title: Solly March

text: March was named by Gareth Southgate as a forward in the England under-21 squad in May 2014. The squad would play a 2015 UEFA European Under-21 Championship qualification match against Wales and at least four games at the Toulon Tournament. March had not previously played for England at any level. He made his England under-20 debut when starting in a 3–0 win over Qatar on 22 May. On 27 March 2017, March scored his first international goal in an under-21 friendly against Denmark with a shot from outside the box in a 4–0 away victory.


title: Solly March

text: March originally played on the wing either in midfield or as part of a forward line. Steve King, his former manager at Lewes, described March as a "technically very good" player who "has bags of energy, is a box-to-box player, has a good left foot, a good shot, he sees things early and the weight of his passes is very good." Since the appointment of Graham Potter as head coach at Brighton, March has predominantly been used as a left wing-back.


title: Solly March

text: In May 2017, following Brighton & Hove Albion's promotion to the Premier League, March became engaged to girlfriend Amelia Goldman after proposing to her in Dubai. March and Goldman married in November 2017, and their first child, a daughter, was born in August 2019.


title: Public defender

text: A public defender is a lawyer appointed to represent people who otherwise cannot reasonably afford to hire a lawyer to defend themselves in a trial. Several countries provide people with public defenders, including the UK, Hungary and Singapore, and some states of Australia. Brazil is the only country in which an office of government-paid lawyers with the specific purpose of providing full legal assistance and representation to the needy free of charge is established in the constitution. The Sixth Amendment to the US Constitution, as interpreted by the Supreme Court, requires the US government to provide legal counsel to indigent defendants in criminal cases. Public defenders in the United States are lawyers employed by or under contract with county, state or federal governments.


title: Public defender

text: In civil law countries, following the model from the French Napoleonic Code of criminal procedure, the courts typically appoint private attorneys at the expense of the state.


title: Public defender

text: The Australian states of Victoria and New South Wales both have dedicated Public Defenders chambers. These chambers retain barristers who are employed by the state government to represent legally-aided clients who are charged with serious indictable offences. In New South Wales, Public Defenders only appear in criminal matters, both at trial and appellate level, while in Victoria, Public Defenders also undertake some family law and civil work.


title: Public defender

text: The New South Wales Senior Public Defender is Belinda Rigg, Senior Counsel, who was the first female public defender in NSW upon her appointment in 2019. In Victoria, the Chief Public Defender is Tim Marsh.


title: Public defender

text: In Queensland, the Legal Aid Office (Queensland) was merged with the Public Defender's Office in 1991, in an expanded service providing clients to access family, civil and all criminal law services.


title: Public defender

text: The Constitution of Brazil uniquely provides for a public defenders' office ("Defensoria Pública") at both state and federal levels. Public defense is a right to poor people, who must declare, formally, that they cannot afford regular legal aid, to benefit from public defenders' services.


title: Public defender

text: Public defenders, like prosecutors and judges, are admitted to their positions through civil service examination. The public defender's office assists the poor and lower middle-class in both civil and criminal matters, although the poorest states in the country are still struggling to set up a state public defenders office.


title: Public defender

text: Public defense in Brazil dates back to 1897, when a decree mandated government-funded legal assistance in the state of Rio de Janeiro, then called Legal Assistance ("Assistência Jurídica"). The Constitution of 1937 extended "Assistência Jurídica" to the entire country, but without the same effectiveness that is derived from the current, 1988 Constitution.


title: Public defender

text: Germany provides legal representation, legal advice, and help in covering court costs in civil cases to those who cannot raise the necessary funds to hire an attorney, but only when there is a reasonable chance of success. In criminal cases where the defendant faces at least one year of imprisonment, the defendant has the right to legal counsel. Although there is a right to legal defense, there is no organized public defender system. Instead, any lawyer can be appointed to provide counsel to a specific defendant, and the defendant can select a specific lawyer. Questions of payment are deferred until the end of a trial, and the court will decide the cost of the case to the losing party. The defendant will not be charged for legal services if acquitted. If convicted, the defendant will be required to pay the lawyer's expenses unless the court finds that the defendant is indigent.


title: Public defender

text: In Hungary, the police, the public prosecutor or the court (depending on what individual cases require) appoints a criminal defender at the state's cost to defend those who can not afford a chosen lawyer. The defence counsel's participation is required by the Criminal Procedure Act. Usually a private lawyer is appointed, one for each defendant, and conflict of interest between contradicting suspects is avoided, e.g. the same lawyer may not represent two accused whose evidence is mutually contradictory. If convicted, although in principle the defendant is liable for the fee, it is rarely pursued.


title: Public defender

text: In India, free legal aid is provided by National legal services authority. It is available at all the levels of court.


title: Public defender

text: Legal assistance in Singapore is provided by the State and the Pro Bono Services Office of the Law Society.


title: Public defender

text: The State provides legal assistance in criminal cases where the accused faces the death penalty. The government also provides legal representation and advice in civil cases such as for divorce, child custody, adoption, wrongful dismissal, letters of administration/probate, tenancy disputes, claims in contract and tort, through the Ministry of Law's Legal Aid Bureau (LAB). Assistance from the LAB is not free, and most clients are required to contribute towards the costs of the work done, but the amount a client is charged depends on a number of factors, among them the client's financial means.


title: Public defender

text: The Pro Bono Services Office of the Law Society runs the Criminal Legal Aid Scheme, which provides criminal legal assistance to the poor and needy who are unable to afford a lawyer, and are facing charges in a Singapore court for non death-penalty offences under statutes covered by CLAS.


title: Public defender

text: There are a small number of Public Defender Service offices in England and Wales with lawyers employed directly by the Legal Aid Agency to provide advice in police stations and representation in magistrates and crown courts. The Public Defender Service has existed since 2001, a department of the Legal Aid Agency, an Executive Agency of the Ministry of Justice (UK). It has four offices across England and Wales. The majority of state funded criminal defence work, however, is provided by private duty solicitors contracted to the Legal Aid Agency and paid by the case under the legal aid scheme.


title: Public defender

text: In Scotland a wider network of Public Defender Solicitor Office (PDSO) lawyers employed by the Scottish Legal Aid Board (SLAB) are available to represent those accused of crimes in addition to private lawyers (duty solicitors) paid under the legal aid scheme. The PDSO is a not-for-profit organisation funded through SLAB.


title: Public defender

text: The 1963 US Supreme Court case "Gideon v. Wainwright" held that the Sixth Amendment's right to counsel provision requires the government to provide legal counsel to indigent defendants in criminal cases. Different jurisdictions, however, use different approaches in providing legal counsel for criminal defendants who can't afford private attorneys. Exactly which defendants qualify as "indigent" also varies by jurisdiction: Often a state will stipulate a maximum income threshold above which a defendant is not considered to be indigent, and thus does not qualify for a public defender. This threshold may vary depending on the severity of the crime with which a defendant is charged. For example, a defendant's income may be too high to entitle him or her to a public defender in misdemeanor proceedings, but sufficiently low to qualify them as indigent when faced with a felony charge.


title: Public defender

text: The term public defender in the United States is often used to describe a lawyer who is appointed by a court to represent a defendant who cannot afford to hire an attorney. More correctly, a public defender is a lawyer who works for a public defender's office, a government-funded agency that provides legal representation to indigent defendants. The court appoints the public defender's office to represent the defendant, and the office assigns a lawyer to the defendant's case. In the federal criminal court system and some states and counties, representation is through a publicly funded public defender office. The state of Oregon is the only state in which indigent defense is exclusively provided by non-profit firms which are contracted and funded by the state.


title: Public defender

text: Other courts may appoint private lawyers who have agreed to represent indigent defendants, with appointment being either on a contractual basis, through which the lawyer accepts an agreed number of cases from the court for the term of the contract, or a case-by-case basis. The majority of the states in the U.S. employ some combination of these delivery models.


title: Braciola

text: Braciola may refer to an Italian dish, consisting of slices of meat that are pan-fried or grilled, often in their own juice or in a small amount of light olive oil. They are different from the finer cut "fettine" ("small/thin slices"), which never have bone and are generally thinner.


title: Braciola

text: In Sicilian cuisine, Italian-American cuisine and Italian Australian cuisine, "braciola" (plural "braciole") are thin slices of meat (typically pork, chicken, beef, or swordfish) that are rolled as a roulade (this category of rolled food is known as "involtini" in Italian) with cheese and bread crumbs and fried. In Sicilian, this dish is also called "bruciuluni".


title: Braciola

text: Braciole can be cooked along with meatballs and Italian sausage in a Neapolitan ragù or tomato sauce, which some call "sarsa" or "succu" (Sicilian), or 'Sunday gravy' in some areas of the northeastern United States. They can also be prepared without tomato sauce. There exist many variations on the recipe, including variations of cheese and the addition of vegetables, such as eggplant. Braciole are not exclusively eaten as a main dish, but also as a side dish at dinner, or in a sandwich at lunch.


title: Braciola

text: After being stuffed and rolled, braciole are often tied with string or pinned with wooden toothpicks to hold in the stuffing. After pan-frying to brown, the rolls of meat are placed into the sauce to finish cooking, still secured with string or toothpicks.


title: Racing

text: In sport, racing is a competition of speed, in which competitors try to complete a given task in the shortest amount of time. Typically this involves traversing some distance, but it can be any other task involving speed to reach a specific goal.


title: Racing

text: A race may be run continuously to finish or may be made up of several segments called heats, stages or legs. A heat is usually run over the same course at different times. A stage is a shorter section of a much longer course or a time trial.


title: Racing

text: Early records of races are evident on pottery from ancient Greece, which depicted running men vying for first place. A chariot race is described in Homer's "Iliad".


title: Racing

text: The word "race" comes from a Norse word. This Norse word arrived in France during the invading of Normandy and gave the word "raz" which means "swift water" in Brittany, as in a mill race; it can be found in "Pointe du Raz" (the most western point of France, in Brittany), and ""raz-de-marée"" (tsunami). The word race to mean a "contest of speed" was first recorded in the 1510s.


title: Racing

text: A race and its name are often associated with the place of origin, the means of transport and the distance of the race. As a couple of examples, see the Dakar Rally or the Athens Marathon.


title: Racing

text: Running a distance is the most basic form of racing, but races may also be done by climbing, swimming, walking, or other types of human locomotion. Races may be conducted with animals such as camels, dogs, horses, pigeons, pigs, snails, or turtles. They also may by done in vehicles such as aircraft, bicycles, boats, cars, or motorcycles; or with another means of transport such as skates, skateboards, skis, sleds, snowboards, or wheelchair. In a relay race members of a team take turns in racing parts of a circuit or performing a certain racing form.


title: Racing

text: Orienteering races add an additional task of using a map and compass to navigate from point to point in diverse and usually unfamiliar terrain.


title: Racing

text: A race can also involve any other type of goal like eating. A common speed eating challenge is a hot dog eating race, where contestants try to eat more hot dogs than the other racers.


title: Racing

text: Racing can also be done in more humoristic and entertaining ways such as the Sausage Race, the Red Bull Trolley Grand Prix and wok racing. Racing can be entertained from around the world.


title: Racing

text: A sprint finish is a racing tactic used in many forms of racing where a competitor accelerates towards top speed in the final stages of a race. This tactic is mostly associated with long-distance forms of running and cycling, which often feature large groups of competitors racing at a slower pace for much of the race – this slower aerobic racing allows for the subsequent anaerobic activity required for sprinting. The tactic relies upon keeping greater energy reserves than your opponent until the last part of the race in order to be able to reach the finish point first. It is the opposing tactic to keeping a steady optimal pace throughout a race to maximise your energy efficiency (see running economy).


title: Racing

text: In track and field, distances from 1500 metres upwards often feature sprint finishes. They can also be found in cross country and road running events, even up to the marathon distance. A runner's ability to sprint at the end of a race is also known as their finishing kick. Multisport races, such as the triathlon, often have running as the final section and sprint finish tactics are applied as they are in running-only events.


title: Racing

text: In cycling, sprint finishes are an integral part of the sport and are used in both track cycling and road cycling. Cycling sprints are often highly tactical, particularly on the track, with cyclists occasionally coming to a near halt at points before reaching a high speed finish. The longer track races such as scratch races often feature sprint finishes, as maintaining a steady pace within the peloton allows opponents to conserve energy through drafting. Road races are similar in this respect, in both short criterium races and long-distance races. Sprint tactics also form a major part of points classifications in road events, where cycling sprinters specialise in reaching an intermediate point first, thus gaining extra points and resulting prizes.


title: Racing

text: Sprint finish tactics are also used in speedskating, cross-country skiing, long-distance swimming, horse racing and other animal racing sports. The finishes of races which are outright sprinting events in themselves, such as the 100 metres track race, are not normally referred to as sprint finishes, as all competitors are already sprinting by default (thus it is not a racing tactic).


title: Harsh Goenka

text: Harsh Vardhan Goenka (born 10 December 1957) is the current chairman of US$3.80 billion worth Indian RPG Group conglomerate. He is the eldest son of R. P. Goenka and chairman of RPG Group since 1988. He is listed as 77th richest Indian and number 1281 among world billionaire by Forbes. He graduated in economics from St Xavier’s College, Kolkata and thereafter pursued his MBA from the International Institute for Management Development, Switzerland. He has one younger brother Sanjiv Goenka with whom he amicably divided the business assets under advice from their father.


title: Harsh Goenka

text: He has held positions as president of Indian Merchants' Chamber and member-executive committee at Federation of Indian Chambers of Commerce & Industry. He is a member of the board of governors of the National Institute of Industrial Engineering (NITIE), one of the leading technical educational institutes in India. He is also a member of foundation board of International Institute for Management Development, Switzerland, his "alma mater".


title: Harsh Goenka

text: Earlier, at an age of 28, he was specially appointed member of Estimates Committee for 1985–86 set up by Government of India, Ministry of Finance, Central Board Excise And Customs. In 2018, when Israeli Prime Minister Netanyahu visited Mumbai, he was one of the 10 corporate leaders of India who held power break-fast meet with him on bi-lateral trade with India in various sectors of industry.


title: Harsh Goenka

text: He has been criticized for the regressive jokes he posted on Twitter that invited widespread outrage from feminists.


title: SonicFox

text: Dominique McLean, known professionally as SonicFox, is an American professional esports player of several fighting games. McLean is recognized for their versatility and ability to pick up a new game or character and master it for professional play relatively quickly. McLean has topped many tournaments, including six Evolution Championship Series (EVO) events for five different game franchises. They are the highest paid fighting game esports player in the world as of August 4, 2019, with over $600,000 in earnings. McLean was named Esports Player of the Year at The Game Awards 2018 and included in "Forbes" 2020 "30 Under 30" for Games.


title: SonicFox

text: McLean is openly gay and non-binary as well as a furry. They are known to often participate in fighting game tournaments in the fursuit of their fursona, a blue-and-white anthropomorphic fox.


title: SonicFox

text: McLean's older brother, Christian, got McLean interested in fighting video games when McLean was three years old. Over the next several years, while McLean continued to play games, they came into the furry fandom around the age of ten or eleven, and developed the "SonicFox" character.


title: SonicFox

text: Around 2011, McLean was playing in non-competitive online "Mortal Kombat" games, and their online friends encouraged them to try their skills at an offline "Mortal Kombat" tournament in 2012. While McLean only came in ninth at the event, they were enthralled with the competitive atmosphere, and they have continued to participate in various fighting game championships.


title: SonicFox

text: McLean achieved a 6–0 victory at the "" tournament at Evo 2014. "News.com.au" reported in December 2015 that McLean had not lost a single tournament in the previous 18 months, and that they earned $150,000 USD within the span of two weeks by winning "Mortal Kombat" tournaments.


title: SonicFox

text: McLean was named the "Esports Player of the Year" at The Game Awards 2018 ceremony, earning media attention for their acceptance speech. "Forbes" included McLean on their 2020 "30 Under 30" in the Games category.


title: SonicFox

text: McLean was raised in Townsend, Delaware. As of 2018, McLean was a student at the New York Institute of Technology. McLean chose to focus on academics while still maintaining a balance between their professional gaming and school life. In September 2019, McLean came out on Twitter as non-binary. McLean publicly uses singular they pronouns, reserving use of masculine pronouns only for those who they are close to, in order to help normalize the use of singular they.


title: Colloidal gold

text: Colloidal gold is a sol or colloidal suspension of nanoparticles of gold in a fluid, usually water. The colloid is usually either wine-red coloured (for spherical particles less than 100 nm) or blue/purple (for larger spherical particles or nanorods).


title: Colloidal gold

text: Due to their optical, electronic, and molecular-recognition properties, gold nanoparticles are the subject of substantial research, with many potential or promised applications in a wide variety of areas, including electron microscopy, electronics, nanotechnology, materials science, and biomedicine.


title: Colloidal gold

text: The properties of colloidal gold nanoparticles, and thus their potential applications, depend strongly upon their size and shape. For example, rodlike particles have both a transverse and longitudinal absorption peak, and anisotropy of the shape affects their self-assembly.


title: Colloidal gold

text: Used since ancient times as a method of staining glass colloidal gold was used in the 4th-century Lycurgus Cup, which changes color depending on the location of light source.


title: Colloidal gold

text: During the Middle Ages, soluble gold, a solution containing gold salt, had a reputation for its curative property for various diseases. In 1618, Francis Anthony, a philosopher and member of the medical profession, published a book called "Panacea Aurea, sive tractatus duo de ipsius Auro Potabili" (Latin: gold potion, or two treatments of potable gold). The book introduces information on the formation of colloidal gold and its medical uses. About half a century later, English botanist Nicholas Culpepper published book in 1656, "Treatise of Aurum Potabile", solely discussing the medical uses of colloidal gold.


title: Colloidal gold

text: In 1676, Johann Kunckel, a German chemist, published a book on the manufacture of stained glass. In his book "Valuable Observations or Remarks About the Fixed and Volatile Salts-Auro and Argento Potabile, Spiritu Mundi and the Like", Kunckel assumed that the pink color of Aurum Potabile came from small particles of metallic gold, not visible to human eyes. In 1842, John Herschel invented a photographic process called chrysotype (from the Greek χρῡσός meaning "gold") that used colloidal gold to record images on paper.


title: Colloidal gold

text: Modern scientific evaluation of colloidal gold did not begin until Michael Faraday's work in the 1850s. In 1856, in a basement laboratory of Royal Institution, Faraday accidentally created a ruby red solution while mounting pieces of gold leaf onto microscope slides. Since he was already interested in the properties of light and matter, Faraday further investigated the optical properties of the colloidal gold. He prepared the first pure sample of colloidal gold, which he called 'activated gold', in 1857. He used phosphorus to reduce a solution of gold chloride. The colloidal gold Faraday made 150 years ago is still optically active. For a long time, the composition of the 'ruby' gold was unclear. Several chemists suspected it to be a gold tin compound, due to its preparation. Faraday recognized that the color was actually due to the miniature size of the gold particles. He noted the light scattering properties of suspended gold microparticles, which is now called Faraday-Tyndall effect.


title: Colloidal gold

text: In 1898, Richard Adolf Zsigmondy prepared the first colloidal gold in diluted solution. Apart from Zsigmondy, Theodor Svedberg, who invented ultracentrifugation, and Gustav Mie, who provided the theory for scattering and absorption by spherical particles, were also interested in the synthesis and properties of colloidal gold.


title: Colloidal gold

text: With advances in various analytical technologies in the 20th century, studies on gold nanoparticles has accelerated. Advanced microscopy methods, such as atomic force microscopy and electron microscopy, have contributed the most to nanoparticle research. Due to their comparably easy synthesis and high stability, various gold particles have been studied for their practical uses. Different types of gold nanoparticle are already used in many industries, such as electronics.


title: Colloidal gold

text: Colloidal gold has been used by artists for centuries because of the nanoparticle’s interactions with visible light. Gold nanoparticles absorb and scatter light resulting in colours ranging from vibrant reds (smaller particles) to blues to black and finally to clear and colorless (larger particles), depending on particle size, shape, local refractive index, and aggregation state. These colors occur because of a phenomenon called localized surface plasmon resonance (LSPR), in which conduction electrons on the surface of the nanoparticle oscillate in resonance with incident light.


title: Colloidal gold

text: As a general rule, the wavelength of light absorbed increases as a function of increasing nano particle size. For example, pseudo-spherical gold nanoparticles with diameters ~ 30 nm have a peak LSPR absorption at ~530 nm.


title: Colloidal gold

text: Changes in the apparent color of a gold nanoparticle solution can also be caused by the environment in which the colloidal gold is suspended The optical properties of gold nanoparticles depends on the refractive index near the nanoparticle surface, therefore both the molecules directly attached to the nanoparticle surface (i.e. nanoparticle ligands) and/or the nanoparticle solvent both may influence observed optical features. As the refractive index near the gold surface increases, the NP LSPR will shift to longer wavelengths In addition to solvent environment, the extinction peak can be tuned by coating the nanoparticles with non-conducting shells such as silica, bio molecules, or aluminium oxide.


title: Colloidal gold

text: When gold nano particles aggregate, the optical properties of the particle change, because the effective particle size, shape, and dielectric environment all change.


title: Colloidal gold

text: Colloidal gold and various derivatives have long been among the most widely used labels for antigens in biological electron microscopy. Colloidal gold particles can be attached to many traditional biological probes such as antibodies, lectins, superantigens, glycans, nucleic acids, and receptors.Particles of different sizes are easily distinguishable in electron micrographs, allowing simultaneous multiple-labelling experiments.


title: Colloidal gold

text: In addition to biological probes, gold nanoparticles can be transferred to various mineral substrates, such as mica, single crystal silicon, and atomically flat gold(III), to be observed under atomic force microscopy (AFM).


title: Colloidal gold

text: Gold nanoparticles can be used to optimize the biodistribution of drugs to diseased organs, tissues or cells, in order to improve and target drug delivery.


title: Colloidal gold

text: Nanoparticle-mediated drug delivery is feasible only if the drug distribution is otherwise inadequate. These cases include drug targeting of unstable (proteins, siRNA, DNA), delivery to the difficult sites (brain, retina, tumors, intracellular organelles) and drugs with serious side effects (e.g. anti-cancer agents). The performance of the nanoparticles depends on the size and surface functionalities in the particles. Also, the drug release and particle disintegration can vary depending on the system (e.g. biodegradable polymers sensitive to pH). An optimal nanodrug delivery system ensures that the active drug is available at the site of action for the correct time and duration, and their concentration should be above the minimal effective concentration (MEC) and below the minimal toxic concentration (MTC).


title: Colloidal gold

text: Gold nanoparticles are being investigated as carriers for drugs such as Paclitaxel. The administration of hydrophobic drugs require molecular encapsulation and it is found that nanosized particles are particularly efficient in evading the reticuloendothelial system.


title: Colloidal gold

text: In cancer research, colloidal gold can be used to target tumors and provide detection using SERS (surface enhanced Raman spectroscopy) "in vivo".These gold nanoparticles are surrounded with Raman reporters, which provide light emission that is over 200 times brighter than quantum dots.It was found that the Raman reporters were stabilized when the nanoparticles were encapsulated with a thiol-modified polyethylene glycol coat.This allows for compatibility and circulation "in vivo".To specifically target tumor cells, the polyethylenegylated gold particles are conjugated with an antibody (or an antibody fragment such as scFv), against, e.g. epidermal growth factor receptor, which is sometimes overexpressed in cells of certain cancer types. Using SERS, these pegylated gold nanoparticles can then detect the location of the tumor.


title: Colloidal gold

text: Gold nanoparticles accumulate in tumors, due to the leakiness of tumor vasculature, and can be used as contrast agents for enhanced imaging in a time-resolved optical tomography system using short-pulse lasers for skin cancer detection in mouse model.It is found that intravenously administrated spherical gold nanoparticles broadened the temporal profile of reflected optical signals and enhanced the contrast between surrounding normal tissue and tumors.


title: Colloidal gold

text: Gold nanoparticles have shown potential as intracellular delivery vehicles for siRNA oligonucleotides with maximal therapeutic impact.


title: Colloidal gold

text: Gold nanoparticles show potential as intracellular delivery vehicles for antisense oligonucleotides (single and double stranded DNA) by providing protection against intracellular nucleases and ease of functionalization for selective targeting.


title: Colloidal gold

text: Gold nanorods are being investigated as photothermal agents for in-vivo applications. Gold nanorods are rod-shaped gold nanoparticles whose aspect ratios tune the surface plasmon resonance (SPR) band from the visible to near-infrared wavelength.The total extinction of light at the SPR is made up of both absorption and scattering.For the smaller axial diameter nanorods (~10 nm), absorption dominates, whereas for the larger axial diameter nanorods (>35 nm) scattering can dominate.As a consequence, for in-vivo studies, small diameter gold nanorods are being used as photothermal converters of near-infrared light due to their high absorption cross-sections. Since near-infrared light transmits readily through human skin and tissue, these nanorods can be used as ablation components for cancer, and other targets. When coated with polymers, gold nanorods have been observed to circulate in-vivo with half-lives longer than 6 hours, bodily residence times around 72 hours, and little to no uptake in any internal organs except the liver.


title: Colloidal gold

text: Despite the unquestionable success of gold nanorods as photothermal agents in preclinical research, they have yet to obtain the approval for clinical use because the size is above the renal excretion threshold. In 2019, the first NIR-absorbing plasmonic ultrasmall-in-nano architecture has been reported, and jointly combine: (i) a suitable photothermal conversion for hyperthermia treatments, (ii) the possibility of multiple photothermal treatments and (iii) renal excretion of the building blocks after the therapeutic action.


title: Colloidal gold

text: Considerable interest has been shown in the use of gold and other heavy-atom-containing nanoparticles to enhance the dose delivered to tumors. Since the gold nanoparticles are taken up by the tumors more than the nearby healthy tissue, the dose is selectively enhanced. The biological effectiveness of this type of therapy seems to be due to the local deposition of the radiation dose near the nanoparticles. This mechanism is the same as occurs in heavy ion therapy.


title: Colloidal gold

text: Researchers have developed simple inexpensive methods for on-site detection of hydrogen sulfide present in air based on the antiaggregation of gold nanoparticles (AuNPs). Dissolving into a weak alkaline buffer solution leads to the formation of HS-, which can stabilize AuNPs and ensure they maintain their red color allowing for visual detection of toxic levels of .


title: Colloidal gold

text: Gold nanoparticles are incorporated into biosensors to enhance its stability, sensitivity, and selectivity. Nanoparticle properties such as small size, high surface-to-volume ratio, and high surface energy allow immobilization of large range of biomolecules. Gold nanoparticle, in particular, could also act as "electron wire" to transport electrons and its amplification effect on electromagnetic light allows it to function as signal amplifiers. Main types of gold nanoparticle based biosensors are optical and electrochemical biosensor.


title: Colloidal gold

text: Gold nanoparticles improve the sensitivity of optical sensor by response to the change in local refractive index. The angle of the incidence light for surface plasmon resonance, an interaction between light wave and conducting electrons in metal, changes when other substances are bounded to the metal surface. Because gold is very sensitive to its surroundings' dielectric constant, binding of an analyte would significantly shift gold nanoparticle's SPR and therefore allow more sensitive detection. Gold nanoparticle could also amplify the SPR signal. When the plasmon wave pass through the gold nanoparticle, the charge density in the wave and the electron I the gold interacted and resulted in higher energy response, so called electron coupling. Since the analyte and bio-receptor now bind to the gold, it increases the apparent mass of the analyte and therefore amplified the signal.


title: Colloidal gold

text: These properties had been used to build DNA sensor with 1000-fold sensitive than without the Au NP. Humidity sensor was also built by altering the atom interspacing between molecules with humidity change, the interspacing change would also result in a change of the Au NP's LSPR.


title: Colloidal gold

text: Electrochemical sensor convert biological information into electrical signals that could be detected. The conductivity and biocompatibility of Au NP allow it to act as "electron wire". It transfers electron between the electrode and the active site of the enzyme. It could be accomplished in two ways: attach the Au NP to either the enzyme or the electrode. GNP-glucose oxidase monolayer electrode was constructed use these two methods. The Au NP allowed more freedom in the enzyme's orientation and therefore more sensitive and stable detection. Au NP also acts as immobilization platform for the enzyme. Most biomolecules denatures or lose its activity when interacted with the electrode. The biocompatibility and high surface energy of Au allow it to bind to a large amount of protein without altering its activity and results in a more sensitive sensor. Moreover, Au NP also catalyzes biological reactions. Gold nanoparticle under 2 nm has shown catalytic activity to the oxidation of styrene.


title: Colloidal gold

text: Gold nanoparticles have been coated with peptides and glycans for use in immunological detection methods. The possibility to use glyconanoparticles in ELISA was unexpected, but the method seems to have a high sensitivity and thus offers potential for development of specific assays for diagnostic identification of antibodies in patient sera


title: Colloidal gold

text: Gold nanoparticles capped with organic ligands, such as alkanethiol molecules, can self-assemble into large monolayers (>cmformula_1). The particles are first prepared in organic solvent, such as chloroform or toluene, and are then spread into monolayers either on a liquid surface or on a solid substrate.Such interfacial thin films of nanoparticles have close relationship with Langmuir-Blodgett monolayers made from surfactants.


title: Colloidal gold

text: The mechanical properties of nanoparticle monolayers have been studied extensively. For 5 nm spheres capped with dodecanethiol, the Young's modulus of the monolayer is on the order of GPa. The mechanics of the membranes are guided by strong interactions between ligand shells on adjacent particles. Upon fracture, the films crack perpendicular to the direction of strain at a fracture stress of 11 formula_2 2.6 MPa, comparable to that of cross-linked polymer films. Free-standing nanoparticle membranes exhibit bending rigidity on the order of 10formula_3 eV, higher than what is predicted in theory for continuum plates of the same thickness, due to nonlocal microstructural constraints such as nonlocal coupling of particle rotational degrees of freedom. On the other hand, resistance to bending is found to be greatly reduced in nanoparticle monolayers that are supported at the air/water interface, possibly due to screening of ligand interactions in a wet environment.


title: Colloidal gold

text: In many different types of colloidal gold syntheses, the interface of the nanoparticles can display widely different character – ranging from an interface similar to a self-assembled monolayer to a disordered boundary with no repeating patterns. Beyond the Au-Ligand interface, conjugation of the interfacial ligands with various functional moieties (from small organic molecules to polymers to DNA to RNA) afford colloidal gold much of its vast functionality.


title: Colloidal gold

text: After initial nanoparticle synthesis, colloidal gold ligands are often exchanged with new ligands designed for specific applications. For example, Au NPs produced via the Turkevich-style (or Citrate Reduction) method are readily reacted via ligand exchange reactions, due to the relatively weak binding between the carboxyl groups and the surfaces of the NPs. This ligand exchange can produce conjugation with a number of biomolecules from DNA to RNA to proteins to polymers (such as PEG) to increase biocompatibility and functionality. For example, ligands have been shown to enhance catalytic activity by mediating interactions between adsorbates and the active gold surfaces for specific oxygenation reactions. Ligand exchange can also be used to promote phase transfer of the colloidal particles. Ligand exchange is also possible with alkane thiol-arrested NPs produced from the Brust-type synthesis method, although higher temperatures are needed to promote the rate of the ligand detachment. An alternative method for further functionalization is achieved through the conjugation of the ligands with other molecules, though this method can cause the colloidal stability of the Au NPs to breakdown.


title: Colloidal gold

text: In many cases, as in various high-temperature catalytic applications of Au, the removal of the capping ligands produces more desirable physicochemical properties. The removal of ligands from colloidal gold while maintaining a relatively constant number of Au atoms per Au NP can be difficult due to the tendency for these bare clusters to aggregate. The removal of ligands is partially achievable by simply washing away all excess capping ligands, though this method is ineffective in removing all capping ligand. More often ligand removal achieved under high temperature or light ablation followed by washing. Alternatively, the ligands can be electrochemically etched off.


title: Colloidal gold

text: The precise structure of the ligands on the surface of colloidal gold NPs impact the properties of the colloidal gold particles. Binding conformations and surface packing of the capping ligands at the surface of the colloidal gold NPs tend to differ greatly from bulk surface model adsorption, largely due to the high curvature observed at the nanoparticle surfaces. Thiolate-gold interfaces at the nanoscale have been well-studied and the thiolate ligands are observed to pull Au atoms off of the surface of the particles to for “staple” motifs that have significant Thiyl-Au(0) character. The citrate-gold surface, on the other hand, is relatively less-studied due to the vast number of binding conformations of the citrate to the curved gold surfaces. A study performed in 2014 identified that the most-preferred binding of the citrate involves two carboxylic acids and the hydroxyl group of the citrate binds three surface metal atoms.


title: Colloidal gold

text: As gold nanoparticles (AuNPs) are further investigated for targeted drug delivery in humans, their toxicity needs to be considered. For the most part, it is suggested that AuNPs are biocompatible, but the concentrations at which they become toxic needs to be determined, and if those concentrations fall within the range of used concentrations. Toxicity can be tested "in vitro" and "in vivo". "In vitro" toxicity results can vary depending on the type of the cellular growth media with different protein compositions, the method used to determine cellular toxicity (cell health, cell stress, how many cells are taken into a cell), and the capping ligands in solution. "In vivo" assessments can determine the general health of an organism (abnormal behavior, weight loss, average life span) as well as tissue specific toxicology (kidney, liver, blood) and inflammation and oxidative responses. "In vitro" experiments are more popular than "in vivo" experiments because "in vitro" experiments are more simplistic to perform than "in vivo" experiments.


title: Colloidal gold

text: While AuNPs themselves appear to have low or negligible toxicity, and the literature shows that the toxicity has much more to do with the ligands rather than the particles themselves, the synthesis of them involves chemicals that are hazardous. Sodium borohydride, a harsh reagent, is used to reduce the gold ions to gold metal. The gold ions usually come from chloroauric acid, a potent acid. Because of the high toxicity and hazard of reagents used to synthesize AuNPs, the need for more “green” methods of synthesis arose.


title: Colloidal gold

text: Some of the capping ligands associated with AuNPs can be toxic while others are nontoxic. In gold nanorods (AuNRs), it has been shown that a strong cytotoxicity was associated with CTAB-stabilized AuNRs at low concentration, but it is thought that free CTAB was the culprit in toxicity . Modifications that overcoat these AuNRs reduces this toxicity in human colon cancer cells (HT-29) by preventing CTAB molecules from desorbing from the AuNRs back into the solution.


title: Colloidal gold

text: Ligand toxicity can also be seen in AuNPs. Compared to the 90% toxicity of HAuCl4 at the same concentration, AuNPs with carboxylate termini were shown to be non-toxic. Large AuNPs conjugated with biotin, cysteine, citrate, and glucose were not toxic in human leukemia cells (K562) for concentrations up to 0.25 M. Also, citrate-capped gold nanospheres (AuNSs) have been proven to be compatible with human blood and did not cause platelet aggregation or an immune response. However, citrate-capped gold nanoparticles sizes 8-37 nm were found to be lethally toxic for mice, causing shorter lifespans, severe sickness, loss of appetite and weight, hair discoloration, and damage to the liver, spleen, and lungs; gold nanoparticles accumulated in the spleen and liver after traveling a section of the immune system.


title: Colloidal gold

text: There are mixed-views for polyethylene glycol (PEG)-modified AuNPs. These AuNPs were found to be toxic in mouse liver by injection, causing cell death and minor inflammation. However, AuNPs conjugated with PEG copolymers showed negligible toxicity towards human colon cells (Caco-2).


title: Colloidal gold

text: AuNP toxicity also depends on the overall charge of the ligands. In certain doses, AuNSs that have positively-charged ligands are toxic in monkey kidney cells (Cos-1), human red blood cells, and E. coli because of the AuNSs interaction with the negatively-charged cell membrane; AuNSs with negatively-charged ligands have been found to be nontoxic in these species.


title: Colloidal gold

text: In addition to the previously mentioned "in vivo" and "in vitro" experiments, other similar experiments have been performed. Alkylthiolate-AuNPs with trimethlyammonium ligand termini mediate the translocation of DNA across mammalian cell membranes "in vitro" at a high level, which is detrimental to these cells. Corneal haze in rabbits have been healed "in vivo" by using polyethylemnimine-capped gold nanoparticles that were transfected with a gene that promotes wound healing and inhibits corneal fibrosis.


title: Colloidal gold

text: Toxicity in certain systems can also be dependent on the size of the nanoparticle. AuNSs size 1.4 nm were found to be toxic in human skin cancer cells (SK-Mel-28), human cervical cancer cells (HeLa), mouse fibroblast cells (L929), and mouse macrophages (J774A.1), while 0.8, 1.2, and 1.8 nm sized AuNSs were less toxic by a six-fold amount and 15 nm AuNSs were nontoxic. There is some evidence for AuNP buildup after injection in "in vivo" studies, but this is very size dependent. 1.8 nm AuNPs were found to be almost totally trapped in the lungs of rats. Different sized AuNPs were found to buildup in the blood, brain, stomach, pancreas, kidneys, liver, and spleen.


title: Colloidal gold

text: Biosafety and biokinetics investigations on biodegradable ultrasmall-in-nano architectures have demonstrated that gold nanoparticles are able to avoid metal accumulation in organisms through escaping by the renal pathway.


title: Colloidal gold

text: Generally, gold nanoparticles are produced in a liquid ("liquid chemical methods") by reduction of chloroauric acid ().To prevent the particles from aggregating, stabilizing agents are added.Citrate acts both as the reducing agent and colloidal stabilizer.


title: Colloidal gold

text: They can be functionalized with various organic ligands to create organic-inorganic hybrids with advanced functionality.


title: Colloidal gold

text: This simple method was pioneered by J. Turkevich et al. in 1951 and refined by G. Frens in the 1970s. It produces modestly monodisperse spherical gold nanoparticles of around 10–20 nm in diameter.Larger particles can be produced, but at the cost of monodispersity and shape. In this method, hot chloroauric acid is treated with sodium citrate solution, producing colloidal gold. The Turkevich reaction proceeds via formation of transient gold nanowires. These gold nanowires are responsible for the dark appearance of the reaction solution before it turns ruby-red.


title: Colloidal gold

text: A capping agent is used during nanoparticle synthesis to inhibit particle growth and aggregation. The chemical blocks or reduces reactivity at the periphery of the particle—a good capping agent has a high affinity for the new nuclei. Citrate ions or tannic acid function both as a reducing agent and a capping agent. Less sodium citrate results in larger particles.


title: Colloidal gold

text: This method was discovered by Brust and Schiffrin in the early 1990s, and can be used to produce gold nanoparticles in organic liquids that are normally not miscible with water (like toluene). It involves the reaction of a chlorauric acid solution with tetraoctylammonium bromide (TOAB) solution in toluene and sodium borohydride as an anti-coagulant and a reducing agent, respectively.


title: Colloidal gold

text: Here, the gold nanoparticles will be around 5–6 nm. NaBH is the reducing agent, and TOAB is both the phase transfer catalyst and the stabilizing agent.


title: Colloidal gold

text: TOAB does not bind to the gold nanoparticles particularly strongly, so the solution will aggregate gradually over the course of approximately two weeks. To prevent this, one can add a stronger binding agent, like a thiol (in particular, alkanethiols), which will bind to gold, producing a near-permanent solution. Alkanethiol protected gold nanoparticles can be precipitated and then redissolved. Thiols are better binding agents because there is a strong affinity for the gold-sulfur bonds that form when the two substances react with each other. Tetra-dodecanthiol is a commonly used strong binding agent to synthesize smaller particles.


title: Colloidal gold

text: Some of the phase transfer agent may remain bound to the purified nanoparticles, this may affect physical properties such as solubility. In order to remove as much of this agent as possible, the nanoparticles must be further purified by soxhlet extraction.


title: Colloidal gold

text: This approach, discovered by Perrault and Chan in 2009, uses hydroquinone to reduce HAuCl in an aqueous solution that contains 15 nm gold nanoparticle seeds. This seed-based method of synthesis is similar to that used in photographic film development, in which silver grains within the film grow through addition of reduced silver onto their surface. Likewise, gold nanoparticles can act in conjunction with hydroquinone to catalyze reduction of ionic gold onto their surface. The presence of a stabilizer such as citrate results in controlled deposition of gold atoms onto the particles, and growth. Typically, the nanoparticle seeds are produced using the citrate method. The hydroquinone method complements that of Frens, as it extends the range of monodispersed spherical particle sizes that can be produced. Whereas the Frens method is ideal for particles of 12–20 nm, the hydroquinone method can produce particles of at least 30–300 nm.


title: Colloidal gold

text: This simple method, discovered by Martin and Eah in 2010, generates nearly monodisperse "naked" gold nanoparticles in water. Precisely controlling the reduction stoichiometry by adjusting the ratio of NaBH-NaOH ions to HAuCl-HCl ions within the "sweet zone," along with heating, enables reproducible diameter tuning between 3–6 nm. The aqueous particles are colloidally stable due to their high charge from the excess ions in solution. These particles can be coated with various hydrophilic functionalities, or mixed with hydrophobic ligands for applications in non-polar solvents. In non-polar solvents the nanoparticles remain highly charged, and self-assemble on liquid droplets to form 2D monolayer films of monodisperse nanoparticles.


title: Colloidal gold

text: "Bacillus licheniformis" can be used in synthesis of gold nanocubes with sizes between 10 and 100 nanometres. Gold nanoparticles are usually synthesized at high temperatures in organic solvents or using toxic reagents. The bacteria produce them in much milder conditions.


title: Colloidal gold

text: For particles larger than 30 nm, control of particle size with a low polydispersity of spherical gold nanoparticles remains challenging. In order to provide maximum control on the NP structure, Navarro and co-workers used a modified Turkevitch-Frens procedure using sodium acetylacetonate as the reducing agent and sodium citrate as the stabilizer.


title: Colloidal gold

text: Another method for the experimental generation of gold particles is by sonolysis. The first method of this type was invented by Baigent and Müller. This work pioneered the use of ultrasound to provide the energy for the processes involved and allowed the creation of gold particles with a diameter of under 10 nm. In another method using ultrasound, the reaction of an aqueous solution of HAuCl with glucose, the reducing agents are hydroxyl radicals and sugar pyrolysis radicals (forming at the interfacial region between the collapsing cavities and the bulk water) and the morphology obtained is that of nanoribbons with width 30–50 nm and length of several micrometers. These ribbons are very flexible and can bend with angles larger than 90°. When glucose is replaced by cyclodextrin (a glucose oligomer), only spherical gold particles are obtained, suggesting that glucose is essential in directing the morphology toward a ribbon.


title: Colloidal gold

text: An economical, environmentally benign and fast synthesis methodology for gold nanoparticles using block copolymer has been developed by Sakai et al. In this synthesis methodology, block copolymer plays the dual role of a reducing agent as well as a stabilizing agent. The formation of gold nanoparticles comprises three main steps: reduction of gold salt ion by block copolymers in the solution and formation of gold clusters, adsorption of block copolymers on gold clusters and further reduction of gold salt ions on the surfaces of these gold clusters for the growth of gold particles in steps, and finally its stabilization by block copolymers. But this method usually has a limited-yield (nanoparticle concentration), which does not increase with the increase in the gold salt concentration. Ray et al. improved this synthesis method by enhancing the nanoparticle yield by manyfold at ambient temperature.


title: Colloidal gold

text: Antibiotic functionalized metal nanoparticles have been widely studied as a mode to treat multi-drug resistant bacterial strains. For example, kanamycin capped gold-nanoparticles (Kan-AuPs) showed broad spectrum dose dependent antibacterial activity against both gram positive and gram negative bacterial strains in comparison to kanamycin alone.


title: Positive-strand RNA virus

text: Positive-strand RNA viruses (+ssRNA viruses) are a group of related viruses that have positive-sense, single-stranded genomes made of ribonucleic acid. The positive-sense genome can act as messenger RNA (mRNA) and can be directly translated into viral proteins by the host cell's ribosomes. Positive-strand RNA viruses encode an RNA-dependent RNA polymerase (RdRp) which is used during replication of the genome to synthesize a negative-sense antigenome that is then used as a template to create a new positive-sense viral genome.


title: Positive-strand RNA virus

text: Positive-strand RNA viruses are divided between the phyla "Kitrinoviricota", "Lenarviricota", and "Pisuviricota" (specifically classes "Pisoniviricetes" and "Stelpavirictes") all of which are in the kingdom "Orthornavirae" and realm "Riboviria". They are monophyletic and descended from a common RNA virus ancestor. In the Baltimore classification system, +ssRNA viruses belong to Group IV.


title: Positive-strand RNA virus

text: Positive-sense RNA viruses include pathogens such as the Hepatitis C virus, West Nile virus, dengue virus, and the MERS, SARS, and SARS-CoV-2 coronaviruses, as well as less clinically serious pathogens such as the coronaviruses and rhinoviruses that cause the common cold.


title: Positive-strand RNA virus

text: Positive-strand RNA virus genomes usually contain relatively few genes, usually between three and ten, including an RNA-dependent RNA polymerase. Coronaviruses have the largest known RNA genomes, between 27 and 32 kilobases in length, and likely possess replication proofreading mechanisms in the form of an exoribonuclease within nonstructural protein nsp14.


title: Positive-strand RNA virus

text: Positive-strand RNA viruses have genetic material that can function both as a genome and as messenger RNA; it can be directly translated into protein in the host cell by host ribosomes. The first proteins to be expressed after infection serve genome replication functions; they recruit the positive-strand viral genome to viral replication complexes formed in association with intracellular membranes. These complexes contain proteins of both viral and host cell origin, and may be associated with the membranes of a variety of organelles—often the rough endoplasmic reticulum, but also including membranes derived from mitochondria, vacuoles, the Golgi apparatus, chloroplasts, peroxisomes, plasma membranes, autophagosomal membranes, and novel cytoplasmic compartments.


title: Positive-strand RNA virus

text: The replication of the positive-sense RNA genome proceeds through double-stranded RNA intermediates, and the purpose of replication in these membranous invaginations may be the avoidance of cellular response to the presence of dsRNA. In many cases subgenomic RNAs are also created during replication. After infection, the entirety of the host cell's translation machinery may be diverted to the production of viral proteins as a result of the very high affinity for ribosomes by the viral genome's internal ribosome entry site (IRES) elements; in some viruses, such as poliovirus and rhinoviruses, normal protein synthesis is further disrupted by viral proteases degrading components required to initiate translation of cellular mRNA.


title: Positive-strand RNA virus

text: All positive-strand RNA virus genomes encode RNA-dependent RNA polymerase, a viral protein that synthesizes RNA from an RNA template. Host cell proteins recruited by +ssRNA viruses during replication include RNA-binding proteins, chaperone proteins, and membrane remodeling and lipid synthesis proteins, which collectively participate in exploiting the cell's secretory pathway for viral replication.


title: Positive-strand RNA virus

text: Numerous positive-strand RNA viruses can undergo genetic recombination when at least two viral genomes are present in the same host cell. The capability for recombination among +ssRNA virus pathogens of humans is common. RNA recombination appears to be a major driving force in determining genome architecture and the course of viral evolution among "Picornaviridae" (e.g. poliovirus). In the "Retroviridae" (e.g. HIV), genome damage appears to be avoided during reverse transcription by strand switching, a form of recombination. Recombination occurs in the "Coronaviridae" (e.g. SARS). Recombination in RNA viruses appears to be an adaptation for coping with genome damage. Recombination can also occur infrequently between +ssRNA viruses of the same species but of divergent lineages. The resulting recombinant viruses may sometimes cause an outbreak of infection in humans, as in the case of SARS and MERS.


title: Positive-strand RNA virus

text: Positive-strand RNA viruses are common in plants. In tombusviruses and carmoviruses, RNA recombination occurs frequently during replication. The ability of the RNA-dependent RNA polymerase of these viruses to switch RNA templates suggests a copy choice model of RNA recombination that may be an adaptive mechanism for coping with damage in the viral genome. Other +ssRNA viruses of plants have also been reported to be capable of recombination, such as Brom mosaic bromovirus and Sindbis virus.


title: Positive-strand RNA virus

text: Positive-strand RNA viruses are found in three phyla: "Kitrinoviricota", "Lenarviricota", and "Pisuviricota", each of which are assigned to the kingdom "Orthornavirae" in the realm "Riboviria". In the Baltimore classification system, which groups viruses together based on their manner of mRNA synthesis, +ssRNA viruses are group IV.


title: Positive-strand RNA virus

text: The first +ssRNA phylum is "Kitrinoviricota". The phylum contains what have been referred to as the "alphavirus supergroup" and "flavivirus supergroup" along with various other short-genome viruses. Four classes in the phylum are recognized: "Alsuviricetes", the alphavirus supergroup, which contains a large number of plant viruses and arthropod viruses; "Flasuviricetes", which contains flaviviruses, "Magsaviricetes", which contains nodaviruses and sinhaliviruses; and "Tolucaviricetes", which primarily contains plant viruses.


title: Positive-strand RNA virus

text: "Lenarviricota" is the second +ssRNA phylum. It contains the class "Leviviricetes", which infect prokaryotes, and the apparent descendants of leviviruses, which infect eukaryotes. The phylum is divided into four classes: "Leviviricetes", which contains leviviruses and their relatives, "Amabiliviricetes", which contains narnaviruses and their relatives, "Howeltoviricetes", which contains mitoviruses and their relatives, and "Miaviricetes", which contains botourmiaviruses and their relatives. Based on phylogenetic analysis of RdRp, all other RNA viruses are considered to comprise a sister clade in relation to "Lenarviricota".


title: Positive-strand RNA virus

text: The third phylum that contains +ssRNA viruses is "Pisuviricota", which has been informally called the "picornavirus supergroup". The phylum contains a large assemblage of eukaryotic viruses known to infect animals, plants, fungi, and protists. The phylum contains three classes, two of which contain only +ssRNA viruses: "Pisoniviricetes", which contains nidoviruses, picornaviruses, and sobeliviruses, and "Stelpaviricetes", which contains potyviruses and astroviruses. The third class is "Duplopiviricetes", whose members are double-stranded RNA viruses that are descended from +ssRNA viruses.


title: Thunder Road Films

text: Thunder Road Films is a film and television financing and production company founded by Basil Iwanyk. It is based in Santa Monica, California.


title: Thunder Road Films

text: Producer Basil Iwanyk founded the film and television financing and production company "Thunder Road Films" in the mid 2000s. In January 2012, Peter Lawson left The Weinstein Company to join Thunder Road as a President of Production, and then left in January 2014 for a job as exec VP of production and acquisitions at Open Road Films. As of October 2014, Jonathan Fuhrman is Thunder Road's Executive Vice President (EVP) of Business Affairs.


title: Thunder Road Films

text: In July 2011, after leaving Warner Bros. Television, Thunder Road signed a first-look deal with Sony Pictures Television to develop television projects.


title: Thunder Road Films

text: In May 2013, Thunder Road signed on a deal with Cutting Edge Group to finance the company's film music slate, and from that the first film getting covered was "John Wick".


title: Thunder Road Films

text: In June 2014, Thunder Road and Christian Angermayer's Film House Germany signed a deal to strengthen Thunder Road's financial capability to develop projects. In October 2014, Thunder Road and PalmStar Media signed on a deal in which the Thunder Road would receive $200 million annually to finance five to six $20–50 million budgeted indies within a year. It would also enable the company to co-finance the development and production of larger studio projects.


title: Thunder Road Films

text: In May 2015, Thunder Road renewed its slate agreement with Cutting Edge Group and its investment arm, Conduct, which finances the music budgets of films and television programs in exchange for IP rights to each project's original music.


title: Thunder Road Films

text: In September 2020, Thunder Road teamed with Redbox on joint venture Asbury Park Pictures for the purpose of making 12 films over the next three years. The films we be budgeted in the range of $10 million-$12 million, and be distributed via Redbox kiosks and on demand service.


title: Thunder Road Films

text: Thunder Road has been producing films since 2006, which included 2006's "Firewall" and "We Are Marshall", 2009's "Brooklyn's Finest", 2010's "Clash of the Titans" and "The Town". The company also produced the three installments of The Expendables series. Clash of the Titans' sequel "Wrath of the Titans" was also produced by the company which released in 2012.


title: The Way We Were (song)

text: "The Way We Were" is a song by American singer Barbra Streisand from her fifteenth studio album of the same name. It was released as the album's lead single on September 27, 1973 through Columbia Records. The 7" single was distributed in two different formats, with the standard edition featuring B-side track "What Are You Doing the Rest of Your Life?"; the Mexico release instead included an instrumental B-side. The song was written by Alan Bergman, Marilyn Bergman, and Marvin Hamlisch, while production was solely handled by Marty Paich. "The Way We Were" was specifically produced for the record, in addition to three other tracks, including her then-upcoming single "All in Love Is Fair" (1974).


title: The Way We Were (song)

text: Its lyrics detail the melancholic relationship between the two main characters in the 1973 film of the same name. Its appeal was noted by several music critics, who felt its impact helped revive Streisand's career. The song also won two Academy Awards, which were credited to the songwriters of the track. The single was also a commercial success, topping the charts in both Canada and the United States, while peaking in the top 40 in Australia and the United Kingdom. Additionally, "The Way We Were" was 1974's most successful recording in the United States, where it was placed at number one on the "Billboard" Year-End Hot 100 singles list. It has since been certified Platinum by the RIAA for sales of over one million units. Streisand has also included "The Way We Were" on various compilation albums, with it most recently appearing on 2010's "".


title: The Way We Were (song)

text: Several renditions and versions of the single exist, including one by American singer Andy Williams, who sang it for his thirty-second studio album of the same name in 1974. American band Gladys Knight & the Pips also recorded a cover for "I Feel a Song" (1974), which was commercially successful; it reached number four in the United Kingdom and number 11 in the United States.


title: The Way We Were (song)

text: American composer and producer Marvin Hamlisch created the final melody for "The Way We Were", which initially was a problem between himself and the singer. Streisand had asked Hamlisch to produce a composition in minor key, but he instead wrote it in major key due to his fear of the song's lyrics being revealed too quickly.


title: The Way We Were (song)

text: Shortly following the commercial success of "The Way We Were", Columbia Records began compiling tracks for the singer's then-upcoming fifteenth studio album. Since time was limited, the record consists of several non-album compositions recorded by Streisand, including the aforementioned title and her preceding single "All in Love Is Fair" (1974). According to the liner notes of her 1991 greatest hits album "Just for the Record", "The Way We Were", "All in Love is Fair", "Being at War with Each Other", and "Something So Right" were the only tracks specifically created for the album. The recording and two other variants were also included on the original soundtrack for the film: the original, the instrumental, and the "Finale" version. Individually, it was released as a 7" single in the United States on September 27, 1973 through Columbia Records; the aforementioned edition included the studio version of "The Way We Were", in addition to the B-side single "What Are You Doing the Rest of Your Life?", a cover of the 1969 Michael Dees song. The Japanese release featured the same versions with slightly different durations, while the version intended for the Mexico market includes the instrumental version of "The Way We Were" as the B-side track instead.


title: The Way We Were (song)

text: Hamlisch and Alan and Marilyn Bergman wrote "The Way We Were" while Marty Paich handled its production. In particular, the lyrics detail the personal life of Katie Morosky, the character she portrays in the film. Specifically, her troubling relationship with Robert Redford's Hubbell Gardiner is explained, "Memories light the corners of my mind / Misty watercolor memories of the way we were" and "Memories may be beautiful and yet". Streisand sings, "What's too painful to remember / We quickly choose to forget", where she longs for nostalgia, which "Rolling Stone"s Stephen Holden described as an implication that "resonate[s] in the current social malaise". In the beginning of what seems to be a bridge, she whispers, "If we had the chance to do it all again / Tell me would we? Could we?".


title: The Way We Were (song)

text: "The Way We Were" received significant success after its original release in North America; Jon Landau of "Rolling Stone" claimed that its impact proved worthy enough to revive her career as a musical artist. However, he was more critical of the singer "ignor[ing] the line-by-line variations in [the] song's meaning". Nevertheless, the mass appeal of the single was labeled by Turner Classic Movies's Andrea Passafiume as "one of the most recognizable songs in the world". Hamlisch and the Bergmans won the Academy Award for Best Original Song at the 46th Academy Awards; the former musician also won the Oscar for Best Original Score for the film. The tune also won the Golden Globe Award for Best Original Song in 1974 and the Grammy Award for Song of the Year in 1975. According to the National Endowment for the Arts and Recording Industry Association of America (RIAA) in their list of the top 365 "Songs of the Century", the single was placed at number 298.


title: The Way We Were (song)

text: In the United States, "The Way We Were" debuted at number 92 on the "Billboard" Hot 100 for the week ending November 24, 1973, where it served as the issue's seventh-highest debut. After steadily climbing the list for ten consecutive weeks, it topped the chart on February 2, 1974, where it knocked Ringo Starr's version of "You're Sixteen" (1973) from the highest spot. After being temporarily displaced by The Love Unlimited Orchestra's debut single "Love's Theme", Streisand reclaimed the number one rank for two more weeks beginning February 16 of the same year. "The Way We Were" departed "Billboard"s Hot 100 on April 27 at the position of number 53; in total, it spent 23 consecutive weeks among the chart's ranking. On the "Billboard" Year-End Hot 100 singles of 1974 list, the single also topped the chart on the list of the year's 100 highest-ranking songs. On August 19, 1997, in addition to several of Streisand's recordings, "The Way We Were" was certified Platinum in the United States by the RIAA for sales exceeding one million copies. On the "Billboard" Adult Contemporary chart, where it was then referred to as the Easy Listening chart, it reached the number one spot on January 12, 1974 and held that position for two weeks.


title: The Way We Were (song)

text: Outside of Streisand's native country, the single found similar commercial success. In Canada, "The Way We Were" entered the chart compiled by "RPM" at number 45, where it was the week's third-highest debut. On its seventh week, it reached the top position that was previously held by Terry Jacks' cover of "Seasons in the Sun" (1973). It spent a total of 13 weeks in Canada before departing at its position at number 58. It also topped the Adult Contemporary chart in its 11th week, also in 1974. In their year-end chart, "The Way We Were" was ranked as Canada's eighth best-selling single of 1974. In the final year of Australia's chart compiled by "Go-Set", Streisand's recording peaked at number six. It also reached its peak position in the United Kingdom at number 31 for the week of March 30, 1974.


title: The Way We Were (song)

text: Streisand has performed "The Way We Were" on numerous occasions and is often considered to be one of her signature songs. On her third live album, "One Voice" (1986), the single was included alongside a live video of the singer performing it. In September 1994, Streisand released "The Concert", which also included a live rendition of "The Way We Were" as performed at the Madison Square Garden in Manhattan. At a series of live concerts in 1999 and 2000 in Las Vegas, the singer sang several songs from her catalog and was billed as one of her final live performances; the entirety of the event was then included on "" (2000), including the "Introduction" segment which featured "The Way We Were" in addition to "You'll Never Know", "Something's Coming", and a live interview with actress Shirley MacLaine. The single was also placed on "Live in Concert 2006" (2006) and "Back to Brooklyn" (2013), with its appearance on the latter consisting of a medley of both "The Way We Were" and "Through the Eyes of Love".


title: The Way We Were (song)

text: Several renditions of "The Way We Were" have been released since its initial distribution in 1973. American singer Andy Williams recorded a cover of the track for his 1974 and thirty-second studio album of the same name. AllMusic's William Ruhlmann was divided on Williams' interpretation and claimed that fans of Streisand's version would not be interested in this one. However, Mike Parker from the "Daily Express" considered his version and the album as a whole as a classic. American actress and singer Doris Day performed the song in a CBS special, "Doris Day Today", in 1975. Bing Crosby recorded the song for his album "Feels Good, Feels Right" in 1976. He also sang it at his London Palladium concerts that year and in 1977. Dorothy Squires included it for her 1978 LP called "Rain Rain Go Away" which was produced by Norman Newell. In 2008, the singer-songwriter Beyoncé, sang a rendition of the song in front of Streisand herself at the 2008 Kennedy Center Honors. In 2018, the group Il Divo included the translated version "Toi et Moi" on their album "Timeless." The song was sung twice on "Angel", firstly by Mercedes McNab as Harmony Kendall and later by Andy Hallett as Lorne.


title: The Way We Were (song)

text: In 2014, Streisand re-recorded the track with Lionel Richie for her thirty-fourth studio album, "Partners" (2014). Walter Afanasieff's contributions and added background vocals to the aforementioned edition were acclaimed by "Los Angeles Times" Mikael Wood, who described the composition as a "fluttering" one. "The Way We Were" has also been selected for inclusion on several of Streisand's compilation albums, including "Barbra Streisand's Greatest Hits Vol. 2" (1978), "Memories" (1981), "Just for the Record" (1991), "The Essential Barbra Streisand" (2002), and "" (2010).


title: The Way We Were (song)

text: American R&B band Gladys Knight & the Pips recorded a cover of "The Way We Were" as part of a blend with the song "Try to Remember", released on their 1974 studio album "I Feel a Song". The cover/blend was released by Buddah Records on March 14, 1975 in a 7" format, paired with the B-side singles "Love Finds Its Own Way" and "The Need to Be". Due to the inclusion of "Try to Remember", the song features additional writing by Tom Jones and Harvey Schmidt. Alex Henderson from AllMusic was surprised regarding their version, calling it an "unlikely remake". He further critiqued Knight's "ironic" spoken monologue on the track by assuming she's "reflecting on the nostalgia that seems to be human nature". However, Rashod Ollison from "The Virginian-Pilot" declared it a "stirring remake" and liked the track's live orchestra. He further lauded the B-side track "The Need to Be" for being a "deeply soulful declaration of independence". Knight's rendition of "The Way We Were" was sampled in 1993 for "Can It Be All So Simple" by the Wu-Tang Clan.


title: The Way We Were (song)

text: On the United States' "Billboard" Hot 100, "The Way We Were" reached its highest position of number 11 on August 2, 1975. It spent a total of 17 weeks charting before decreasing weekly until meeting its final position at number 57 for the week ending August 16, 1975. In Canada, it peaked at number 29 on the list compiled by "RPM". It also entered the Adult Contemporary charts in both the United States and Canada, ranking at numbers two and three, respectively. In the United Kingdom, the Gladys Knight & the Pips version was more successful than Streisand's. It peaked at number four in that country, becoming their first top ten single; it would tie with their 1977 single "Baby, Don't Change Your Mind" as their highest-peaking track.


title: Forward contract

text: In finance, a forward contract or simply a forward is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on at the time of conclusion of the contract, making it a type of derivative instrument. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the "delivery price", which is equal to the forward price at the time the contract is entered into.


title: Forward contract

text: The price of the underlying instrument, in whatever form, is paid before control of the instrument changes. This is one of the many forms of buy/sell orders where the time and date of trade is not the same as the value date where the securities themselves are exchanged. Forwards, like other derivative securities, can be used to hedge risk (typically currency or exchange rate risk), as a means of speculation, or to allow a party to take advantage of a quality of the underlying instrument which is time-sensitive.


title: Forward contract

text: The value of a forward position "at maturity" depends on the relationship between the delivery price (formula_1) and the underlying price (formula_2) at that time.


title: Forward contract

text: Since the final value (at maturity) of a forward position depends on the spot price which will then be prevailing, this contract can be viewed, from a purely financial point of view, as ""a bet on the future spot price""


title: Forward contract

text: Suppose that Bob wants to buy a house a year from now. At the same time, suppose that Alice currently owns a house that she wishes to sell a year from now. Both parties could enter into a forward contract with each other. Suppose that they both agree on the sale price in one year's time of (more below on why the sale price should be this amount). Alice and Bob have entered into a forward contract. Bob, because he is buying the underlying, is said to have entered a long forward contract. Conversely, Alice will have the short forward contract.


title: Forward contract

text: At the end of one year, suppose that the current market valuation of Alice's house is . Then, because Alice is obliged to sell to Bob for only , Bob will make a profit of . To see why this is so, one needs only to recognize that Bob can buy from Alice for and immediately sell to the market for . Bob has made the difference in profit. In contrast, Alice has made a potential loss of , and an actual profit of .


title: Forward contract

text: The similar situation works among currency forwards, in which one party opens a forward contract to buy or sell a currency (e.g. a contract to buy Canadian dollars) to expire/settle at a future date, as they do not wish to be exposed to exchange rate/currency risk over a period of time. As the exchange rate between U.S. dollars and Canadian dollars fluctuates between the trade date and the earlier of the date at which the contract is closed or the expiration date, one party gains and the counterparty loses as one currency strengthens against the other. Sometimes, the buy forward is opened because the investor will actually need Canadian dollars at a future date such as to pay a debt owed that is denominated in Canadian dollars. Other times, the party opening a forward does so, not because they need Canadian dollars nor because they are hedging currency risk, but because they are speculating on the currency, expecting the exchange rate to move favorably to generate a gain on closing the contract.


title: Forward contract

text: In a currency forward, the notional amounts of currencies are specified (ex: a contract to buy million Canadian dollars equivalent to, say at the current rate—these two amounts are called the notional amount(s)). While the notional amount or reference amount may be a large number, the cost or margin requirement to command or open such a contract is considerably less than that amount, which refers to the leverage created, which is typical in derivative contracts.


title: Forward contract

text: Continuing on the example above, suppose now that the initial price of Alice's house is and that Bob enters into a forward contract to buy the house one year from today. But since Alice knows that she can immediately sell for and place the proceeds in the bank, she wants to be compensated for the delayed sale. Suppose that the risk free rate of return R (the bank rate) for one year is 4%. Then the money in the bank would grow to , risk free. So Alice would want at least one year from now for the contract to be worthwhile for her – the opportunity cost will be covered.


title: Forward contract

text: For liquid assets ("tradeables"), spot–forward parity provides the link between the spot market and the forward market. It describes the relationship between the spot and forward price of the underlying asset in a forward contract. While the overall effect can be described as the "cost of carry", this effect can be broken down into different components, specifically whether the asset:


title: Forward contract

text: For an asset that provides no income, the relationship between the current forward (formula_5) and spot (formula_6) prices is


title: Forward contract

text: where formula_8 is the continuously compounded risk free rate of return, and "T" is the time to maturity. The intuition behind this result is that given you want to own the asset at time "T", there should be no difference in a perfect capital market between buying the asset today and holding it and buying the forward contract and taking delivery. Thus, both approaches must cost the same in present value terms. For an arbitrage proof of why this is the case, see Rational pricing below.


title: Forward contract

text: where formula_11 the present value of the discrete income at time formula_12, and formula_13 is the continuously compounded dividend yield over the life of the contract. The intuition is that when an asset pays income, there is a benefit to holding the asset rather than the forward because you get to receive this income. Hence the income (formula_14 or formula_15) must be subtracted to reflect this benefit. An example of an asset which pays discrete income might be a stock, and an example of an asset which pays a continuous yield might be a foreign currency or a stock index.


title: Forward contract

text: For investment assets which are commodities, such as gold and silver, storage costs must also be considered. Storage costs can be treated as 'negative income', and like income can be discrete or continuous. Hence with storage costs, the relationship becomes:


title: Forward contract

text: where formula_18 the present value of the discrete storage cost at time formula_12, and formula_20 is the continuously compounded storage cost where it is proportional to the price of the commodity, and is hence a 'negative yield'. The intuition here is that because storage costs make the final price higher, we have to add them to the spot price.


title: Forward contract

text: Consumption assets are typically raw material commodities which are used as a source of energy or in a production process, for example crude oil or iron ore. Users of these consumption commodities may feel that there is a benefit from physically holding the asset in inventory as opposed to holding a forward on the asset. These benefits include the ability to "profit from" (hedge against) temporary shortages and the ability to keep a production process running, and are referred to as the "convenience yield". Thus, for consumption assets, the spot-forward relationship is:


title: Forward contract

text: where formula_23 is the convenience yield over the life of the contract. Since the convenience yield provides a benefit to the holder of the asset but not the holder of the forward, it can be modelled as a type of 'dividend yield'. However, it is important to note that the convenience yield is a non cash item, but rather reflects the market's expectations concerning future availability of the commodity. If users have low inventories of the commodity, this implies a greater chance of shortage, which means a higher convenience yield. The opposite is true when high inventories exist.


title: Forward contract

text: The relationship between the spot and forward price of an asset reflects the net cost of holding (or carrying) that asset relative to holding the forward. Thus, all of the costs and benefits above can be summarised as the "cost of carry", formula_24. Hence,


title: Forward contract

text: The market's opinion about what the spot price of an asset will be in the future is the "expected future spot price". Hence, a key question is whether or not the current forward price actually predicts the respective spot price in the future. There are a number of different hypotheses which try to explain the relationship between the current forward price, formula_27 and the expected future spot price, formula_28.


title: Forward contract

text: The economists John Maynard Keynes and John Hicks argued that in general, the natural hedgers of a commodity are those who wish to sell the commodity at a future point in time. Thus, hedgers will collectively hold a net short position in the forward market. The other side of these contracts are held by speculators, who must therefore hold a net long position. Hedgers are interested in reducing risk, and thus will accept losing money on their forward contracts. Speculators on the other hand, are interested in making a profit, and will hence only enter the contracts if they "expect" to make money. Thus, if speculators are holding a net long position, it must be the case that the expected future spot price is greater than the forward price.


title: Forward contract

text: This market situation, where formula_33, is referred to as normal backwardation. Forward/futures prices converge with the spot price at maturity, as can be seen from the previous relationships by letting T go to 0 (see also basis); then normal backwardation implies that futures prices for a certain maturity are increasing over time. The opposite situation, where formula_36, is referred to as contango. Likewise, contango implies that futures prices for a certain maturity are falling over time.


title: Forward contract

text: Forward contracts are very similar to futures contracts, except they are not exchange-traded, or defined on standardized assets. Forwards also typically have no interim partial settlements or "true-ups" in margin requirements like futures, that is the parties do not exchange additional property securing the party at gain and the entire unrealized gain or loss builds up while the contract is open. Therefore forward contracts have a significant counterparty risk which is also the reason why they are not readily available to retail investors. However, being traded over the counter (OTC), forward contracts specification can be customized and may include mark-to-market and daily margin calls.


title: Forward contract

text: Having no upfront cashflows is one of the advantages of a forward contract compared to its futures counterpart. Especially when the forward contract is denominated in a foreign currency, not having to post (or receive) daily settlements simplifies cashflow management.


title: Forward contract

text: Compared to the futures markets it is very difficult to close out one's position, that is to rescind the forward contract. For instance while being long in a forward contract, entering short into another forward contract might cancel out delivery obligations but adds to credit risk exposure as there are now three parties involved. Closing out a contract almost always involves reaching out to the counterparty.


title: Forward contract

text: Compared to their futures counterparts, forwards (especially Forward Rate Agreements) need convexity adjustments, that is a drift term that accounts for future rate changes. In futures contracts, this risk remains constant whereas a forward contract's risk changes when rates change.


title: Forward contract

text: Outright prices, as opposed to premium points or forward points, are quoted in absolute price units. Outrights are used in markets where there is no (unitary) spot price or rate for reference, or where the spot price (rate) is not easily accessible.


title: Forward contract

text: Conversely, in markets with easily accessible spot prices or basis rates, in particular the Foreign exchange market and OIS market, forwards are usually quoted using premium points or forward points. That is using the spot price or basis rate as reference forwards are quoted as the difference in pips between the outright price and the spot price for FX, or the difference in basis points between the forward rate and the basis rate for interest rate swaps and forward rate agreements.


title: Forward contract

text: Note: The term "outright" is used in the futures markets in a similar way but is contrasted with futures spreads instead of premium points, which is more than just a quoting convention, and in particular involves the simultaneous transaction in two outright futures.


title: Forward contract

text: If formula_37 is the spot price of an asset at time formula_38, and formula_8 is the continuously compounded rate, then the forward price at a future time formula_40 must satisfy formula_41.


title: Forward contract

text: Case 1: Suppose that formula_42. Then an investor can execute the following trades at time formula_38:


title: Forward contract

text: At time formula_40 the investor can reverse the trades that were executed at time formula_38. Specifically, and mirroring the trades 1., 2. and 3. the investor


title: Forward contract

text: The sum of the inflows in 1.' and 2.' equals formula_53, which by hypothesis, is positive. This is an arbitrage profit. Consequently, and assuming that the non-arbitrage condition holds, we have a contradiction. This is called a cash and carry arbitrage because you "carry" the asset until maturity.


title: Forward contract

text: Case 2: Suppose that formula_54. Then an investor can do the reverse of what he has done above in case 1. This means selling one unit of the asset, investing this money into a bank account and entering a long forward contract costing 0.


title: Forward contract

text: Note: if you look at the convenience yield page, you will see that if there are finite assets/inventory, the reverse cash and carry arbitrage is not always possible. It would depend on the elasticity of demand for forward contracts and such like.


title: Forward contract

text: Suppose that formula_55 is the time value of cash flows "X" at the contract expiration time formula_40. The forward price is then given by the formula:


title: Forward contract

text: If these price relationships do not hold, there is an arbitrage opportunity for a riskless profit similar to that discussed above. One implication of this is that the presence of a forward market will force spot prices to reflect current expectations of future prices. As a result, the forward price for nonperishable commodities, securities or currency is no more a predictor of future price than the spot price is - the relationship between forward and spot prices is driven by interest rates. For perishable commodities, arbitrage does not have this


title: Forward contract

text: Allaz and Vila (1993) suggest that there is also a strategic reason (in an imperfect competitive environment) for the existence of forward trading, that is, forward trading can be used even in a world without uncertainty. This is due to firms having Stackelberg incentives to anticipate their production through forward contracts.


title: Dimension (vector space)

text: In mathematics, the dimension of a vector space "V" is the cardinality (i.e., the number of vectors) of a basis of "V" over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension.


title: Dimension (vector space)

text: For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. We say formula_1 is ' if the dimension of formula_1 is finite, and ' if its dimension is infinite.


title: Dimension (vector space)

text: The dimension of the vector space formula_1 over the field formula_4 can be written as formula_5 or as formula_6 read "dimension of formula_1 over formula_4". When formula_4 can be inferred from context, formula_10 is typically written.


title: Dimension (vector space)

text: as a standard basis, and therefore formula_13 More generally, formula_14 and even more generally, formula_15 for any field formula_16


title: Dimension (vector space)

text: The complex numbers formula_17 are both a real and complex vector space; we have formula_18 and formula_19 So the dimension depends on the base field.


title: Dimension (vector space)

text: The only vector space with dimension formula_20 is formula_21 the vector space consisting only of its zero element.


title: Dimension (vector space)

text: To show that two finite-dimensional vector spaces are equal, the following criterion can be used: if formula_1 is a finite-dimensional vector space and formula_22 is a linear subspace of formula_1 with formula_28 then formula_29


title: Dimension (vector space)

text: The space formula_30 has the standard basis formula_31 where formula_32 is the formula_33-th column of the corresponding identity matrix. Therefore, formula_30 has dimension formula_35


title: Dimension (vector space)

text: Any two finite dimensional vector spaces over formula_4 with the same dimension are isomorphic. Any bijective map between their bases can be uniquely extended to a bijective linear map between the vector spaces. If formula_37 is some set, a vector space with dimension formula_38 over formula_4 can be constructed as follows: take the set formula_40 of all functions formula_41 such that formula_42 for all but finitely many formula_43 in formula_44 These functions can be added and multiplied with elements of formula_4 to obtain the desired formula_4-vector space.


title: Dimension (vector space)

text: If formula_47 is a field extension, then formula_4 is in particular a vector space over formula_49 Furthermore, every formula_4-vector space formula_1 is also a formula_52-vector space. The dimensions are related by the formula


title: Dimension (vector space)

text: In particular, every complex vector space of dimension formula_54 is a real vector space of dimension formula_55


title: Dimension (vector space)

text: Some formulae relate the dimension of a vector space with the cardinality of the base field and the cardinality of the space itself.


title: Dimension (vector space)

text: If formula_1 is a vector space over a field formula_4 then and if the dimension of formula_1 is denoted by formula_59 then:


title: Dimension (vector space)

text: A vector space can be seen as a particular case of a matroid, and in the latter there is a well-defined notion of dimension. The length of a module and the rank of an abelian group both have several properties similar to the dimension of vector spaces.


title: Dimension (vector space)

text: The Krull dimension of a commutative ring, named after Wolfgang Krull (1899–1971), is defined to be the maximal number of strict inclusions in an increasing chain of prime ideals in the ring.


title: Dimension (vector space)

text: The dimension of a vector space may alternatively be characterized as the trace of the identity operator. For instance,


title: Dimension (vector space)

text: Firstly, it allows for a definition of a notion of dimension when one has a trace but no natural sense of basis. For example, one may have an algebra formula_65 with maps formula_66 (the inclusion of scalars, called the "unit") and a map formula_67 (corresponding to trace, called the "counit"). The composition formula_68 is a scalar (being a linear operator on a 1-dimensional space) corresponds to "trace of identity", and gives a notion of dimension for an abstract algebra. In practice, in bialgebras, this map is required to be the identity, which can be obtained by normalizing the counit by dividing by dimension (formula_69), so in these cases the normalizing constant corresponds to dimension.


title: Dimension (vector space)

text: Alternatively, it may be possible to take the trace of operators on an infinite-dimensional space; in this case a (finite) trace is defined, even though no (finite) dimension exists, and gives a notion of "dimension of the operator". These fall under the rubric of "trace class operators" on a Hilbert space, or more generally nuclear operators on a Banach space.


title: Dimension (vector space)

text: A subtler generalization is to consider the trace of a "family" of operators as a kind of "twisted" dimension. This occurs significantly in representation theory, where the character of a representation is the trace of the representation, hence a scalar-valued function on a group formula_70 whose value on the identity formula_71 is the dimension of the representation, as a representation sends the identity in the group to the identity matrix: formula_72 The other values formula_73 of the character can be viewed as "twisted" dimensions, and find analogs or generalizations of statements about dimensions to statements about characters or representations. A sophisticated example of this occurs in the theory of monstrous moonshine: the formula_74-invariant is the graded dimension of an infinite-dimensional graded representation of the monster group, and replacing the dimension with the character gives the McKay–Thompson series for each element of the Monster group.


title: Schistocyte

text: A schistocyte or schizocyte (from Greek for "divided" and for "hollow" or "cell") is a fragmented part of a red blood cell. Schistocytes are typically irregularly shaped, jagged, and have two pointed ends.


title: Schistocyte

text: Several microangiopathic diseases, including disseminated intravascular coagulation and thrombotic microangiopathies, generate fibrin strands that sever red blood cells as they try to move past a thrombus, creating schistocytes.


title: Schistocyte

text: Schistocytes are often seen in patients with hemolytic anemia. They are frequently a consequence of mechanical artificial heart valves, hemolytic uremic syndrome, and thrombotic thrombocytopenic purpura, among other causes. Excessive schistocytes present in blood can be a sign of microangiopathic hemolytic anemia (MAHA).