 ] are available through Stanford University. Another set is available from Harvard and MIT. [ 25 ]
Specialized software tools for statistical analysis to determine the extent of over- or under-expression of a gene in a microarray experiment relative to a reference state have also been developed to aid in identifying genes or gene sets associated with particular phenotypes . One such method of analysis, known as Gene Set Enrichment Analysis (GSEA), uses a Kolmogorov-Smirnov -style statistic to identify groups of genes that are regulated together. [ 1 ] This third-party statistics package offers the user information on the genes or gene sets of interest, including links to entries in databases such as NCBI's GenBank and curated databases such as Biocarta [ 26 ] and Gene Ontology . Protein complex enrichment analysis tool (COMPLEAT) provides similar enrichment analysis at the level of protein complexes. [ 27 ] The tool can identify the dynamic protein complex regulation under different condition or time points. Related system, PAINT [ 28 ] and SCOPE [ 29 ] performs a statistical analysis on gene promoter regions, identifying over and under representation of previously identified transcription factor response elements. Another statistical analysis tool is Rank Sum Statistics for Gene Set Collections (RssGsc), which uses rank sum probability distribution functions to find gene sets that explain experimental data. [ 30 ] A further approach is contextual meta-analysis, i.e. finding out how a gene cluster responds to a variety of experimental contexts. Genevestigator is a public tool to perform contextual meta-analysis across contexts such as anatomical parts, stages of development, and response to diseases, chemicals, stresses, and neoplasms .
Significance analysis of microarrays (SAM) is a statistical technique , established in 2001 by Virginia Tusher, Robert Tibshirani and Gilbert Chu , for determining whether changes in gene expression are statistically significant. With the advent of DNA microarrays , it is now possible to measure the expression of thousands of genes in a single hybridization experiment. The data generated is considerable, and a method for sorting out what is significant and what isn't is essential. SAM is distributed by Stanford University in an R-package . [ 31 ]
SAM identifies statistically significant genes by carrying out gene specific t-tests and computes a statistic d j for each gene j , which measures the strength of the relationship between gene expression and a response variable. [ 32 ] [ 33 ] [ 34 ] This analysis uses non-parametric statistics , since the data may not follow a normal distribution . The response variable describes and groups the data based on experimental conditions. In this method, repeated permutations of the data are used to determine if the expression of any gene is significant related to the response. The use of permutation-based analysis accounts for correlations in genes and avoids parametric assumptions about the distribution of individual genes. This is an advantage over other techniques (e.g., ANOVA and Bonferroni ), which assume equal variance and/or independence of genes. [ 35 ]
the number of permutations is set by the user when imputing correct values for the data set to run SAM
Types: [ 32 ]
SAM calculates a test statistic for relative difference in gene expression based on permutation analysis of expression data and calculates a false discovery rate. The principal calculations of the program are illustrated below. [ 32 ] [ 33 ] [ 34 ]
The s o constant is chosen to minimize the coefficient of variation of d i . r i is equal to the expression levels (x) for gene i under y experimental conditions.
F a l s e d i s c o v e r y r a t e ( F D R ) = M e d i a n ( o r 90 t h p e r c e n t i l e ) o f # o f f a l s e l y c a l l e d g e n e s N u m b e r o f g e n e s c a l l e d s i g n i f i c a n t {\displaystyle \mathrm {False\ discovery\ rate\ (FDR)={\frac {Median\ (or\ 90^{th}\ percentile)\ of\ \#\ of\ falsely\ called\ genes}{Number\ of\ genes\ called\ significant}}} }
Fold changes (t) are specified to guarantee genes called significant change at least a pre-specified amount. This means that the absolute value of the average expression levels of a gene under each of two conditions must be greater than the fold change (t) to be called positive and less than the inverse of the fold change (t) to be called negative.
The SAM algorithm can be stated as:
Entire arrays may have obvious flaws detectable by visual inspection, pairwise comparisons to arrays in the same experimental group, or by analysis of RNA degradation. [ 39 ] Results may improve by removing these arrays from the analysis entirely.
Depending on the type of array, signal related to nonspecific binding of the fluorophore can be subtracted to achieve better results. One approach involves subtracting the average
signal intensity of the area between spots. A variety of tools for background correction and further analysis are available from TIGR, [ 40 ] Agilent ( GeneSpring ), [ 41 ] and Ocimum Bio Solutions (Genowiz). [ 42 ]
Visual identification of local artifacts, such as printing or washing defects, may likewise suggest the removal of individual spots. This can take a substantial amount of time depending on the quality of array manufacture. In addition, some procedures call for the elimination of all spots with an expression value below a certain intensity threshold. | https://en.wikipedia.org/wiki/Significance_analysis_of_microarrays |
The significand [ 1 ] (also coefficient , [ 1 ] sometimes argument , [ 2 ] or more ambiguously mantissa , [ 3 ] fraction , [ 4 ] [ 5 ] [ nb 1 ] or characteristic [ 6 ] [ 3 ] ) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits . For negative numbers, it does not include the initial minus sign.
Depending on the interpretation of the exponent , the significand may represent an integer or a fractional number , which may cause the term "mantissa" to be misleading, since the mantissa of a logarithm is always its fractional part. [ 7 ] [ 8 ] Although the other names mentioned are common, significand is the word used by IEEE 754 , an important technical standard for floating-point arithmetic. [ 9 ] In mathematics , the term "argument" may also be ambiguous, since "the argument of a number" sometimes refers to the length of a circular arc from 1 to a number on the unit circle in the complex plane . [ 10 ]
The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10 −2 power term, also called characteristics , [ 11 ] [ 12 ] [ 13 ] where −2 is the exponent (and 10 is the base). Its value is given by the following arithmetic:
This same value can also be represented in scientific notation with the significand 1.2345 as a fractional coefficient, and +2 as the exponent (and 10 as the base):
Schmid, however, called this representation with a significand ranging between 1.0 and 10 a modified normalized form . [ 12 ] [ 13 ]
For base 2, this 1.xxxx form is also called a normalized significand .
Finally, the value can be represented in the format given by the Language Independent Arithmetic standard and several programming language standards, including Ada , C , Fortran and Modula-2 , as
Schmid called this representation with a significand ranging between 0.1 and 1.0 the true normalized form . [ 12 ] [ 13 ]
For a normalized number , the most significant digit is always non-zero. When working in binary , this constraint uniquely determines this digit to always be 1. As such, it is not explicitly stored, being called the hidden bit .
The significand is characterized by its width in (binary) digits , and depending on the context, the hidden bit may or may not be counted toward the width. For example, the same IEEE 754 double-precision format is commonly described as having either a 53-bit significand, including the hidden bit, or a 52-bit significand, [ citation needed ] excluding the hidden bit. IEEE 754 defines the precision p to be the number of digits in the significand, including any implicit leading bit (e.g., p = 53 for the double-precision format), thus in a way independent from the encoding, and the term to express what is encoded (that is, the significand without its leading bit) is trailing significand field .
In 1914, Leonardo Torres Quevedo introduced floating-point arithmetic in his Essays on Automatics , [ 14 ] where he proposed the format n ; m , showing the need for a fixed-sized significand as currently used for floating-point data. [ 15 ]
In 1946, Arthur Burks used the terms mantissa and characteristic to describe the two parts of a floating-point number ( Burks [ 11 ] et al. ) by analogy with the then-prevalent common logarithm tables: the characteristic is the integer part of the logarithm (i.e. the exponent), and the mantissa is the fractional part. The usage remains common among computer scientists today.
The term significand was introduced by George Forsythe and Cleve Moler in 1967 [ 16 ] [ 17 ] [ 18 ] [ 5 ] and is the word used in the IEEE standard [ 19 ] as the coefficient in front of a scientific notation number discussed above. The fractional part is called the fraction .
To understand both terms, notice that in binary, 1 + mantissa ≈ significand, and the correspondence is exact when storing a power of two. This fact allows for a fast approximation of the base-2 logarithm, leading to algorithms e.g. for computing the fast square-root and fast inverse-square-root . The implicit leading 1 is nothing but the hidden bit in IEEE 754 floating point, and the bitfield storing the remainder is thus the mantissa .
However, whether or not the implicit 1 is included is a major point of confusion with both terms—and especially so with mantissa . In keeping with the original usage in the context of log tables, it should not be present.
For those contexts where 1 is considered included, William Kahan , [ 1 ] lead creator of IEEE 754, and Donald E. Knuth , prominent computer programmer and author of The Art of Computer Programming , [ 6 ] condemn the use of mantissa . This has led to declining use of the term mantissa in all contexts. In particular, the current IEEE 754 standard does not mention it. | https://en.wikipedia.org/wiki/Significand |
The Significant New Alternatives Policy (also known as Section 612 of the Clean Air Act or SNAP , promulgated at 40 CFR part 82 Subpart G) is a program of the EPA to determine acceptable chemical substitutes, and establish which are prohibited or regulated by the EPA. [ 1 ] It also establishes a program by which new alternatives may be accepted, and promulgates timelines to the industry regarding phase-outs of substitutes.
Originally, Section 612 was limited by ozone-depleting chemicals. However, after passing regulations to phase-out R134a , an HFC refrigerant with no ozone-depleting potential, this phase-out was defended by a subsidiary of DuPont siding with the EPA as it was challenged by a major manufacturer of R134a, and was struck down in 2017. This decision was upheld in 2018. [ 2 ] [ 3 ] In 2021, a new law was passed as part of the appropriations bill extending the EPA's scope to substances with high GWP as well. [ 4 ]
The EPA looks at available chemical substitutes in the following industrial sectors:
Evaluations are ongoing as technological understanding improves, and can only prohibit substance where the EPA has determined other available substitutes that pose less overall risk to human health and the environment. [ 5 ]
In order to submit new proposed chemicals, along with general contact and marketing information, for a complete submittal, the EPA requires reports on:
[ 6 ]
One important, changing aspect of SNAP is its effect on the HVAC industry. Particularly because it decides which refrigerants may be legally used, it coordinates refrigerant phaseouts in the U.S., and which are prohibited against venting in concordance with Section 608 . The following is a list of accepted refrigerants, or phase-out periods according to the EPA. | https://en.wikipedia.org/wiki/Significant_New_Alternatives_Policy |
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