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Vulnerability assessment (computing) | Assessment types | Host assessment A host assessment looks for system-level vulnerabilities such as insecure file permissions, application level bugs, backdoor and Trojan horse installations. It requires specialized tools for the operating system and software packages being used, in addition to administrative access to each system that should be tested. Host assessment is often very costly in term of time, and thus is only used in the assessment of critical systems. Tools like COPS and Tiger are popular in host assessment. |
Vulnerability assessment (computing) | Assessment types | Network assessment In a network assessment one assess the network for known vulnerabilities. It locates all systems on a network, determines what network services are in use, and then analyzes those services for potential vulnerabilities. This process does not require any configuration changes on the systems being assessed. Unlike host assessment, network assessment requires little computational cost and effort. |
Vulnerability assessment (computing) | Vulnerability assessment vs penetration testing | Vulnerability assessment and penetration testing are two different testing methods. They are differentiated on the basis of certain specific parameters. |
Record locator | Record locator | In airline reservation systems, a record locator is an alphanumeric or alpha code used to identify and access a specific record on an airline’s reservation system. An airline’s reservation system automatically generates a unique record locator whenever a customer makes a reservation or booking, commonly known in the industry as an itinerary. When an itinerary is entered into the reservation system it is commonly known as a passenger name record (PNR). An itinerary may be entered into the system by a passenger, travel agent or airline employee. The record locator typically appears on the itinerary provided to the passenger, and may be described as a confirmation number, reservation number, confirmation code, booking reference, booking code, or vendor locator, or other description, depending on the reservation system. |
Record locator | Format | Record locators are created by each computer reservation system (CRS) and are specific to that CRS. They are typically 6 alphanumeric characters in length, though reservation systems using record locators of 7 or 8 characters exist. Record locators are unique within a given CRS at a specific point in time. Because the number of character combinations in characters is finite, albeit very large, record locators may be reused once the PNRs to which they refer have been purged from the CRS. Because 1, I and L can be confused (also 0 and o) these characters are not always used in record locators. The pool of available character combinations is further reduced because the locator is actually a location address and there are rules about what character combinations can be used for such addresses. |
Record locator | Use | When a reservation is made, a passenger name record (PNR) is created in the computer reservation system (CRS) used by the person making the booking, and the CRS will automatically generate a record locator for the PNR. If the only flight(s) are operated by the airline on which the booking is being made, then only one PNR will exist. However, if a booking contains flights of more than one airline, then the reservation for both flights will typically be made through the first airline. The first airline will send messages and a copy of the PNR to the second airline confirming the reservation and the second airline will create a separate PNR with its own record locator generated by the second airline’s CRS. If the booking is made through a travel agent then a PNR (and record locator) will exist in the system used by the agency and further PNRs (each with their own record locator) will exist in each airline reservation system. |
Record locator | Use | In recent years many airlines have stopped running their own reservation systems and have become clients of global distribution systems that provide hosting services. Where this occurs a single PNR (with just one record locator) may be created in the hosting system containing details of all the flights for which that hosting system is responsible. For example, a reservation for passenger traveling from London to Paris on Air France returning BA booked through AF will reside in one PNR in the Amadeus system with just one record locator because both airlines use Amadeus for reservations. If that booking is made through a travel agent using Amadeus, the same single PNR/record locator will exist. However, if the reservation is made via an agency using a different system (e.g. Sabre) there will be two PNRs (one in Sabre and one in Amadeus) each with its own locator. |
Record locator | Use | Airline systems pass record locators between themselves as part of the confirmation process. Should a record locator fail to be passed between two systems the PNR can still be retrieved using flight number/date and name, or the ticket number. |
Record locator | Example record locators | Example record locators are RMT33W, KZVGX5, IIRCYC.
In the past, the Reservec 2 system had eight character record locators in the form xxnnnnxx where x was a letter and n a decimal digit. Some CPARS (Compact Programmed Airlines Reservations System) systems used five character locators. |
Ecological model of competition | Ecological model of competition | The ecological model of competition is a reassessment of the nature of competition in the economy. Traditional economics models the economy on the principles of physics (force, equilibrium, inertia, momentum, and linear relationships). This can be seen in the economics lexicon: terms like labour force, market equilibrium, capital flows, and price elasticity. This is probably due to historical coincidence. Classical Newtonian physics was the state of the art in science when Adam Smith was formulating the first principles of economics in the 18th century. |
Ecological model of competition | Ecological model of competition | According to the ecological model, it is more appropriate to model the economy on biology (growth, change, death, evolution, survival of the fittest, complex inter-relationships, non-linear relationships). Businesses operate in a complex environment with interlinked sets of determinants. Companies co-evolve: they influence, and are influenced by, competitors, customers, governments, investors, suppliers, unions, distributors, banks, and others. We should look at this business environment as a business ecosystem that both sustains, and threatens the firm. A company that is not well matched to its environment might not survive. Companies that are able to develop a successful business model and turn a core competency into a sustainable competitive advantage will thrive and grow. Very successful firms may come to dominate their industry (referred to as category killers). |
Rehearsal (educational psychology) | Rehearsal (educational psychology) | Rehearsal in educational psychology refers to the "cognitive process in which information is repeated over and over as a possible way of learning and remembering it". There are two types of memory rehearsal. The first type is called maintenance rehearsal. A person can do this by saying aloud or thinking of material repeatably until it becomes a part of the working memory. However, the material may fade from the working memory quickly. An example of this is looking up a phone number but forgetting it before being able to dial it into the phone. This is a common form of rote learning. Rote learning is learning or memorization by repetition, often without an understanding of the reasoning or relationships involved in the material that is learned. However, the material may register eventually and take large amounts of time and hard work. Maintenance rehearsal is viewed in educational psychology as an ineffective way of getting information to the long-term memory. |
Rehearsal (educational psychology) | Rehearsal (educational psychology) | Another type of rehearsal is elaborative rehearsal. This entails connecting new material learned, with already existing long term memories. In this type of rehearsal repetitive tactics are not successful. A strategy such as engaging the brain of the learners in an elaboration exercise will help the memories be more storable and retrievable in the future. |
Rehearsal (educational psychology) | Case study | In the study of "The Effects of Elaboration and Rehearsal on Long-Term Retention of Shape Names by Kindergarteners", the two promising instructional paradigms, elaboration and overt rehearsal were put to test. Elaboration strategies include paraphrasing or summarizing the material to be learned, creating analogies, generative note-taking (where the student actually reorganizes and connects ideas in their notes in contrast to passive, linear note-taking), explaining the ideas in the material to be learned to someone else, and question asking and answering. |
Scenic design | Scenic design | Scenic design (also known as scenography, stage design, or set design) is the creation of theatrical scenery. Scenic designers create sets and scenery that aim to support the overall artistic goals of the production. There has been some consideration that scenic design is also production design; however, it is generally considered to be a part of the visual production of a film or television. |
Scenic design | Scenic designer | The scenic designer works with the director and other designers to establish an overall visual concept for the production and design the stage environment. They are responsible for developing a complete set of design drawings that include the following: basic ground plan showing all stationary and scenic elements.
composite ground plan showing all moving scenic elements, indicating both their onstage and storage positions.
section of the stage space incorporating all elements.
front elevations of every scenic element, and additional elevations or sections of units as required.Many scenic designers use 3D CAD models to produce these design drawings.In the process of planning, scenic designers often make models. Models are often made before the final drawings that are delivered to the scene shop for construction. |
Scenic design | Responsibility | The scenic designer is responsible for collaborating with the theatre director and other members of the creative team to create an environment for the production. Scenic designers are responsible for creating scale models of the scenery, renderings, paint elevations and scale construction drawings as part of their communication with other production staff. Communicating the details of the scenic environment to the technical director, production manager, charge scenic artist and prop master are among the most important duties of a scenic designer. |
Scenic design | Training | In Europe and Australia, scenic designers take a more holistic approach to theatrical design and will often be responsible not only for scenic design but costume, lighting and sound and are referred to as theatre designers or scenographers or production designers. |
Scenic design | Notable set designers | Notable scenic designers, past and present, include: Adolphe Appia, Boris Aronson, Alexandre Benois, Alison Chitty, Antony McDonald, Barry Kay, Caspar Neher, Cyro Del Nero, Aleksandra Ekster, David Gallo, Edward Gordon Craig, Es Devlin, Ezio Frigerio, Christopher Gibbs, Franco Zeffirelli, George Tsypin, Howard Bay, Inigo Jones, Jean-Pierre Ponnelle, Jo Mielziner, John Lee Beatty, Josef Svoboda, Ken Adam, Léon Bakst, Luciano Damiani, Maria Björnson, Ming Cho Lee, Natalia Goncharova, Nathan Altman, Nicholas Georgiadis, Oliver Smith, Ralph Koltai, Emanuele Luzzati, Neil Patel, Robert Wilson, Russell Patterson, Brian Sidney Bembridge, Santo Loquasto, Sean Kenny, Todd Rosenthal, Robin Wagner, Tony Walton, Louis Daguerre, Ralph Funicello, and Roger Kirk. |
1,5-Bis(diphenylphosphino)pentane | 1,5-Bis(diphenylphosphino)pentane | 1,5-Bis(diphenylphosphino)pentane is an organophosphorus compound with the formula C29H30P2. It can be prepared by reacting 1,5-dibromopentane with lithium diphenylphosphide, or diphenylphosphine in presence of caesium hydroxide. It reacts with copper(I) iodide to give a luminescent dinuclear complex [CuIPh2P(CH2)5PPh2]2. |
Guard goose | Guard goose | The guard goose is a domestic goose that is used as a guard animal both on farms and in other situations. |
Guard goose | Goose behavior | Geese are considered to have excellent eyesight and to be "watchful and inquisitive", with strong territorial instincts. Goose attacks on humans are commonly reported. One case in 2001 set a legal precedent, resulting in a workers' compensation payout of over $17,000 for an injured delivery person, the first Illinois workers' compensation claim due to wildlife. In another case, several geese protecting their goslings knocked an Englishman off his bicycle resulting in hospitalization. One Buffalo, New York resident claimed over $2 million in damages for a goose attack while on a neighbor's property. At times, park rangers have killed entire flocks of aggressive geese. Canada geese in Cincinnati parks have been responsible for knocking people down and breaking their bones, and called "spitting, hissing, biting attack missiles".The same aggressive, territorial behavior can be utilized in the guard capacity. Geese are intelligent enough to discern unusual people or sounds from usual stimuli. Their loud honking will alert humans when the geese are alarmed. |
Guard goose | History of use | Guard geese have been used throughout history, and in modern times. In ancient Rome, geese are credited by the historian Livy for giving the alarm when Gauls invaded (see Battle of the Allia). Geese were subsequently revered in the supplicia canum annual sacrifice, and the Romans later founded a temple to Juno, to whom the geese were considered sacred. |
Guard goose | History of use | On modern farms, geese are said to be good deterrents to predators of other domestic fowl, and against snakes. A handbook on industrial security recommends them for protecting warehouses and other isolated physical assets. They are reported to have been used to guard United States Air Defense Command installations in Germany; as the Scotch Watch at Ballantine's Distillery in Dumbarton, Scotland; and to protect a police station in Xinjiang, China.Due to their tendency to make noise when approached by strangers, about 500 geese were used to supplement dogs, drones, and humans to patrol the 533-km boundary between Chongzuo and Vietnam during the COVID-19 pandemic. An official commented that the birds, one of the most common livestock in the region, are sensitive to sounds and can sometimes be more aggressive than dogs. |
Guard goose | Breeds | Some sources list the African goose, Roman goose (Tufted Roman), Pomeranian goose (Saddleback Pomeranian), and Chinese goose as the best breeds for guard duty. Chinese geese are said to be loud, and African geese both loud and large. |
Human Media Lab | Human Media Lab | The Human Media Lab (HML) is a research laboratory in Human-Computer Interaction at Queen's University's School of Computing in Kingston, Ontario. Its goals are to advance user interface design by creating and empirically evaluating disruptive new user interface technologies, and educate graduate students in this process. The Human Media Lab was founded in 2000 by Prof. Roel Vertegaal and employs an average of 12 graduate students. |
Human Media Lab | Human Media Lab | The laboratory is known for its pioneering work on flexible display interaction and paper computers, with systems such as PaperWindows (2004), PaperPhone (2010) and PaperTab (2012). HML is also known for its invention of ubiquitous eye input, such as Samsung's Smart Pause and Smart Scroll technologies. |
Human Media Lab | Research | In 2003, researchers at the Human Media Lab helped shape the paradigm Attentive User Interfaces, demonstrating how groups of computers could use human social cues for considerate notification. Amongst HML's early inventions was the eye contact sensor, first demonstrated to the public on ABC Good Morning America. Attentive User Interfaces developed at the time included an early iPhone prototype that used eye tracking electronic glasses to determine whether users were in a conversation, an attentive television that play/paused contents upon looking away, mobile Smart Pause and Smart Scroll (adopted in Samsung's Galaxy S4) as well as a technique for calibration-free eye tracking by placing invisible infrared markers in the scene. |
Human Media Lab | Research | Current research at the Human Media Lab focuses on the development of Organic User Interfaces: user interfaces with a non-flat display. In 2004, researchers at the HML built the first bendable paper computer, PaperWindows, which premiered at CHI 2005. It featured multiple flexible, hires, colour, wireless, thin-film multitouch displays through real-time depth-cam 3D Spatial Augmented Reality. In May 2007 HML coined the term Organic User Interfaces. Early Organic User Interfaces developed at HML included the first multitouch spherical display, and Dynacan, an interactive pop can: early examples of everyday computational things with interactive digital skins. |
Human Media Lab | Research | In 2010, the Human Media Lab, with Arizona State University, developed the world's first functional flexible smartphone, PaperPhone. It pioneered bend interactions and was first shown to the public at ACM CHI 2011 in Vancouver. In 2012, the Human Media Lab introduced the world's first pseudo-holographic, live size 3D video conferencing system, TeleHuman.In 2013, HML researchers unveiled PaperTab, the world's first flexible tablet PC, at CES 2013 in Las Vegas, in collaboration with Plastic Logic and Intel. |
Human Media Lab | Location and Facilities | The Human Media Lab is located in Jackson Hall on Queen's University campus in Kingston, Ontario. The facilities were designed by Karim Rashid. |
Oil of catechumens | Oil of catechumens | The Oil of Catechumens, also known as the Oil of Exorcism, is the oil used in some traditional Christian churches during baptism; it is believed to strengthen the one being baptized to turn away from evil, temptation and sin. |
Oil of catechumens | Oil of catechumens | The Oil of Exorcism was mentioned in the ancient Christian Apostolic Tradition as being "used before baptisms to put to flight any contagions that might obstruct the impending baptismal graces." The Egyptian Church Order teaches that it is blessed during the Easter Vigil, the first liturgy of Eastertide.The catechumen, the person prepared for baptism, is also anointed as a symbol of being the heir of the Kingdom of God, as kings and queens are anointed at coronations, and empowered for their Christian life as prophets were anointed for their ministry. |
Oil of catechumens | Oil of catechumens | The Oil of Catechumens is intended to help strengthen the person about to be baptized, and prepare them for the struggle (ascesis) of the Christian life, the way a wrestler in ancient Greece and Rome was anointed before a wrestling match. |
Oil of catechumens | Eastern Orthodoxy | In the Eastern Orthodox Church, the oil of catechumens is blessed by the priest during the baptismal rite. After the consecration of the baptismal water, a vessel of pure olive oil is brought to the priest by the deacon. The priest breathes on the oil three times and blesses it thrice, and says the prayer of blessing. |
Oil of catechumens | Eastern Orthodoxy | O Master, Lord God of our fathers, Who didst send unto them that were in the ark of Noah the dove, having in its beak a twig of olive, the token of reconciliation and of salvation from the flood the foreshadowing of the mystery of grace; and didst provide the fruit of the olive for the fulfilling of Thy holy Mysteries; Who thereby fillest them that were under the Law with Thy Holy Spirit, and perfectest them that are under grace: Do Thou Thyself bless also this holy oil with the power, and operation, and indwelling of Thy Holy Spirit, that it may be an anointing unto incorruption, an armour of righteousness, to the renewing of soul and body, to the averting of every assault of the devil, to deliverance from all evil of those who shall be anointed with it in faith, or who are partakers thereof; unto Thy glory, and the glory of Thine Only-begotten Son, and Thy most holy and good and life-creating Spirit, now and ever, and unto the ages of ages. Amen.The priest then pours a portion of the oil into the baptismal font, making the Sign of the Cross with the oil three times, as all sing Alleluia. The priest gathers some of the oil floating on the surface of the water onto the first two fingers of his right hand and anoints the catechumen, making the Sign of the Cross on the brow, breast, between the shoulders, on the ears, hands and feet. The catechumen is then immediately baptized. |
Oil of catechumens | Eastern Orthodoxy | This anointing before baptism should not be confused with chrismation, which is a separate Sacred Mystery (Sacrament), though it is usually performed immediately after Baptism. |
Oil of catechumens | Roman Catholicism | In the Roman Catholic Church, the Oil of Catechumens is specially blessed by a bishop or a priest along with Chrism and oil of the sick at the Mass of Chrism which takes place on Holy Thursday.
During the baptismal rite, the priest or deacon says the following words as he anoints with the oil in the shape of a cross, "We anoint you with the oil of salvation in the name of Christ our Savior; may he strengthen you with his power, who lives and reigns for ever and ever." |
Whamola | Whamola | The Whamola is a bass instrument used in funk-jazz styles of music. The name is a portmanteau of whammy bar and viola. |
Whamola | Whamola | The Whamola is a direct descendant of the washtub bass, an American folk instrument popular with skiffle and jug bands, and features a single string which is manipulated via a pulley-and-lever system. The pulley mechanism is mounted in place of the tuning pegs at the top of a double-bass-style neck, which is attached to a wooden or metal body featuring a bridge, pickup and stand. The Whamola is played by hitting the string with a drum stick and either fretting it against the neck with the other hand or using the lever to alter its tension and change the pitch. |
Whamola | Whamola | Whamolas are rare, and are usually made by musicians for personal use, as opposed to professional luthiers, though the instrument has gained mass exposure and growing popularity in recent years due to its being played by contemporary bassists like Les Claypool. A song prominently featuring the instrument appears on the Les Claypool Frog Brigade's 2002 album Purple Onion, and a remix of that track is the basis for the opening theme of the tenth season of South Park. Primus also regularly play a "Drum and Whamola Jam" in concert, as documented by their 2004 live DVD Hallucino-Genetics. |
Knee of a curve | Knee of a curve | In mathematics, a knee of a curve (or elbow of a curve) is a point where the curve visibly bends, specifically from high slope to low slope (flat or close to flat), or in the other direction. This is particularly used in optimization, where a knee point is the optimum point for some decision, for example when there is an increasing function and a trade-off between the benefit (vertical y axis) and the cost (horizontal x axis): the knee is where the benefit is no longer increasing rapidly, and is no longer worth the cost of further increases – a cutoff point of diminishing returns. |
Knee of a curve | Knee of a curve | In heuristic use, the term may be used informally, and a knee point identified visually, but in more formal use an explicit objective function is used, and depends on the particular optimization problem. A knee may also be defined purely geometrically, in terms of the curvature or the second derivative. |
Knee of a curve | Definitions | The knee of a curve can be defined as a vertex of the graph. This corresponds with the graphical intuition (it is where the curvature has a maximum), but depends on the choice of scale.
The term "knee" as applied to curves dates at least to the 1910s, and is found more commonly by the 1940s, being common enough to draw criticism. The unabridged Webster's Dictionary (1971 edition) gives definition 3h of knee as: an abrupt change in direction in a curve (as on a graph); esp one approaching a right angle in shape. |
Knee of a curve | Criticism | Graphical notions of a "knee" of a curve, based on curvature, are criticized due to their dependence on the coordinate scale: different choices of scale result in different points being the "knee". This criticism dates at least to the 1940s, being found in Worthing & Geffner (1943, Preface), who criticize: references to the significance of a so-called knee of a curve when the location of the knee was a function of the chosen coordinate scales |
Knee of a curve | Applications | Elbow method Maximum power point tracking |
DHRS4 | DHRS4 | Dehydrogenase/reductase SDR family member 4 is an enzyme that in humans is encoded by the DHRS4 gene. |
Oxidative folding | Oxidative folding | Oxidative protein folding is a process that is responsible for the formation of disulfide bonds between cysteine residues in proteins. The driving force behind this process is a redox reaction, in which electrons pass between several proteins and finally to a terminal electron acceptor. |
Oxidative folding | In prokaryotes | In prokaryotes, the mechanism of oxidative folding is best studied in Gram-negative bacteria. This process is catalysed by protein machinery residing in the periplasmic space of bacteria. The formation of disulfide bonds in a protein is made possible by two related pathways: an oxidative pathway, which is responsible for the formation of the disulfides, and an isomerization pathway that shuffles incorrectly formed disulfides. |
Oxidative folding | Oxidative pathway | The oxidative pathway relies, just like the isomerization pathway, on a protein relay. The first member of this protein relay is a small periplasmic protein (21 kDa) called DsbA, which has two cysteine residues that must be oxidized for it to be active. When in its oxidized state, the protein is able to form disulfide bonds between cysteine residues in newly synthesized, and yet unfolded proteins by the transfer of its own disulfide bond onto the folding protein. After the transfer of this disulfide bond, DsbA is in a reduced state. For it to act catalytically again, it must be reoxidized. This is made possible by a 21 kDa inner membrane protein, called DsbB, which has two pairs of cysteine residues. A mixed disulfide is formed between a cysteine residue of DsbB and one of DsbA. Eventually, this cross-link between the two proteins is broken by a nucleophilic attack of the second cystein residue in the DsbA active site. On his turn, DsbB is reoxidized by transferring electrons to oxidized ubiquinone, which passes them to cytochrome oxidases, which finally reduce oxygen; this is in aerobic conditions. As molecular oxygen serves as the terminal electron acceptor in aerobic conditions, oxidative folding is conveniently coupled to it through the respiratory chain. In anaerobic conditions however, DsbB passes its electrons to menaquinone, followed by a transfer of electrons to fumarate reductase or nitrate reductase. |
Oxidative folding | Isomerization pathway | Especially for proteins that contain more than one disulfide bond, it is important that incorrect disulfide bonds become rearranged. This is carried out in the isomerization pathway by the protein DsbC, that acts as a disulfide isomerase. DsbC is a dimer, consisting of two identical 23 kDa subunits and has four cysteine residues in each subunit. One of these cysteines (Cys-98) attacks an incorrect disulfide in a misfolded protein and a mixed disulfide is formed between DsbC and this protein. Next, the attack of a second cysteine residue results in the forming of a more stable disulfide in the refolded protein. This may be a cysteine residue either from the earlier misfolded protein or one from DsbC. In the last case, DsbC becomes oxidized and must be reduced in order to play another catalytic role. There is also a second isomerase that can reorganize incorrect disulfide bonds. This protein is called DsbG and it is also a dimer that serves as a chaperone. To fulfil their role as isomerases, DsbC and DsbG must be kept in a reduced state. This is carried out by DsbD, which must be reduced itself to be functional. Thioredoxin, which itself is reduced by thioredoxin reductase and NADPH, ensures the reduction of the DsbD protein. |
Oxidative folding | Isomerization pathway | Because these two pathways coexist next to each other in the same periplasmic compartment, there must be a mechanism to prevent oxidation of DsbC by DsbB. This mechanism indeed exists as DsbB can distinguish between DsbA and DsbC because this latter has the ability to dimerize. |
Oxidative folding | In eukaryotes | A very similar pathway is followed in eukaryotes, in which the protein relay consists of proteins with very analogous properties as those of the protein relay in Gram-negative bacteria. However, a major difference between prokaryotes and eukaryotes is found in the fact that the process of oxidative protein folding occurs in the endoplasmatic reticulum (ER) in eukaryotes. A second difference is that in eukaryotes, the use of molecular oxygen as a terminal electron acceptor is not linked to the process of oxidative folding through the respiratory chain as is the case in bacteria. In fact, one of the proteins involved in the oxidative folding process uses a flavin-dependent reaction to pass electrons directly to molecular oxygen. |
Oxidative folding | In eukaryotes | A homolog of DsbA, called protein disulfide isomerase (PDI), is responsible for the formation of the disulfide bonds in unfolded eukaryotic proteins. This protein has two thioredoxine-like active sites, which both contain two cysteine residues. By transferring the disulfide bond between these two cysteine residues onto the folding protein it is responsible for the latter's oxidation. In contrast to bacteria, where the oxidative and isomerization pathways are carried out by different proteins, PDI is also responsible for the reduction and isomerization of the disulfide bonds. For PDI to catalyse the formation of disulfide bonds in unfolded proteins, it must be reoxidized. This is carried out by an ER membrane-associated protein, Ero1p, which is no homolog of DsbB. This Ero1p protein forms a mixed disulfide with PDI, which is resolved by a nucleophilic attack of the second cystein residue in one of the active sites of PDI. As result, oxidized PDI is obtained. Ero1p itself is oxidized by transferring electrons to molecular oxygen. As it is an FAD-binding protein, this transfer of electrons is strongly favoured when Ero1p is bound to FAD. Also a transport system that imports FAD into the ER lumen has been described in eukaryotes. Furthermore, it has been shown that the ability to reduce or rearrange incorrect disulfide bonds in missfolded proteins is provided by the oxidation of reduced glutathione (GSH) to oxidized glutathione (GSSG). |
Oxidative folding | ROS and diseases | Because of the property of Ero1p to transfer electrons directly to molecular oxygen via a flavin-dependent reaction, its activity may produce reactive oxygen species (ROS). In bacteria, this problem is solved by coupling oxidative folding to the respiratory chain. There, the reduction of molecular oxygen to water is carried out by a complex series of proteins, which catalyse this reaction very efficiently. In eukaryotes, the respiratory chain is separated from oxidative folding since cellular respiration takes place in the mitochondria and the formation of disulfide bonds occurs in the ER. Because of this, there is much more risk that ROS are produced in eukaryotic cells during oxidative folding. As is known these ROS may cause many diseases such as atherosclerosis and some neurodegenerative diseases. |
Oxidative folding | Examples | Classical examples of proteins in which the process of oxidative folding is well studied are bovine pancreatic trypsin inhibitor (BPTI) and ribonuclease A (RNaseA). These two proteins have multiple disulfide bonds and so they are very useful to follow and understand the process of oxidative folding. Another example is alkaline phosphatase, which contains two essential disulfides. It was used as an indicator protein to screen the effect of mutations in DsbA. |
Tetrahydrofurfuryl alcohol | Tetrahydrofurfuryl alcohol | Tetrahydrofurfuryl alcohol (THFA) is an organic compound with the formula HOCH2C4H7O. In terms of its structure, it consists of a tetrahydrofuran ring substituted in the 2-position with a hydroxymethyl group. It is a colorless liquid that is used as a specialty solvent and synthetic intermediate, e.g. to 3,4-dihydropyran. It is prepared by hydrogenation of furfural. It is a precursor to 1,5-pentanediol. |
Tetrahydrofurfuryl alcohol | Other uses | THFA is often used in epoxy resin formulations in either the epoxy component or amine hardener as well as other general resin applications. |
Phaethontis quadrangle | Phaethontis quadrangle | The Phaethontis quadrangle is one of a series of 30 quadrangle maps of Mars used by the United States Geological Survey (USGS) Astrogeology Research Program. The Phaethontis quadrangle is also referred to as MC-24 (Mars Chart-24).The name comes from Phaethon, the son of Helios.The Phaethontis quadrangle lies between 30° and 65 ° south latitude and 120° and 180 ° west longitude on Mars. This latitude range is where numerous gullies have been discovered. An old feature in this area, called Terra Sirenum lies in this quadrangle; Mars Reconnaissance Orbiter discovered iron/magnesium smectites there. Part of this quadrangle contains what is called the Electris deposits, a deposit that is 100–200 metres (330–660 ft) thick. It is light-toned and appears to be weak because of few boulders. Among a group of large craters is Mariner Crater, first observed by the Mariner IV spacecraft in the summer of 1965. It was named after that spacecraft. A low area in Terra Sirenum is believed to have once held a lake that eventually drained through Ma'adim Vallis. Russia's Mars 3 probe landed in the Phaethontis quadrangle at 44.9° S and 160.1° W in December 1971. It landed at a speed of 75 km per hour, but survived to radio back 20 seconds of signal, then it went dead. Its message just appeared as a blank screen. |
Phaethontis quadrangle | Martian gullies | The Phaethontis quadrangle is the location of many gullies that may be due to recent flowing water. Some are found in the Gorgonum Chaos and in many craters near the large craters Copernicus and Newton (Martian crater). Gullies occur on steep slopes, especially on the walls of craters. Gullies are believed to be relatively young because they have few, if any craters. Moreover, they lie on top of sand dunes which themselves are considered to be quite young. Usually, each gully has an alcove, channel, and apron. Some studies have found that gullies occur on slopes that face all directions, others have found that the greater number of gullies are found on poleward facing slopes, especially from 30-44 S.Although many ideas have been put forward to explain them, the most popular involve liquid water coming from an aquifer, from melting at the base of old glaciers, or from the melting of ice in the ground when the climate was warmer. Because of the good possibility that liquid water was involved with their formation and that they could be very young, scientists are excited. Maybe the gullies are where we should go to find life. |
Phaethontis quadrangle | Martian gullies | There is evidence for all three theories. Most of the gully alcove heads occur at the same level, just as one would expect of an aquifer. Various measurements and calculations show that liquid water could exist in aquifers at the usual depths where gullies begin. One variation of this model is that rising hot magma could have melted ice in the ground and caused water to flow in aquifers. Aquifers are layer that allow water to flow. They may consist of porous sandstone. The aquifer layer would be perched on top of another layer that prevents water from going down (in geological terms it would be called impermeable). Because water in an aquifer is prevented from going down, the only direction the trapped water can flow is horizontally. Eventually, water could flow out onto the surface when the aquifer reaches a break—like a crater wall. The resulting flow of water could erode the wall to create gullies. Aquifers are quite common on Earth. A good example is "Weeping Rock" in Zion National Park Utah.As for the next theory, much of the surface of Mars is covered by a thick smooth mantle that is thought to be a mixture of ice and dust. This ice-rich mantle, a few yards thick, smoothes the land, but in places it has a bumpy texture, resembling the surface of a basketball. The mantle may be like a glacier and under certain conditions the ice that is mixed in the mantle could melt and flow down the slopes and make gullies. Because there are few craters on this mantle, the mantle is relatively young. An excellent view of this mantle is shown below in the picture of the Ptolemaeus Crater Rim, as seen by HiRISE. |
Phaethontis quadrangle | Martian gullies | The ice-rich mantle may be the result of climate changes. Changes in Mars's orbit and tilt cause significant changes in the distribution of water ice from polar regions down to latitudes equivalent to Texas. During certain climate periods water vapor leaves polar ice and enters the atmosphere. The water comes back to ground at lower latitudes as deposits of frost or snow mixed generously with dust. The atmosphere of Mars contains a great deal of fine dust particles. Water vapor will condense on the particles, then fall down to the ground due to the additional weight of the water coating. When Mars is at its greatest tilt or obliquity, up to 2 cm of ice could be removed from the summer ice cap and deposited at midlatitudes. This movement of water could last for several thousand years and create a snow layer of up to around 10 meters thick. When ice at the top of the mantling layer goes back into the atmosphere, it leaves behind dust, which insulating the remaining ice. Measurements of altitudes and slopes of gullies support the idea that snowpacks or glaciers are associated with gullies. Steeper slopes have more shade which would preserve snow. |
Phaethontis quadrangle | Martian gullies | Higher elevations have far fewer gullies because ice would tend to sublimate more in the thin air of the higher altitude.The third theory might be possible since climate changes may be enough to simply allow ice in the ground to melt and thus form the gullies. During a warmer climate, the first few meters of ground could thaw and produce a "debris flow" similar to those on the dry and cold Greenland east coast. Since the gullies occur on steep slopes only a small decrease of the shear strength of the soil particles is needed to begin the flow. Small amounts of liquid water from melted ground ice could be enough. Calculations show that a third of a mm of runoff can be produced each day for 50 days of each Martian year, even under current conditions. |
Phaethontis quadrangle | Associated features of gullies | Sometimes other features appear near gullies. At the base of some gullies there may be depressions or curved ridges. These have been called "spatulate depressions." These depressions form after glacial ice disappears. Steep walls often develop glaciers during certain climates. When the climate changes, the ice in the glaciers sublimates in the thin Martian atmosphere. Sublimation is when a substance goes directly from a solid state to a gas state. Dry ice on Earth does this. So when the ice at the base of a steep wall sublimates, a depression results. Also, more ice from higher up will tend to flow downward. This flow will stretch the surface rocky debris thereby forming transverse crevasses. Such formations have been termed "washboard terrain" because they resemble the old fashioned washboards. The parts of gullies and some associated features of gullies are shown below in a HiRISE images. |
Phaethontis quadrangle | Possible pingos | The radial and concentric cracks visible here are common when forces penetrate a brittle layer, such as a rock thrown through a glass window. These particular fractures were probably created by something emerging from below the brittle Martian surface. Ice may have accumulated under the surface in a lens shape; thus making these cracked mounds. Ice being less dense than rock, pushed upwards on the surface and generated these spider web-like patterns. A similar process creates similar sized mounds in arctic tundra on Earth. Such features are called “pingos,”, an Inuit word. Pingos would contain pure water ice; thus they could be sources of water for future colonists of Mars. |
Phaethontis quadrangle | Concentric crater fill | Concentric crater fill, like lobate debris aprons and lineated valley fill, is believed to be ice-rich. Based on accurate topography measures of height at different points in these craters and calculations of how deep the craters should be based on their diameters, it is thought that the craters are 80% filled with mostly ice. That is, they hold hundreds of meters of material that probably consists of ice with a few tens of meters of surface debris. The ice accumulated in the crater from snowfall in previous climates. Recent modeling suggests that concentric crater fill develops over many cycles in which snow is deposited, then moves into the crater. Once inside the crater shade and dust preserve the snow. The snow changes to ice. The many concentric lines are created by the many cycles of snow accumulation. Generally snow accumulates whenever the axial tilt reaches 35 degrees. |
Phaethontis quadrangle | Magnetic stripes and plate tectonics | The Mars Global Surveyor (MGS) discovered magnetic stripes in the crust of Mars, especially in the Phaethontis and Eridania quadrangles (Terra Cimmeria and Terra Sirenum). The magnetometer on MGS discovered 100 km wide stripes of magnetized crust running roughly parallel for up to 2000 km. These stripes alternate in polarity with the north magnetic pole of one pointing up from the surface and the north magnetic pole of the next pointing down. When similar stripes were discovered on Earth in the 1960s, they were taken as evidence of plate tectonics. Researchers believe these magnetic stripes on Mars are evidence for a short, early period of plate tectonic activity. When the rocks became solid they retained the magnetism that existed at the time. A magnetic field of a planet is believed to be caused by fluid motions under the surface. However, there are some differences, between the magnetic stripes on Earth and those on Mars. The Martian stripes are wider, much more strongly magnetized, and do not appear to spread out from a middle crustal spreading zone. Because the area containing the magnetic stripes is about 4 billion years old, it is believed that the global magnetic field probably lasted for only the first few hundred million years of Mars' life, when the temperature of the molten iron in the planet's core might have been high enough to mix it into a magnetic dynamo. There are no magnetic fields near large impact basins like Hellas. The shock of the impact may have erased the remnant magnetization in the rock. So, magnetism produced by early fluid motion in the core would not have existed after the impacts.When molten rock containing magnetic material, such as hematite (Fe2O3), cools and solidifies in the presence of a magnetic field, it becomes magnetized and takes on the polarity of the background field. This magnetism is lost only if the rock is subsequently heated above a particular temperature (the Curie point which is 770 °C for iron). The magnetism left in rocks is a record of the magnetic field when the rock solidified. |
Phaethontis quadrangle | Chloride deposits | Using data from Mars Global Surveyor, Mars Odyssey and the Mars Reconnaissance Orbiter, scientists have found widespread deposits of chloride minerals. A picture below shows some deposits within the Phaethontis quadrangle. Evidence suggests that the deposits were formed from the evaporation of mineral enriched waters. The research suggests that lakes may have been scattered over large areas of the Martian surface. Usually chlorides are the last minerals to come out of solution. Carbonates, sulfates, and silica should precipitate out ahead of them. Sulfates and silica have been found by the Mars Rovers on the surface. Places with chloride minerals may have once held various life forms. Furthermore, such areas should preserve traces of ancient life.Based on chloride deposits and hydrated phyllosilicates, Alfonso Davila and others believe there is an ancient lakebed in Terra Sirenum that had an area of 30,000 km2 (12,000 sq mi) and was 200 metres (660 ft) deep. Other evidence that supports this lake are normal and inverted channels like ones found in the Atacama desert. |
Phaethontis quadrangle | Fossae | The Elysium quadrangle is home to large troughs (long narrow depressions) called fossae in the geographical language used for Mars. Troughs are created when the crust is stretched until it breaks. The stretching can be due to the large weight of a nearby volcano. Fossae/pit craters are common near volcanoes in the Tharsis and Elysium system of volcanoes. |
Phaethontis quadrangle | Craters | The density of impact craters is used to determine the surface ages of Mars and other solar system bodies. The older the surface, the more craters present. Crater shapes can reveal the presence of ground ice. |
Phaethontis quadrangle | Craters | The area around craters may be rich in minerals. On Mars, heat from the impact melts ice in the ground. Water from the melting ice dissolves minerals, and then deposits them in cracks or faults that were produced with the impact. This process, called hydrothermal alteration, is a major way in which ore deposits are produced. The area around Martian craters may be rich in useful ores for the future colonization of Mars. Studies on the earth have documented that cracks are produced and that secondary minerals veins are deposited in the cracks. Images from satellites orbiting Mars have detected cracks near impact craters. Great amounts of heat are produced during impacts. The area around a large impact may take hundreds of thousands of years to cool. |
Phaethontis quadrangle | Craters | Many craters once contained lakes. Because some crater floors show deltas, we know that water had to be present for some time. Dozens of deltas have been spotted on Mars. Deltas form when sediment is washed in from a stream entering a quiet body of water. It takes a bit of time to form a delta, so the presence of a delta is exciting; it means water was there for a time, maybe for many years. Primitive organisms may have developed in such lakes; hence, some craters may be prime targets for the search for evidence of life on the Red Planet. |
Phaethontis quadrangle | Craters | List of craters The following is a list of craters in the quadrangle. The crater's central location is of the quadrangle, craters that its central location is in another quadrangle is listed by eastern, western, northern or southern part.
1Partly located in the quadrangle while another part is in a different quadrangle along with the crater's diameter |
Phaethontis quadrangle | Linear ridge networks | Linear ridge networks are found in various places on Mars in and around craters. Ridges often appear as mostly straight segments that intersect in a lattice-like manner. They are hundreds of meters long, tens of meters high, and several meters wide. It is thought that impacts created fractures in the surface, these fractures later acted as channels for fluids. Fluids cemented the structures. With the passage of time, surrounding material was eroded away, thereby leaving hard ridges behind. |
Phaethontis quadrangle | Linear ridge networks | Since the ridges occur in locations with clay, these formations could serve as a marker for clay which requires water for its formation. Water here could have supported past life in these locations. Clay may also preserve fossils or other traces of past life. |
Phaethontis quadrangle | Dunes | Sand dunes have been found in many places on Mars. The presence of dunes shows that the planet has an atmosphere with wind, for dunes require wind to pile up the sand. Most dunes on Mars are black because of the weathering of the volcanic rock basalt. Black sand can be found on Earth on Hawaii and on some tropical South Pacific islands. |
Phaethontis quadrangle | Dunes | Sand is common on Mars due to the old age of the surface that has allowed rocks to erode into sand. Dunes on Mars have been observed to move many meters.
Some dunes move along. In this process, sand moves up the windward side and then falls down the leeward side of the dune, thus caused the dune to go toward the leeward side (or slip face).
When images are enlarged, some dunes on Mars display ripples on their surfaces. These are caused by sand grains rolling and bouncing up the windward surface of a dune. The bouncing grains tend to land on the windward side of each ripple. The grains do not bounce very high so it does not take much to stop them. |
Phaethontis quadrangle | Mantle | Much of the Martian surface is covered with a thick ice-rich, mantle layer that has fallen from the sky a number of times in the past. In some places a number of layers are visible in the mantle. |
Phaethontis quadrangle | Channels | There is enormous evidence that water once flowed in river valleys on Mars. Images of curved channels have been seen in images from Mars spacecraft dating back to the early seventies with the Mariner 9 orbiter. Indeed, a study published in June 2017, calculated that the volume of water needed to carve all the channels on Mars was even larger than the proposed ocean that the planet may have had. Water was probably recycled many times from the ocean to rainfall around Mars. |
Phaethontis quadrangle | Dust devil tracks | Because a thin coating of fine bright dust covers much of the surface of Mars, passing dust devils remove the bright dust and expose the underlying dark surface. Dust devils have been seen from the ground and from orbiting spacecraft. They have even blown the dust off of the solar panels of the two Rovers on Mars, thereby greatly extending their lives. |
Dinosaur Game | Dinosaur Game | The Dinosaur Game (also known as the Chrome Dino) is a browser game developed by Google and built into the Google Chrome web browser. The player guides a pixelated Tyrannosaurus rex across a side-scrolling landscape, avoiding obstacles to achieve a higher score. The game was created by members of the Chrome UX team in 2014. |
Dinosaur Game | Gameplay | When a user attempts to navigate to a web page on Google Chrome while being offline, the browser notifies the user that they are not connected to the Internet, with an illustration of a pixelated Tyrannosaurus rex shown on the page. The game can then be launched either by pressing space or ↑ on desktop, or by tapping the dinosaur on Android or iOS mobile devices. Additionally, the game can be accessed by inputting chrome://dino or chrome://network-error/-106 into the Omnibox.During the game, the Lonely T-Rex continuously moves from left to right across a black-and-white desert landscape, with the player attempting to avoid oncoming obstacles such as cacti and Pteranodons by jumping or ducking. Pressing space, ↑, or tapping the dinosaur on mobile devices will cause the dinosaur to "leap", while pressing the ↓ key will cause the dinosaur to "crouch". As the game progresses, the speed of play gradually increases until the user hits an obstacle or a Pterosaur, prompting an instant game over. |
Dinosaur Game | Gameplay | Once the player reaches around 700 points, the game switches from dark gray graphics on a white background to pale gray graphics on a black background, representing a shift from day to night, with daytime sky graphics also becoming nighttime sky graphics. The color scheme then alternates as the game progresses. The game was designed to reach its maximum score after approximately 17 million years of playtime, in reference to how long the T-Rex existed before it went extinct during the Cretaceous–Paleogene extinction event.If a network administrator disables the Dinosaur Game, an error message appears when attempting to play the game, which features an image of a meteor heading towards the Lonely T-Rex. |
Dinosaur Game | Development | The game was created by members of the Chrome UX team in 2014, which consisted of Sebastien Gabriel, Alan Bettes, and Edward Jung. Gabriel designed the player character, named the "Lonely T-Rex". During development, the game was given the codename "Project Bolan", in reference to Marc Bolan, the lead singer of the T. Rex band. The developers chose the dinosaur theme as a reference to the game's function, a joke that not having an internet connection is equivalent to living in the "prehistoric ages". The game was released in September 2014; initially, it did not work on older devices, so the code was updated and re-released in December of the same year. The pteranodons were added as obstacles with a browser update in 2015.In September 2018, an Easter egg was added to the game in celebration of Chrome's 10th birthday and the game's fourth birthday, with a birthday cake appearing in the desert and a birthday hat appearing on the Lonely T-Rex if the cake is "eaten". In November of the same year, Google introduced a feature to save the player's high score. The game's source code is available on the Chromium site.In 2021, Google introduced a widget in March for iOS 14 which led players to chrome://dino; a similar widget was introduced to Android later that year. In July, an Olympic torch Easter egg for the 2020 Tokyo Olympics simulating various Olympic activities was added. Upon reaching the torch, the dino transforms into various Olympic games such as swimming, running, and many others. Instead of the usual cacti and pterodactyl obstacles, the dino now encounters challenges related to the Olympics. |
Dinosaur Game | Reception | The game received widespread recognition, with the creators revealing in September 2018 that approximately 270 million games were played monthly. |
Dinosaur Game | In popular culture | The Dinosaur Game is referenced in the "couch gag" opening segment of the season 34 premiere of The Simpsons, "Habeas Tortoise". |
Dinosaur Game | Related media | In May 2020, a Microsoft Edge update added Surf, a game where players control a surfer attempting to evade obstacles and collect powerups. Like the Dinosaur Game, it is accessible from an error page when the browser is offline. The game allows for character customization and multiple control schemes.In August 2020, MSCHF and 100 Thieves partnered to create a modified version of the game titled Dino Swords, which featured a small arsenal of weapons and time-slowing pills; when mismanaged, the weapons could backfire and harm the dinosaur. |
Potato fruit | Potato fruit | The potato fruit is the part of the potato plant that, after flowering, produces a toxic, green cherry tomato-like fruit. |
Potato fruit | Characteristics | After flowering, potato plants produce small green fruits that resemble green cherry tomatoes, each containing about 300 seeds. Like all other parts of the plant except the tubers, the fruit contain the toxic alkaloid solanine and are therefore unsuitable for consumption. All new potato varieties are grown from seeds, also called "true potato seed", "TPS" or "botanical seed" to distinguish it from seed tubers. New varieties grown from seed can be propagated vegetatively by planting tubers, pieces of tubers cut to include at least one or two eyes, or cuttings, a practice used in greenhouses for the production of healthy seed tubers. Plants propagated from tubers are clones of the parent, whereas those propagated from seed produce a range of different varieties. |
Potato fruit | Characteristics | Potato fruits are produced when the plants experience cool temperatures and sufficient water. In 2014, many gardeners in Michigan, United States, were alarmed when they found the green fruit which are not normally produced on the potato plant in that region. This was due to the weather in July that year being cooler and wetter than normal, allowing the plants' flowers sufficient time to be pollinated and produce fruit. |
Potato fruit | In popular culture | Dorothy L. Sayers's short story The Leopard Lady, in the 1939 collection In the Teeth of the Evidence, features a child poisoned by potato berries injected with the alkaloid solanine to increase their toxicity. |
Blennorrhea | Blennorrhea | Blennorrhea is mucous discharge, especially from the urethra or vagina (that is, mucus vaginal discharge). Blennorrhagia is an excess of such discharge, often specifically referring to that seen in gonorrhea. In fact, blennorrhagia is also a German name of gonorrhea that was previously in use, but now no longer in technical use. Still, blennorrhagia is a major symptom of gonorrhea. |
Hangul Compatibility Jamo | Hangul Compatibility Jamo | Hangul Compatibility Jamo is a Unicode block containing Hangul characters for compatibility with the South Korean national standard KS X 1001 (formerly KS C 5601). Its block name in Unicode 1.0 was Hangul Elements. |
Hangul Compatibility Jamo | History | The following Unicode-related documents record the purpose and process of defining specific characters in the Hangul Compatibility Jamo block: |
Sherman–Morrison formula | Sherman–Morrison formula | In mathematics, in particular linear algebra, the Sherman–Morrison formula, named after Jack Sherman and Winifred J. Morrison, computes the inverse of the sum of an invertible matrix A and the outer product, uvT , of vectors u and v . The Sherman–Morrison formula is a special case of the Woodbury formula. Though named after Sherman and Morrison, it appeared already in earlier publications. |
Sherman–Morrison formula | Statement | Suppose A∈Rn×n is an invertible square matrix and u,v∈Rn are column vectors. Then A+uvT is invertible iff 1+vTA−1u≠0 . In this case, (A+uvT)−1=A−1−A−1uvTA−11+vTA−1u.
Here, uvT is the outer product of two vectors u and v . The general form shown here is the one published by Bartlett. |
Sherman–Morrison formula | Proof | (⇐ ) To prove that the backward direction 1+vTA−1u≠0⇒A+uvT is invertible with inverse given as above) is true, we verify the properties of the inverse. A matrix Y (in this case the right-hand side of the Sherman–Morrison formula) is the inverse of a matrix X (in this case A+uvT ) if and only if XY=YX=I We first verify that the right hand side ( Y ) satisfies XY=I .XY=(A+uvT)(A−1−A−1uvTA−11+vTA−1u)=AA−1+uvTA−1−AA−1uvTA−1+uvTA−1uvTA−11+vTA−1u=I+uvTA−1−uvTA−1+uvTA−1uvTA−11+vTA−1u=I+uvTA−1−u(1+vTA−1u)vTA−11+vTA−1u=I+uvTA−1−uvTA−1 To end the proof of this direction, we need to show that YX=I in a similar way as above: YX=(A−1−A−1uvTA−11+vTA−1u)(A+uvT)=I. |
Sherman–Morrison formula | Proof | (In fact, the last step can be avoided since for square matrices X and Y , XY=I is equivalent to YX=I .) (⇒ ) Reciprocally, if 1+vTA−1u=0 , then via the matrix determinant lemma, det det (A)=0 , so (A+uvT) is not invertible. |
Sherman–Morrison formula | Application | If the inverse of A is already known, the formula provides a numerically cheap way to compute the inverse of A corrected by the matrix uvT (depending on the point of view, the correction may be seen as a perturbation or as a rank-1 update). The computation is relatively cheap because the inverse of A+uvT does not have to be computed from scratch (which in general is expensive), but can be computed by correcting (or perturbing) A−1 Using unit columns (columns from the identity matrix) for u or v , individual columns or rows of A may be manipulated and a correspondingly updated inverse computed relatively cheaply in this way. In the general case, where A−1 is a n -by- n matrix and u and v are arbitrary vectors of dimension n , the whole matrix is updated and the computation takes 3n2 scalar multiplications. If u is a unit column, the computation takes only 2n2 scalar multiplications. The same goes if v is a unit column. If both u and v are unit columns, the computation takes only n2 scalar multiplications. |
Sherman–Morrison formula | Application | This formula also has application in theoretical physics. Namely, in quantum field theory, one uses this formula to calculate the propagator of a spin-1 field. The inverse propagator (as it appears in the Lagrangian) has the form (A+uvT) . One uses the Sherman–Morrison formula to calculate the inverse (satisfying certain time-ordering boundary conditions) of the inverse propagator—or simply the (Feynman) propagator—which is needed to perform any perturbative calculation involving the spin-1 field. |