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Beam me up, Scotty-Beam me up, Scotty-Though it has become irrevocably associated with the series and films, the exact phrase was never actually spoken in any Star Trek television episode or film. Despite this, the quote has become a phrase of its own over time. It can be used to describe one's desire to be elsewhere, ... | milkshake721/2.1M-wiki-STEM |
Beam me up, Scotty-Precise quotations-Despite the phrase entering into popular culture, it is a misquotation and has never been said in any of the television series or films, contrary to popular belief. There have, however, been several "near misses" of phrasing.
In the Original Series episodes "The Gamesters of Triske... | milkshake721/2.1M-wiki-STEM |
Beam me up, Scotty-Legacy-The popularity of the misquotation has led to many new phrases, both associated with Star Trek or otherwise. | milkshake721/2.1M-wiki-STEM |
Beam me up, Scotty-Legacy-The misquotation's influence led to James Doohan, the actor who played Scotty, to be misrepresented in his own obituary. In it, he is referenced as the character who "responded to the command, 'Beam me up, Scotty'", despite having never responded to this exact command in the show. Doohan himse... | milkshake721/2.1M-wiki-STEM |
Beam me up, Scotty-Legacy-The pop-culture centric wiki TV Tropes uses the phrase to refer to quotes that are never actually said in a certain work in spite of popular belief.Additionally, the quote was used in Season 3 Episode 3 of Superstore (2017) by Mateo in a scene in which he is speaking to a construction worker n... | milkshake721/2.1M-wiki-STEM |
Paola Bonfante-Paola Bonfante-Paola Bonfante is a Professor Emerita of plant biology at the University of Turin, she has studied symbiosis between fungi and plants (mycorrhizae), associations that involve 90% of plants with significant impacts on ecosystems, as well as on agriculture. | milkshake721/2.1M-wiki-STEM |
Paola Bonfante-Awards and honors-2019: Appointed Commander (“Commendatore”) of the “Order of Merit of the Italian Republic” by the President of the Italian Republic (“motu proprio”) 2010: Award for the Award for the French Food Spirit- Science – Paris, December 16, 2010 2021: The Adam Kondorosi -Academia Europaea Award... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Viral phylodynamics-Viral phylodynamics is defined as the study of how epidemiological, immunological, and evolutionary processes act and potentially interact to shape viral phylogenies.
Since the coining of the term in 2004, research on viral phylodynamics has focused on transmission dynamics in an... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Sources of phylodynamic variation-In coining the term phylodynamics, Grenfell and coauthors postulated that viral phylogenies "... are determined by a combination of immune selection, changes in viral population size, and spatial dynamics".
Their study showcased three features of viral phylogenies, ... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Sources of phylodynamic variation-The relative lengths of internal versus external branches will be affected by changes in viral population size over time Rapid expansion of a virus in a population will be reflected by a "star-like" tree, in which external branches are long relative to internal bran... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Applications-Viral origins Phylodynamic models may aid in dating epidemic and pandemic origins.
The rapid rate of evolution in viruses allows molecular clock models to be estimated from genetic sequences, thus providing a per-year rate of evolution of the virus.
With the rate of evolution measured i... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Applications-Viral control efforts Phylodynamic approaches can also be useful in ascertaining the effectiveness of viral control efforts, particularly for diseases with low reporting rates. For example, the genetic diversity of the DNA-based hepatitis B virus declined in the Netherlands in the late ... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-Most often, the goal of phylodynamic analyses is to make inferences of epidemiological processes from viral phylogenies.
Thus, most phylodynamic analyses begin with the reconstruction of a phylogenetic tree.
Genetic sequences are often sampled at multiple time points, which allows the estima... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-For example, the magnitude of selection can be measured by comparing the rate of nonsynonymous substitution to the rate of synonymous substitution (dN/dS); the population structure of the host population may be examined by calculation of F-statistics; and hypotheses concerning panmixis and s... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-In an effort to bridge the gap between traditional evolutionary approaches and epidemiological models, several analytical methods have been developed to specifically address problems related to phylodynamics.
These methods are based on coalescent theory, birth-death models, and simulation, a... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-More generally, the waiting time for two members of a sample of n gene copies to share a common ancestor is exponentially distributed, with rate λn=(n2)1N .This time interval is labeled Tn , and at its end there are n−1 extant lineages remaining. These remaining lineages will coalesce at ... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-In the absence of selection and population structure, the tree topology may be simulated by picking two lineages uniformly at random after each coalescent interval Ti The expected waiting time to find the MRCA of the sample is the sum of the expected values of the internode intervals, E[TMR... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-Donnelley and Tavaré derived this rate for a time-varying population size under the assumption of constant birth rates: λn(t)=(n2)1N(t) .Because all topologies are equally likely under the neutral coalescent, this model will have the same properties as the constant-size coalescent under a re... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-If the rate of exponential growth is estimated from a gene genealogy, it may be combined with knowledge of the duration of infection or the serial interval D for a particular pathogen to estimate the basic reproduction number, R0 The two may be linked by the following equation: r=R0−1D .Fo... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-Compartmental models Infectious disease epidemics are often characterized by highly nonlinear and rapid changes in the number of infected individuals and the effective population size of the virus. In such cases, birth rates are highly variable, which can diminish the correspondence between ... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-Phylogeography At the most basic level, the presence of geographic population structure can be revealed by comparing the genetic relatedness of viral isolates to geographic relatedness.
A basic question is whether geographic character labels are more clustered on a phylogeny than expected un... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-By repeatedly scrambling the data and calculating transition counts, a null distribution can be constructed and a p-value computed by comparing the observed transition counts to this null distribution.Beyond the presence or absence of population structure, phylodynamic methods can be used to... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-Here, geographic location is treated as a phylogenetic character state, similar in spirit to 'A', 'T', 'G', 'C', so that geographic location is encoded as a substitution model.
The same phylogenetic machinery that is used to infer models of DNA evolution can thus be used to infer geographic ... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Methods-In general, in needing to run simulations rather than compute likelihoods, it may be difficult to make fine-scale inferences on epidemiological parameters, and instead, this work usually focuses on broader questions, testing whether overall genealogical patterns are consistent with one epide... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-Phylodynamics of influenza Human influenza is an acute respiratory infection primarily caused by viruses influenza A and influenza B.
Influenza A viruses can be further classified into subtypes, such as A/H1N1 and A/H3N2.
Here, subtypes are denoted according to their hemagglutinin (H or HA)... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-A similar analysis combining sites across genes shows that while both HA and NA undergo substantial positive selection, internal genes show low rates of amino acid fixation relative to levels of polymorphism, suggesting an absence of positive selection.Further analysis of HA has shown it to... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-This finding suggests that reassortment between segments occurs slowly enough, relative to the actions of positive selection, that genetic hitchhiking causes beneficial mutations in HA and NA to reduce diversity in linked neutral variation in other segments of the genome.
Influenza A/H1N1 s... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-Surveillance data show a clear pattern of strong seasonal epidemics in temperate regions and less periodic epidemics in the tropics. The geographic origin of seasonal epidemics in the Northern and Southern Hemispheres had been a major open question in the field. However, temperate epidemics... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-Because of this, study-specific sampling procedures are a concern in extrapolating to population-level inferences. However, estimates of migration rates that are jointly based on epidemiological and evolutionary simulations appear robust to a large degree of undersampling or oversampling of... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-Work by Koelle and colleagues revisited the dynamics of influenza A/H3N2 evolution following the publication of a paper by Smith and colleagues which showed that the antigenic evolution of the virus occurred in a punctuated manner. The phylodynamic model designed by Koelle and coauthors arg... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-Through incorporating this mapping of viral genotype into viral phenotype (or antigenic cluster) into their model, the authors were able to reproduce the ladder-like phylogeny of influenza's HA protein without generalized strain-transcending immunity.
The reproduction of the ladder-like phy... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-HIV subtypes differ slightly in their transmissibility, virulence, effectiveness of antiretroviral therapy, and pathogenesis.The rate of exponential growth of HIV in Central Africa in the early 20th century preceding the establishment of modern subtypes has been estimated using coalescent a... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-At the opposite extreme, HIV-1 group O, a relatively rare group that is geographically confined to Cameroon and that is mainly spread by heterosexual sex, has grown at a lower rate than either subtype B or C.
HIV-1 sequences sampled over a span of five decades have been used with relaxed mo... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-There is evidence that HIV transmission within heterogeneous sexual networks leaves a trace in HIV phylogenies, in particular making phylogenies more imbalanced and concentrating coalescent events on a minority of lineages.By analyzing phylogenies estimated from HIV sequences from men who h... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-In a separate analysis, Volz et al. found that simple epidemiological dynamics explain phylogenetic clustering of viruses collected from patients with PHI. | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-Patients who were recently infected were more likely to harbor virus that is phylogenetically close to samples from other recently infected patients. Such clustering is consistent with observations in simulated epidemiological dynamics featuring an early period of intensified transmission d... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-Viral adaptation Purifying immune selection dominates evolution of HIV within hosts, but evolution between hosts is largely decoupled from within-host evolution. Immune selection has relatively little influence on HIV phylogenies at the population level for three reasons. | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-First, there is an extreme bottleneck in viral diversity at the time of sexual transmission. Second, transmission tends to occur early in infection before immune selection has had a chance to operate. Finally, the replicative fitness of a viral strain (measured in transmissions per host) is... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Examples-There is some evidence from comparative phylogenetic analysis and epidemic simulations that HIV adapts at the level of the population to maximize transmission potential between hosts. This adaptation is towards intermediate virulence levels, which balances the productive lifetime of the hos... | milkshake721/2.1M-wiki-STEM |
Viral phylodynamics-Future directions-Up to this point, phylodynamic approaches have focused almost entirely on RNA viruses, which often have mutation rates on the order of 10−3 to 10−4 substitutions per site per year.
This allows a sample of around 1000 bases to have power to give a fair degree of confidence in estima... | milkshake721/2.1M-wiki-STEM |
Physical media-Physical media-Physical media refers to the physical materials that are used to store or transmit information in data communications. These physical media are generally physical objects made of materials such as copper or glass. They can be touched and felt, and have physical properties such as weight an... | milkshake721/2.1M-wiki-STEM |
Physical media-Physical media-The term physical media can also be used to describe data storage media like records, cassettes, VHS, LaserDiscs, CDs, DVDs, and Blu-rays, especially when compared with modern streaming media or content that has been downloaded from the Internet onto a hard drive or other storage device as... | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-Copper wire Copper wire is currently the most commonly used type of physical media due to the abundance of copper in the world, as well as its ability to conduct electrical power. Copper is also one of the cheaper metals which makes it more feasible to use.Most copper wires used i... | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-Optical fiber Optical fiber is a thin and flexible piece of fiber made of glass or plastic. Unlike copper wire, optical fiber is typically used for long-distance data communications, being that it allows for data transmission over far distances and can produce high transmission sp... | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-Coaxial cables Coaxial cables have two different layers surrounding a copper core. The inner most layer has an insulator. The next layer has a conducting shield. These are both covered by a plastic jacket. Coaxial cables are used for microwaves, televisions and computers. | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-This was the second transmission medium to be introduced (often called coax), around the mid-1920s. In the center of a coaxial cable is a copper wire that acts as a conductor, where the information travels. The copper wire in coax is thicker than that in twisted-pair, and it is al... | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-Thinnet is used on Ethernet 10BASE2 networks and is the thinner and more flexible of the two. Unlike a thicknet, it uses a Bayonet Niell-Concelman (BNC) on each end to connect to computers. Thinnet is part of the RG-58 family of cable with a maximum cable length of 185 meters and ... | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-Thicknet coaxial cabling is used with Ethernet 10BASE5 networks, has a maximum cable length of 500 meters and transmission speeds of 10 Mbit/s. It's expensive and not commonly used, though it was originally used to directly connect computers. The computer is connected to the trans... | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-Application In the midst of the 1920s, coax was applied to telephone networks as inter-office trunks. Rather than adding more copper cable bundles with 1500 or 1000 pairs of copper wire and cable in them, it was possible to replace those big cables with much smaller coaxial cable. | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-The next major use of coax in telecommunications occurred in the 1950s, when it was deployed as submarine cable to carry international traffic. It was then introduced into the data processing realm in the mid 1960s. Early computer architectures required coax as the media type from... | milkshake721/2.1M-wiki-STEM |
Physical media-Types of physical media-Advantages Broadband system-coax has sufficient frequency range to support multiple channels, allowing greater throughput.
Greater channel capacity - each of the multiple channels offers substantial capacity depending on the service location (6 MHz wide in North America, 8 MHz wid... | milkshake721/2.1M-wiki-STEM |
Physical media-Debate on physical media-With technology constantly changing, there is a debate on whether physical media is still prudent and necessary to an increasingly wireless world. Wireless and physical media may actually complement each other, and physical media will matter more, not less, in a society dominated... | milkshake721/2.1M-wiki-STEM |
Bromine compounds-Bromine compounds-Bromine compounds are compounds containing the element bromine (Br). These compounds usually form the -1, +1, +3 and +5 oxidation states. Bromine is intermediate in reactivity between chlorine and iodine, and is one of the most reactive elements. Bond energies to bromine tend to be l... | milkshake721/2.1M-wiki-STEM |
Bromine compounds-Hydrogen bromide-The simplest compound of bromine is hydrogen bromide, HBr. It is mainly used in the production of inorganic bromides and alkyl bromides, and as a catalyst for many reactions in organic chemistry. Industrially, it is mainly produced by the reaction of hydrogen gas with bromine gas at 2... | milkshake721/2.1M-wiki-STEM |
Bromine compounds-Other binary bromides-Nearly all elements in the periodic table form binary bromides. The exceptions are decidedly in the minority and stem in each case from one of three causes: extreme inertness and reluctance to participate in chemical reactions (the noble gases, with the exception of xenon in the ... | milkshake721/2.1M-wiki-STEM |
Bromine compounds-Bromine halides-The halogens form many binary, diamagnetic interhalogen compounds with stoichiometries XY, XY3, XY5, and XY7 (where X is heavier than Y), and bromine is no exception. Bromine forms a monofluoride and monochloride, as well as a trifluoride and pentafluoride. Some cationic and anionic de... | milkshake721/2.1M-wiki-STEM |
Bromine compounds-Polybromine compounds-Although dibromine is a strong oxidising agent with a high first ionisation energy, very strong oxidisers such as peroxydisulfuryl fluoride (S2O6F2) can oxidise it to form the cherry-red Br+2 cation. A few other bromine cations are known, namely the brown Br+3 and dark brown Br+5... | milkshake721/2.1M-wiki-STEM |
Bromine compounds-Bromine oxides and oxoacids-Bromine oxides are not as well-characterised as chlorine oxides or iodine oxides, as they are all fairly unstable: it was once thought that they could not exist at all. Dibromine monoxide is a dark-brown solid which, while reasonably stable at −60 °C, decomposes at its melt... | milkshake721/2.1M-wiki-STEM |
Bromine compounds-Organobromine compounds-Like the other carbon–halogen bonds, the C–Br bond is a common functional group that forms part of core organic chemistry. Formally, compounds with this functional group may be considered organic derivatives of the bromide anion. Due to the difference of electronegativity betwe... | milkshake721/2.1M-wiki-STEM |
Bromine compounds-Organobromine compounds-An old qualitative test for the presence of the alkene functional group is that alkenes turn brown aqueous bromine solutions colourless, forming a bromohydrin with some of the dibromoalkane also produced. The reaction passes through a short-lived strongly electrophilic bromoniu... | milkshake721/2.1M-wiki-STEM |
Comparison of Pascal and Delphi-Comparison of Pascal and Delphi-Devised by Niklaus Wirth in the late 1960s and early 1970s, Pascal is a programming language. Originally produced by Borland Software Corporation, Embarcadero Delphi is composed of an IDE, set of standard libraries, and a Pascal-based language commonly cal... | milkshake721/2.1M-wiki-STEM |
Comparison of Pascal and Delphi-Comparison of Pascal and Delphi-While developing Pascal, Wirth employed a bootstrapping procedure in which each newer version of the Pascal compiler was written and compiled with its predecessor. Thus, the 'P2' compiler was written in the dialect compilable by 'P1', 'P3' in turn was writ... | milkshake721/2.1M-wiki-STEM |
Comparison of Pascal and Delphi-Comparison of Pascal and Delphi-The Borland dialect, like the popular UCSD Pascal before it, took the 'P4' version of the language as its basis, rather than Wirth's final revision. After much evolution independent of Standard Pascal, the Borland variant became the basis for Delphi. This ... | milkshake721/2.1M-wiki-STEM |
Comparison of Pascal and Delphi-Exclusive features-Following features are mutually exclusive.
The Standard Pascal implementation is not accepted by Delphi and vice versa, the Delphi code is not acceptable in Standard Pascal.
Modulo with negative dividend Standard Pascal has an Euclidean-like definition of the mod opera... | milkshake721/2.1M-wiki-STEM |
Comparison of Pascal and Delphi-Additional or missing features-Following features are present or missing in either language.
Global goto Standard Pascal permits a goto to any label defined in scope.
In Delphi a goto must be within the current routine, i. e. may not leave the begin … end-frame.
Buffer variables Delphi d... | milkshake721/2.1M-wiki-STEM |
Comparison of Pascal and Delphi-Peculiar implementation characteristics-Standard write width In Pascal, if the destination file is a text file, the parameters to write/writeLn have an implemention-defined default total width.
In Delphi, for integer values this is simply 1.
That means always the least amount of space is... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Lead (tack)-A lead, lead line, lead rope (US) or head collar rope (UK), is used to lead an animal such as a horse. Usually, it is attached to a halter. The lead may be integral to the halter or, more often, separate. When separate, it is attached to the halter with a heavy clip or snap so that it can be add... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Variations-A lead can be made from a variety of materials, including cotton, horsehair (woven or braided hair, usually from a horse's tail), leather, nylon or other synthetic materials. Lead ropes, as the name implies, are round and made of various types of rope, usually between 5/8 and 3/4 inch (about 2 cm... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Variations-A lead most often attaches to the halter with a sturdy snap. In some cases, the lead is tied or spliced permanently to the halter. A lead for a horse usually is in the range of 9 to 12 feet (2.7 to 3.7 m) long, but longer and shorter lengths are seen. | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Variations-The lead shank consists of a lead, usually a flat line, with a chain end, or, less often, thin nylon or rope. The chain end ranges from 18 to 30 inches (46 to 76 cm) long and has a snap or clip on the end that attaches to the halter, and a ring on the other end that is attached to the lead line. ... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Variations-For aesthetic purposes, the lead may be the same color as the halter, and sometimes even made of the same materials. | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Use-Leads are used to lead, hold, or tie an animal or string of animals. A horse may be led by a person on the ground, sometimes called "leading in-hand," or may be led by a rider mounted on another horse, a process called "ponying." A "string" of animals refers to animals tied to one another by their leads... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Safety in leading-By tradition, the handler leads a horse from the horse's left ("near") side, though situations may arise when a horse needs to be led from the right ("off") side. In some areas, particularly in the American west, the handler may be in front of the horse while leading, though this technique... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Safety in leading-When leading a horse, the handler usually holds a single thickness of the lead with the right hand, while carrying the gathered slack of the lead in the left. The excess line should be laid in back-and-forth loops that fall on either side of the hand; holding the excess in circular loops, ... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Safety in leading-When used to lead a horse in hand, the materials used in a lead, particularly synthetics, may put a handler at risk of a rope burn should the horse pull the lead from the handler. Some handlers wear gloves while leading a horse. | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Tying-Lead ropes may be used to tie up animals. Common methods of tying off a lead include the halter hitch and a subset of other loop knots, collectively known among equestrians as safety knots and quick release knots. If the animal begins to panic, a person can pull the working end to quickly release the ... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Tying-Animals, usually horses, may also be placed in crossties, usually for grooming, tacking up and related activities. Crossties are commonly made from two lead ropes, each attached to a wall with the snap end placed on either side of the horse's halter. This technique of restraint keeps the horse from mo... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Tying-Flat lead shanks and thin diameter ropes generally lack the strength to securely tie a large animal such as a horse or cow, but may be more comfortable in a person's hand for leading. Ropes of a thick diameter (3/4 in or more) and high tensile strength generally are adequate to tie a large animal that... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Tying-An animal that panics and attempts to escape while tied with a lead can cause itself serious injury or damage the objects to which it is tied. When an animal is left unattended or if a safety knot is improperly tied and cannot be released, views differ as to whether a lead rope should be made strong e... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Use of a shank-Hard jerks on a lead shank can frighten a horse, damage the head, or cause a horse to rear. Light, short tugs are generally enough to get the attention of a horse. The chain should only come into action when pulled, not when hanging loosely. The handler does not hold the chain itself, as it c... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Use of a shank-Chain shank attachments Over the nose: The shank is run through the left ring of the halter (on the side of the face), wrapped once around the noseband of the halter, threaded through the right side nose ring of the halter, and attached on the upper right ring of the halter (near the ears of ... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Use of a shank-Under the chin: the shank is run through the lower left ring of the halter, under the chin, through the lower right ring of the halter, and attached either back to itself or to the upper right ring. This tends to make a horse raise his head, but also has a stronger disciplinary effect. The ch... | milkshake721/2.1M-wiki-STEM |
Lead (tack)-Use of a shank-Chain through mouth: The chain is run through the left lower ring, through the mouth, through the right lower ring, and attached to the upper right ring. This is quite severe and can damage the mouth if used harshly.
Chain over gum: similar to the chain through the mouth, except the chain is ... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Bra–ket notation-Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically designed to ease the types of calculations that f... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Bra–ket notation-Paul Dirac created Bra-ket notation in 1939 to make it easier to write quantum mechanical equations. In his 1939 publication, A New Notation for Quantum Mechanics, Dirac wrote: A Hilbert-space vector, which was denoted in the old notation by the letter ψ, will now be denoted by a speci... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Quantum mechanics-In quantum mechanics, bra–ket notation is used ubiquitously to denote quantum states. The notation uses angle brackets, ⟨ and ⟩ , and a vertical bar | , to construct "bras" and "kets".
A ket is of the form |v⟩ . Mathematically it denotes a vector, v , in an abstract (complex) vec... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Quantum mechanics-A bra is of the form ⟨f| . Mathematically it denotes a linear form f:V→C , i.e. a linear map that maps each vector in V to a number in the complex plane C . Letting the linear functional ⟨f| act on a vector |v⟩ is written as ⟨f|v⟩∈C Assume that on V there exists an inner produ... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Quantum mechanics-For the vector space Cn , kets can be identified with column vectors, and bras with row vectors. Combinations of bras, kets, and linear operators are interpreted using matrix multiplication. If Cn has the standard Hermitian inner product (v,w)=v†w , under this identification, the i... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Quantum mechanics-It is common to suppress the vector or linear form from the bra–ket notation and only use a label inside the typography for the bra or ket. For example, the spin operator σ^z on a two dimensional space Δ of spinors, has eigenvalues {\textstyle \pm {\frac {1}{2}}} with eigenspinors ... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Quantum mechanics-Bra–ket notation was effectively established in 1939 by Paul Dirac; it is thus also known as Dirac notation, despite the notation having a precursor in Hermann Grassmann's use of [ϕ∣ψ] for inner products nearly 100 years earlier. | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-Vectors vs kets In mathematics, the term "vector" is used for an element of any vector space. In physics, however, the term "vector" tends to refer almost exclusively to quantities like displacement or velocity, which have components that relate directly to the three dimensions of space, ... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-In quantum mechanics, a quantum state is typically represented as an element of a complex Hilbert space, for example, the infinite-dimensional vector space of all possible wavefunctions (square integrable functions mapping each point of 3D space to a complex number) or some more abstract ... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-Symbols, letters, numbers, or even words—whatever serves as a convenient label—can be used as the label inside a ket, with the |⟩ making clear that the label indicates a vector in vector space. In other words, the symbol "|A⟩" has a recognizable mathematical meaning as to the kind of var... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-Notation Since kets are just vectors in a Hermitian vector space, they can be manipulated using the usual rules of linear algebra. For example: |A⟩=|B⟩+|C⟩|C⟩=(−1+2i)|D⟩|D⟩=∫−∞∞e−x2|x⟩dx.
Note how the last line above involves infinitely many different kets, one for each real number x. | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-Since the ket is an element of a vector space, a bra ⟨A| is an element of its dual space, i.e. a bra is a linear functional which is a linear map from the vector space to the complex numbers. Thus, it is useful to think of kets and bras as being elements of different vector spaces (see b... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-A bra ⟨ϕ| and a ket |ψ⟩ (i.e. a functional and a vector), can be combined to an operator |ψ⟩⟨ϕ| of rank one with outer product |ψ⟩⟨ϕ|:|ξ⟩↦|ψ⟩⟨ϕ|ξ⟩. | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-Inner product and bra–ket identification on Hilbert space The bra–ket notation is particularly useful in Hilbert spaces which have an inner product that allows Hermitian conjugation and identifying a vector with a continuous linear functional, i.e. a ket with a bra, and vice versa (see Ri... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector: Based on this, the bras and kets can be defined as: and then it is understood that a bra next to a ket implies matrix m... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-The conjugate transpose (also called Hermitian conjugate) of a bra is the corresponding ket and vice versa: because if one starts with the bra then performs a complex conjugation, and then a matrix transpose, one ends up with the ket Writing elements of a finite dimensional (or mutatis mu... | milkshake721/2.1M-wiki-STEM |
Bra–ket notation-Vector spaces-Non-normalizable states and non-Hilbert spaces Bra–ket notation can be used even if the vector space is not a Hilbert space. | milkshake721/2.1M-wiki-STEM |
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