title: Western Ghats

text: The area is ecologically sensitive to development and was declared an ecological hotspot in 1988 through the efforts of ecologist Norman Myers. The area covers five percent of India's land; 27% of all species of higher plants in India (4,000 of 15,000 species) are found here and 1,800 of these are endemic to the region. The range is home to at least 84 amphibian species, 16 bird species, seven mammals, and 1,600 flowering plants which are not found elsewhere in the world. The Government of India has established many protected areas including 2 biosphere reserves, 13 national parks to restrict human access, several wildlife sanctuaries to protect specific endangered species and many reserve forests, which are all managed by the forest departments of their respective state to preserve some of the ecoregions still undeveloped. The Nilgiri Biosphere Reserve, comprising of the evergreen forests of Nagarahole and deciduous forests of Bandipur in Karnataka, adjoining regions of Wayanad-Mukurthi in Kerala and Mudumalai National Park-Sathyamangalam in Tamil Nadu, forms the largest contiguous protected area in the Western Ghats. Silent Valley in Kerala is among the last tracts of virgin tropical evergreen forest in India.


title: Western Ghats

text: In August 2011, the Western Ghats Ecology Expert Panel (WGEEP) designated the entire Western Ghats as an Ecologically Sensitive Area (ESA) and assigned three levels of Ecological Sensitivity to its different regions. The panel, headed by ecologist Madhav Gadgil, was appointed by the Union Ministry of Environment and Forests to assess the biodiversity and environmental issues of the Western Ghats. The Gadgil Committee and its successor, the Kasturirangan Committee, recommended suggestions to protect the Western Ghats. The Gadgil report was criticised as being too environment-friendly and the Kasturirangan report was labelled as being anti-environmental.


title: Western Ghats

text: In 2006, India applied to the UNESCO Man and the Biosphere Programme (MAB) for the Western Ghats to be listed as a protected World Heritage Site. In 2012, the following places were declared as World Heritage Sites:


title: Western Ghats

text: The Western Ghats are home to thousands of animal species including at least 325 globally threatened species.


title: Western Ghats

text: There are at least 139 mammal species. Of the 16 endemic mammals, 13 are threatened. Among the 32 threatened species are the tiger, leopard, lion-tailed macaque, Nilgiri tahr, Asian elephant, Nilgiri langur and gaur. The endemic Malabar large-spotted civet is estimated to number fewer than 250 mature individuals, with no sub-population greater than 50 individuals.


title: Western Ghats

text: The Nilgiri marten, brown palm civet, stripe-necked mongoose, Indian brown mongoose, small Indian civet and leopard cat are the small carnivores living in the forests of the Western Ghats.


title: Western Ghats

text: The hill ranges constitute important wildlife corridors and form an important part of Project Elephant and Project Tiger reserves. The largest tiger population lives in the Western Ghats, where there are seven populations with an estimated population size of 1200 individuals occupying of forest in three major landscape units spread across Karnataka, Tamil Nadu and Kerala. The Western Ghats ecoregion has the largest Indian elephant population in the wild with an estimated 11,000 individuals across eight distinct populations. The endemic Nilgiri tahr, which was on the brink of extinction, has recovered and has an estimated 3,122 individuals in the wild. About 3500 lion-tailed macaques live scattered over several areas in the Western Ghats.


title: Western Ghats

text: At least 227 species of reptiles are found in the Western Ghats. The major population of the snake family Uropeltidae is restricted to the region. Several endemic reptile genera and species occur here, including the cane turtle "Vijayachelys silvatica", lizards like "Salea, Ristella, Kaestlea", and snakes such as "Melanophidium, Plectrurus, Teretrurus, Platyplectrurus, Xylophis", and "Rhabdops". Species-level endemism is much higher and is common to almost all genera present here. Some enigmatic endemic reptiles include venomous snakes such as the striped coral snake, the Malabar pit viper, the large-scaled pitviper and the horseshoe pitviper. The region has a significant population of the mugger crocodile.


title: Western Ghats

text: The amphibians of the Western Ghats are diverse and unique, with more than 80% of the 179 amphibian species being endemic to the rainforests of the mountains. The purple frog was discovered in 2003. Several species of frogs, namely of the genera "Micrixalus, Indirana", and "Nyctibatrachus", are endemic to this region. Endemic genera include the toads "Pedostibes, Ghatophryne", and "Xanthophryne"; arboreal frogs such as "Ghatixalus, Mercurana", and "Beddomixalus"; and microhylids like "Melanobatrachus". New frog species were described from the Western Ghats in 2005, and more recently a new species, monotypic in its genus "Mysticellus", was discovered.


title: Western Ghats

text: The region is also home to many caecilian species. There are many species of amphibians which are yet to be discovered at every elevation of the Western Ghats.


title: Western Ghats

text: , 288 freshwater fish species were listed for the Western Ghats, including 35 also known from brackish or marine water. Several new species have been described from the region since then (e.g., "Dario urops" and "S. sharavathiensis"). There are 118 endemic species, including 13 genera entirely restricted to the Western Ghats ("Betadevario", "Dayella", "Haludaria", "Horabagrus", "Horalabiosa", "Hypselobarbus", "Indoreonectes", "Lepidopygopsis", "Longischistura", "Mesonoemacheilus", "Parapsilorhynchus", "Rohtee" and "Travancoria").


title: Western Ghats

text: There is a higher fish richness in the southern part of the Western Ghats than in the northern, and the highest is in the Chalakudy River, which alone holds 98 species. Other rivers with high species numbers include the Periyar, Bharatapuzha, Pamba and Chaliyar, as well as upstream tributaries of the Kaveri, Pambar, Bhavani and Krishna rivers. The most species rich families are the Cyprinids (72 species), hillstream loaches (34 species; including stone loaches, now regarded a separate family), Bagrid catfishes (19 species) and Sisorid catfishes (12 species). The region is home to several brilliantly coloured ornamental fishes like the Denison (or red line torpedo) barb, melon barb, several species of "Dawkinsia" barbs, zebra loach, "Horabagrus" catfish, dwarf pufferfish and dwarf Malabar pufferfish. The rivers are also home to "Osteobrama bakeri", and larger species such as the Malabar snakehead and Malabar mahseer. A few are adapted to an underground life, including some "Rakthamichthys" swampeels, and the catfish "Horaglanis" and "Kryptoglanis".


title: Western Ghats

text: According to the IUCN, 97 freshwater fish species from the Western Ghats were considered threatened in 2011, including 12 critically endangered, 54 endangered and 31 vulnerable. All but one ("Tor khudree") of these are endemic to the Western Ghats. An additional 26 species from the region are considered data deficient (their status is unclear at present). The primary threats are from habitat loss, but also from overexploitation and introduced species.


title: Western Ghats

text: There are at least 508 bird species. Most of Karnataka's five hundred species of birds are from the Western Ghats region. There are at least 16 species of birds endemic to the Western Ghats including the endangered rufous-breasted laughingthrush, the vulnerable Nilgiri wood-pigeon, white-bellied shortwing and broad-tailed grassbird, the near threatened grey-breasted laughingthrush, black-and-rufous flycatcher, Nilgiri flycatcher, and Nilgiri pipit, and the least concern Malabar (blue-winged) parakeet, Malabar grey hornbill, white-bellied treepie, grey-headed bulbul, rufous babbler, Wayanad laughingthrush, white-bellied blue-flycatcher and the crimson-backed sunbird.


title: Western Ghats

text: There are roughly 6,000 insect species. Of 334 Western Ghats butterfly species, 316 species have been reported from the Nilgiri Biosphere Reserve. The Western Ghats are home to 174 species of odonates (107 dragonflies and 67 damselflies), including 69 endemics. Most of the endemic odonate are closely associated with rivers and streams, while the non-endemics typically are generalists.


title: Western Ghats

text: Seasonal rainfall patterns of the Western Ghats necessitate a period of dormancy for its land snails, resulting in their high abundance and diversity including at least 258 species of gastropods from 57 genera and 24 families. A total of 77 species of freshwater molluscs (52 gastropods and 25 bivalves) have been recorded from the Western Ghats, but the actual number is likely higher. This include 28 endemics. Among the threatened freshwater molluscs are the mussels "Pseudomulleria dalyi", which is a Gondwanan relict, and the snail "Cremnoconchus", which is restricted to the spray zone of waterfalls. According to the IUCN, 4 species of freshwater molluscs are considered endangered and 3 are vulnerable. An additional 19 species are considered data deficient.


title: Western Ghats

text: The dominant forest type here is tropical rainforest. Montane forests, tropical dry forests and tropical moist forests are also found here. Of the 7,402 species of flowering plants occurring in the Western Ghats, 5,588 species are native or indigenous and 376 are exotics naturalised; 1,438 species are cultivated or planted as ornamentals. Among the indigenous species, 2,253 species are endemic to India and of them, 1,273 species are exclusively confined to the Western Ghats. Apart from 593 confirmed subspecies and varieties; 66 species, 5 subspecies and 14 varieties of doubtful occurrence are also reported, amounting to 8,080 taxa of flowering plants.


title: Western Ghats

text: Various plant species are endemic to the Western Ghats, including the palm tree "Bentinckia condapanna" and the flower "Strobilanthes kunthiana". A number of plant species are also Critically Endangered, such as "Dipterocarpus bourdillonii" and "Phyllanthus anamalayanus".


title: Western Ghats

text: "Echinops sahyadricus" is endemic to the mountains, and the specific epithet "sahyadricus" is refers to them.


title: Western Ghats

text: The Western Ghats face a lot of issues. Poaching, deforestation, forest fires, extra hunting and dangers to native tribes are the main threats. Despite the 1972 Indian law of that banned poaching, people still tend to illegally hunt down animals such as tigers, elephants and chital for skin, fur or tusks. Forests here are being destroyed for farming or livestock. Animals that eat livestock are also being killed by farmers. Forest fires take place annually during the dry summer season, especially in the Nagarhole-Bandipur-Wayanad-Mudumalai-Satyamangalam-BRT block which has the most biodiverse locations in the Western Ghats with the largest populations of tigers and elephants residing there.


title: Western Ghats

text: Native tribes of the Western Ghats are being evicted from their homelands. This results in degradation of the tribal culture. The rich biodiversity in both flora and fauna have made the Western Ghats a target for many corporate companies to gain resources. This however is checked by the Government of India and the State Governments to protect the Western Ghats.


title: Voltage

text: Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named "volt". In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The old SI definition for "volt" used power and current; starting in 1990, the quantum Hall and Josephson effect were used, and recently (2019) fundamental physical constants have been introduced for the definition of all SI units and derived units. Voltage difference is denoted symbolically by formula_1, simplified "V", especially in English-speaking countries, or by "U" internationally, for instance in the context of Ohm's or Kirchhoff's circuit laws.


title: Voltage

text: The voltage between points can be caused by the build-up of electric charge (e.g., a capacitor), and from an electromotive force (e.g., electromagnetic induction in generator, inductors, and transformers). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect, and the thermoelectric effect.


title: Voltage

text: A voltmeter can be used to measure the voltage between two points in a system. Often a common reference potential such as the ground of the system is used as one of the points. A voltage can represent either a source of energy or the loss, dissipation, or storage of energy.


title: Voltage

text: There are multiple useful ways to define voltage, including the standard definition mentioned earlier. There are also other useful definitions of work per charge (see ).


title: Voltage

text: Voltage is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages. Therefore, the conventional current in a wire or resistor always flows from higher voltage to lower voltage.


title: Voltage

text: Historically, voltage has been referred to using terms like "tension" and "pressure". Even today, the term "tension" is still used, for example within the phrase "high tension" (HT) which is commonly used in thermionic valve (vacuum tube) based electronics.


title: Voltage

text: In electrostatics, the voltage increase from point formula_2 to some point formula_3 is given by the change in electrostatic potential formula_4 from formula_2 to formula_3. By definition, this is:


title: Voltage

text: In this case, the voltage increase from point A to point B is equal to the work done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration. Mathematically, this is expressed as the line integral of the electric field along that path. In electrostatics, this line integral is independent of the path taken.


title: Voltage

text: Under this definition, any circuit where there are time-varying magnetic fields, such as AC circuits, will not have a well-defined voltage between nodes in the circuit, since the electric force is not a conservative force in those cases. However, at lower frequencies when the electric and magnetic fields are not rapidly changing, then this can be neglected (see electrostatic approximation).


title: Voltage

text: The electric potential can be generalized to electrodynamics, so that differences in electric potential between points are well-defined even in the presence of time-varying fields. However, unlike in electrostatics, the electric field can no longer be expressed only in terms of the electric potential. Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of gauge.


title: Voltage

text: In this general case, some authors use the word "voltage" to refer to the line integral of the electric field, rather than to differences in electric potential. In this case, the voltage rise along some path formula_8 from formula_2 to formula_3 is given by:


title: Voltage

text: In circuit analysis and electrical engineering, lumped element models are used to represent and analyze circuits. These elements are idealized and self-contained circuit elements used to model physical components.


title: Voltage

text: When using a lumped element model, it is assumed that the effects of changing magnetic fields produced by the circuit are suitably contained to each element. Under these assumptions, the electric field in the region exterior to each component is conservative, and voltages between nodes in the circuit are well-defined, where


title: Voltage

text: as long as the path of integration does not pass through the inside of any component. The above is the same formula used in electrostatics. This integral, with the path of integration being along the test leads, is what a voltmeter will actually measure.


title: Voltage

text: If uncontained magnetic fields throughout the circuit are not negligible, then their effects can be modelled by adding mutual inductance elements. In the case of a physical inductor though, the ideal lumped representation is often accurate. This is because the external fields of inductors are generally negligible, especially if the inductor has a closed magnetic path. If external fields are negligible, we find that


title: Voltage

text: is path-independent, and there is a well-defined voltage across the inductor's terminals. This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads.


title: Voltage

text: The volt (symbol: ) is the derived unit for electric potential, voltage, and electromotive force. The volt is named in honour of the Italian physicist Alessandro Volta (1745–1827), who invented the voltaic pile, possibly the first chemical battery.


title: Voltage

text: A simple analogy for an electric circuit is water flowing in a closed circuit of pipework, driven by a mechanical pump. This can be called a "water circuit". The potential difference between two points corresponds to the pressure difference between two points. If the pump creates a pressure difference between two points, then water flowing from one point to the other will be able to do work, such as driving a turbine. Similarly, work can be done by an electric current driven by the potential difference provided by a battery. For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile's starter motor. If the pump isn't working, it produces no pressure difference, and the turbine will not rotate. Likewise, if the automobile's battery is very weak or "dead" (or "flat"), then it will not turn the starter motor.


title: Voltage

text: The hydraulic analogy is a useful way of understanding many electrical concepts. In such a system, the work done to move water is equal to the "pressure drop" (compare p.d.) multiplied by the volume of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to "electrical pressure difference" multiplied by the quantity of electrical charges moved. In relation to "flow", the larger the "pressure difference" between two points (potential difference or water pressure difference), the greater the flow between them (electric current or water flow). (See "electric power".)


title: Voltage

text: Specifying a voltage measurement requires explicit or implicit specification of the points across which the voltage is measured. When using a voltmeter to measure voltage, one electrical lead of the voltmeter must be connected to the first point, one to the second point.


title: Voltage

text: A common use of the term "voltage" is in describing the voltage dropped across an electrical device (such as a resistor). The voltage drop across the device can be understood as the difference between measurements at each terminal of the device with respect to a common reference point (or ground). The voltage drop is the difference between the two readings. Two points in an electric circuit that are connected by an ideal conductor without resistance and not within a changing magnetic field have a voltage of zero. Any two points with the same potential may be connected by a conductor and no current will flow between them.


title: Voltage

text: The voltage between "A" and "C" is the sum of the voltage between "A" and "B" and the voltage between "B" and "C". The various voltages in a circuit can be computed using Kirchhoff's circuit laws.


title: Voltage

text: When talking about alternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added for direct current (DC) and AC, but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.


title: Voltage

text: Instruments for measuring voltages include the voltmeter, the potentiometer, and the oscilloscope. Analog voltmeters, such as moving-coil instruments, work by measuring the current through a fixed resistor, which, according to Ohm's Law, is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a bridge circuit. The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the voltage.


title: Voltage

text: Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) and 220 to 240 volts (AC). The voltage in electric power transmission lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200 kV (AC).


title: Voltage

text: The voltage used in overhead lines to power railway locomotives is between 12 kV and 50 kV (AC) or between 0.75 kV and 3 kV (DC).


title: Voltage

text: Inside a conductive material, the energy of an electron is affected not only by the average electric potential but also by the specific thermal and atomic environment that it is in.


title: Voltage

text: When a voltmeter is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that is affected by thermodynamics.


title: Voltage

text: The quantity measured by a voltmeter is the negative of the difference of the electrochemical potential of electrons (Fermi level) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted electrostatic potential (not measurable with a voltmeter) is sometimes called Galvani potential.


title: Voltage

text: The terms "voltage" and "electric potential" are ambiguous in that, in practice, they can refer to "either" of these in different contexts.


title: Voltage

text: The term "electromotive force" was first used by Volta in a letter to Giovanni Aldini in 1798, and first appeared in a published paper in 1801 in "Annales de chimie et de physique". Volta meant by this a force that was not an electrostatic force, specifically, an electrochemical force. The term was taken up by Michael Faraday in connection with electromagnetic induction in the 1820s. However, a clear definition of voltage and method of measuring it had not been developed at this time. Volta distinguished electromotive force (emf) from "tension" (potential difference): the observed potential difference at the terminals of an electrochemical cell when it was open circuit must exactly balance the emf of the cell so that no current flowed.


title: Swoosie Kurtz

text: Swoosie Kurtz ( ; born September 6, 1944) is an American actress. She is the recipient of an Emmy Award and two Tony Awards.


title: Swoosie Kurtz

text: Kurtz made her Broadway debut in the 1975 revival of "Ah, Wilderness". She has received five Tony Award nominations, winning for both "Fifth of July" (1981) and "The House of Blue Leaves" (1986); her other nominations were for "Tartuffe" (1988), "Frozen" (2004), and "Heartbreak House" (2007).


title: Swoosie Kurtz

text: For her television work, she has received eight Emmy Award nominations, with one win for "Carol and Company" in 1990. Other television credits include the NBC drama "Sisters" (1991–1996), "Huff" (2004–2006), "Pushing Daisies" (2007–2009), and the hit CBS sitcom "Mike & Molly" (2010–2016). Her films include, "Wildcats" (1986), "Dangerous Liaisons" (1988), "Stanley & Iris" (1990), "Citizen Ruth" (1996), "Liar Liar" (1997) and "Bubble Boy" (2001).


title: Swoosie Kurtz

text: Kurtz was born in Omaha, Nebraska, the only child of author Margaret "Margo" (née Rogers;) and Air Force Colonel Frank Allen Kurtz Jr., a decorated World War II American bomber pilot. She got her first name "Swoosie" (which rhymes with Lucy, rather than woozy) from her father. It is derived from the sole surviving example of the early Boeing B-17D Flying Fortress bomber, named "The Swoose" (half swan, half goose), which her father piloted during World War II.


title: Swoosie Kurtz

text: Kurtz's first television appearance at age 17 was on "The Donna Reed Show" 4th-season episode "The Golden Trap" (February, 1962). She also appeared on "To Tell the Truth" at eighteen, identifying her father from two impostors. She made her debut as a series regular on the daytime drama "As The World Turns" in 1971. Kurtz began her career in theater, making her Broadway debut in the 1975 revival of "Ah, Wilderness!". She first gained wide recognition in 1978 for two theatrical productions, "Uncommon Women and Others", the breakthrough play by Wendy Wasserstein in which she appeared in a 1977 workshop at the Eugene O'Neill Theater Center and then Off-Broadway, and the musical "A History of the American Film" for which she won a Drama Desk Award. Kurtz was soon awarded Broadway's "triple crown" (the Tony, Drama Desk, and Outer Critics Circle awards) for her portrayal of Gwen in Lanford Wilson's "Fifth of July". She won a second Tony for her performance as Bananas in a 1986 revival of "The House of Blue Leaves" by John Guare. She starred as playwright Lillian Hellman in the 2002 Nora Ephron play "Imaginary Friends".


title: Swoosie Kurtz

text: In 1978, Kurtz was part of the ensemble cast of Mary Tyler Moore's short-lived variety series "Mary", that also included David Letterman and Michael Keaton. In 1981, Kurtz began two seasons alongside Tony Randall in the sitcom "Love, Sidney", in a role that earned her the first of her 10 Emmy Award nominations. In 1990, she won her first Emmy for a guest-starring role on Carol Burnett's comedy series "Carol & Company".


title: Swoosie Kurtz

text: From 1991 to 1996, Kurtz had her longest-running television role, starring as wealthy divorcee Alex Reed Halsey on the NBC drama "Sisters", a role that earned her two more Emmy Award nominations. She also starred in the ABC television series "Pushing Daisies" as Lily Charles.


title: Swoosie Kurtz

text: In recent years, Kurtz has guest-starred on the hit series "ER" and "Lost" and "Desperate Housewives" and has also had recurring roles as Valerie on the drama "That's Life", as Judy's mother Helen on the sitcom "Still Standing", as Madeleine Sullivan on the Showtime drama series "Huff", and most recently as part of a lesbian married couple with Blythe Danner on the drama series "Nurse Jackie". In 2010, Kurtz began starring on the CBS sitcom "Mike & Molly" as Joyce Flynn. Kurtz has also appeared in a recurring part as Matt LeBlanc's mother in the comedy series "Man with a Plan". In 2021, she began appearing as Mayim Bialik's mother in the comedy series "Call Me Kat".


title: Swoosie Kurtz

text: Although her main focus has been television, Kurtz has starred in several major Hollywood films including the Agatha Christie drama "Caribbean Mystery" (1983), "Dangerous Liaisons" (1988), its remake "Cruel Intentions" (1999), as a lesbian activist in the acclaimed indie film "Citizen Ruth" (1996), and alongside Jim Carrey in "Liar Liar" (1997).


title: Lorenza Izzo

text: Lorenza Francesca Izzo Parsons (; ; born September 19, 1989) is a Chilean actress and model. She has appeared in films, including "Aftershock" (2012), "The Green Inferno" (2013), "Knock Knock" (2015), and Quentin Tarantino's "Once Upon a Time in Hollywood" (2019).


title: Lorenza Izzo

text: Izzo was born in Santiago, Chile, to Chilean model . She is of Italian descent on her father's side. She has a younger sister, Clara Lyon Parsons, who is a model as well. When she was twelve years old, she moved to Atlanta with her father, then working towards a Ph.D. at Georgia Institute of Technology. She was bullied over her strong Chilean accent as a child, but stated she "got over [her] accent pretty fast" after watching the 2002 sports film "Blue Crush" several times. Izzo recalls becoming "obsessed with ["Blue Crush" star] Kate Bosworth."


title: Lorenza Izzo

text: In 2007, Izzo was modeling and studying journalism at the University of the Andes (Universidad de los Andes) when she moved to New York City to study acting at the Lee Strasberg Theatre and Film Institute.


title: Lorenza Izzo

text: In 2010, she made her debut as an actress in "Instrucciones para mi funeral" ("Instructions for my Funeral"), an independent film made by Sebastián Radic as a graduation project.


title: Lorenza Izzo

text: Izzo's modeling career reached its peak in 2011 when Izzo and her mother were invited to São Paulo Fashion Week where they met Gisele Bundchen. The meeting resulted in Izzo becoming the new face of Colcci, a Brazilian fashion company. The same year, Izzo appeared in "" ("Sorry About Your Wedding") a comedy by Chilean director Nicolás López.


title: Lorenza Izzo

text: In 2012, with one commercial feature movie to her name and three more then-about to be released "Que pena tu familia" ("What a Pity About Your Family"), "Aftershock", and "The Green Inferno" (directed by her then-future husband, now ex-husband, Eli Roth), Izzo moved to Los Angeles, when she soon secured small roles in "Hemlock Grove" and the failed television pilot "I Am Victor".


title: Lorenza Izzo

text: In 2015, Izzo starred alongside Keanu Reeves and Ana de Armas in "Knock Knock" (her second horror film directed by Eli Roth), filmed in Santiago's Chicureo neighbourhood.


title: Lorenza Izzo

text: On November 8, 2014, Izzo married American actor and director Eli Roth on the beach of Zapallar, Chile. The pair were introduced through mutual friend and director Nicolás López during production of 2013's "The Green Inferno". López was unaware Izzo could speak English and she was originally to play a small role in the film. After Izzo revealed she could speak English fluently, Roth ended up casting her in the lead, where they "spent the whole shooting process together". She attributes the start of their relationship to "the randomness of the world". In July 2018, the couple filed for divorce, and settled their divorce in August 2019. Izzo publicly came out as pansexual in an online interview with actress Emily Hampshire for the 2020 Pride Month.


title: Suede (band)

text: Suede (also known in the US as The London Suede) are an English rock band formed in London in 1989 by singer Brett Anderson, guitarist Justine Frischmann, and bass player Mat Osman. Drawing inspiration from glam rock, Suede were dubbed "The Best New Band in Britain" by "Melody Maker" in 1992, and attracted much attention from the British music press. The following year their debut album "Suede" went to the top of the UK Albums Chart, becoming the fastest-selling debut album in almost ten years. It won the Mercury Music Prize and helped foster 'Britpop' as a musical movement, though the band distanced themselves from the term.


title: Suede (band)

text: The recording sessions for their second album, "Dog Man Star", were fraught with difficulty and ended with guitarist and composer Bernard Butler departing after confrontations with the other members. Guitarist and composer Richard Oakes replaced him and joined the band right before the accompanying tour. Although a commercial disappointment at the time, the album was met with a generally enthusiastic reception on release and has over time been lauded as one of rock music's great albums. In 1994, Suede would become a component of the Britpop "big four", along with Oasis, Blur and Pulp.


title: Suede (band)

text: In 1996, following the recruitment of keyboard player Neil Codling, Suede went on to greater commercial success with "Coming Up". The album reached number one in the UK, producing five top ten singles and becoming Suede's biggest-selling album worldwide. Despite problems within the band, Suede's fourth album, "Head Music" (1999), was a British chart-topper. The album was promoted heavily with the band receiving considerable press coverage on its release, however the response from fans and critics was less enthusiastic than for previous records. Codling left the band in 2001, citing chronic fatigue syndrome, and was replaced by Alex Lee. The band's fifth album, "A New Morning" (2002), the first following the collapse of Nude Records, was a commercial disappointment, and the band disbanded the following year. In 2004, Anderson briefly reunited with Butler to form The Tears, before embarking on a solo career two years later.


title: Suede (band)

text: After much speculation Suede reformed in 2010 for a series of concerts. Three years on from their reunion gigs, Suede released their sixth album, "Bloodsports". It was well received by critics and returned the band to the top ten in the UK. Their seventh album, "Night Thoughts", followed in 2016 and became an even bigger critical and commercial success than its predecessor. Their eighth studio album, "The Blue Hour", was released in September 2018. It became the group's first top five record since "Head Music". Their ninth and most recent studio album, "Autofiction", was released in September 2022.


title: Suede (band)

text: Brett Anderson and Justine Frischmann met in 1988 while studying at University College London and became a couple soon afterwards. Together with Anderson's childhood friend Mat Osman, they decided they had the core of a band, and spent hours a day playing songs by Roxy Music, The Smiths, David Bowie and The Cure. After deciding that neither Anderson nor Frischmann had the skill to be a lead guitarist, the band placed an advert in "NME" in the magazine's 28 October 1989 issue seeking to fill the position: "Young guitar player needed by London based band. Smiths, Commotions, Bowie, Pet Shop Boys. No Musos. Some things are more important than ability. Call Brett." The advert attracted the interest of nineteen-year-old Bernard Butler, who soon auditioned to join the band. The band settled on the name Suede. Lacking a drummer, the band initially used a drum machine. Despite Frischmann's efforts as the band's "de facto" manager, the band primarily played small-scale gigs around Camden Town in London.


title: Suede (band)

text: Suede's first breakthrough came with their second demo "Specially Suede" which they sent to compete in "Demo Clash", a radio show on Greater London Radio run by the DJ Gary Crowley. "Wonderful Sometimes" won "Demo Clash" for five Sundays in a row during 1990, leading to a recording contract with the Brighton-based indie label RML. The song appeared on a cassette compilation in April 1990 representing Suede's first official release. After a series of gigs with an unreliable drum machine, Suede decided to recruit a full-time drummer. Justin Welch briefly fulfilled the role, though he only lasted six weeks before joining the Crawley band Spitfire. He did, though, stay long enough to record two songs with the band, which were set to be released as the "Be My God"/"Art" single on RML Records. The band was dissatisfied with the result, and most of the 500 copies pressed were destroyed. Suede placed another advert seeking a replacement. To the band's surprise, it was answered by the Smiths’ former drummer, Mike Joyce. He ultimately turned down the job as he felt Suede still had to forge their own identity. He felt that by being in a band that had similarities to the Smiths, he would have done them more harm than good. In June 1990, Suede found a permanent drummer, Simon Gilbert, through Ricky Gervais, who would later become a household name for co-writing and starring in the TV series "The Office". Both worked at the University of London Union (ULU). After hearing the demo and realising the band did not have a drummer, Gilbert asked to audition.


title: Suede (band)

text: By spring 1991, Anderson and Frischmann had broken up. Frischmann started dating Blur frontman Damon Albarn. She believed the band could accommodate the new situation. The situation grew tense, Butler recalled: "She'd turn up late for rehearsals and say the worst thing in the world – 'I've been on a Blur video shoot.' That was when it ended, really. I think it was the day after she said that that Brett phoned me up and said, 'I've kicked her out.'" After Frischmann's departure the character of the group changed. "If Justine hadn't left the band," Anderson said, "I don't think we'd have got anywhere. It was a combination of being personally motivated, and the chemistry being right once she'd left." Anderson and Butler became close friends and began writing several new songs together. Still, the band's music was out of step with the music of its London contemporaries as well as the American grunge bands. Anderson said, "For the whole of 1991, A&R men wouldn't give us a second look."


title: Suede (band)

text: Through the end of 1991 and early 1992, Suede received a number of favourable mentions in the music press, receiving slots at shows hosted by "NME" and attended by significant musical figures such as the former Smiths singer, Morrissey. A gig at the ULU in October 1991, which caught the media's attention, was Frischmann's final gig. John Mulvey of the "NME", the journalist who first wrote about Suede was there. He said, "They had charm, aggression, and... if not exactly eroticism, then something a little bit dangerous and exciting."


title: Suede (band)

text: After seeing the band perform at an "NME" show in January 1992, Saul Galpern approached them about signing to his independent record label Nude Records. Suede eventually signed a two single deal to Nude in February 1992 for the sum of £3,132. Following Nude's offer, Suede attracted further interest from Island Records and East West Records, who were keen to sign the band long term. Suede were being hailed as "the next big thing" and, before the release of the band's first single, "Melody Maker" featured the band on the cover on 25 April, with the headline "Suede: The Best New Band in Britain". The band's first single, "The Drowners", attracted attention for its sharp contrast to the dying Madchester scene and the US grunge sound of the time. A moderate hit, "The Drowners" reached number 49 on the UK Singles Chart in May. The band was then approached by Geffen Records and, although the Geffen deal was very attractive (Galpern described it as "insane"), the band still had other offers to consider. In September 1992, Suede released a second single, "Metal Mickey", which reached number 17 in the charts. It was the only Suede single to enter the US Modern Rock top 10, peaking at number 7. Shortly after the release of "Metal Mickey", Suede signed to Nude/Sony. Galpern was determined to sign the band in the long term and struck a deal with Sony – making them a tiny independent label with major company backing. The contract gave Suede creative controls such as the artwork on their releases.


title: Suede (band)

text: Anderson soon became notorious for causing controversy, such as his infamous quote that resurfaced in interviews and articles in the following years, that he was "a bisexual man who never had a homosexual experience". In February 1993, Suede went from highly touted indie band to major chart contenders with their third single, "Animal Nitrate", which went into the UK top ten. The single earned them a last-minute invitation to play at that year's Brit Awards ceremony. Writing in 2005, "The Times"' Victoria Segal looked back to the band's early career, saying Suede's "sexually fluid lyrics made them a rallying point for the alienated, one of the few British bands since the Smiths who united as much as they divided." Comparisons were being made with David Bowie, though Suede sounded nothing quite like anybody else around at the time, and soon they fell upon what critics quickly deemed was a new movement. Anderson recalls, "I had always been fascinated by suburbia, and I liked to throw these twisted references to small-town British life into songs. This was before we had that horrible term Britpop."


title: Suede (band)

text: Before Suede had released an album, they dominated the music press on the strength of just three singles, setting high expectations for the forthcoming album. "Suede" entered the British charts at number one, registering the biggest initial sales of a debut album since Frankie Goes to Hollywood's "Welcome to the Pleasuredome" a decade before. It sold over 100,000 copies in its first week of release, going gold on its second day. At the time it was hailed as "the most eagerly awaited debut since "Never Mind The Bollocks" by the Sex Pistols." Some notable press at the time was the front cover of the April 1993 issue of "Select", which is seen by many as the start of Britpop. The album won the 1993 Mercury Prize. The band donated the entire £25,000 in prize money to Cancer Research. This was the only album released in the US under the name "Suede", where it remains the band's highest selling release.


title: Suede (band)

text: Following the success of the album, the band toured extensively in Europe, receiving major coverage by MTV. In July, Suede gave a benefit concert for Red Hot Organization at "The Grand" in London, inviting Siouxsie Sioux to perform a version of Lou Reed's "Caroline Says" with Butler. Suede then prepared for an American tour in summer 1993. During the tour, tensions began to develop between Butler and the rest of the band. On the first American tour tensions peaked in Los Angeles, when Butler disappeared during a soundcheck. The gig went ahead, but for the rest of the tour the two parties barely spoke. The tensions grew worse on the second American tour mainly because Butler's father had died, which forced Suede to cancel the tour prematurely. Butler disliked the band's indulgence on the tour during his bereavement, in which he became so alienated from the band that he even travelled separately. Suede's American success was limited as they had already begun to be upstaged by their opening act, The Cranberries, who received the support from MTV that Suede lacked. At times, Butler left the stage while Suede were performing and persuaded a member of The Cranberries to fill in for him. Moreover, a lounge singer's lawsuit forced the band to stop using the trademarked American name "Suede". For their subsequent releases and shows in the United States, the band used the name "The London Suede". Anderson was not happy about having to change the band's name for the US market, saying, "The London Suede is not the name I chose for the band, I didn't change it happily, and I'm not going to pretend I did."


title: Suede (band)

text: In February 1994, the band released the stand-alone single "Stay Together", which became their highest-charting single at the time, reaching number three in the UK. The single was backed by a collection of strong B-sides. The new expansive sound, however, fractured the band and led to the departure of Butler. Despite the success of the single, the band has since distanced itself totally from the song, an aversion usually attributed to problems with Butler at the time. In the aftermath of "Stay Together", Anderson isolated himself in a house in Highgate and began to write songs for Suede's next album. It was at this time that Anderson distanced himself from what was dubbed the "laddish Britpop movement," which he was seen by many to have set the scene for its emergence. Bands such as Blur, Oasis and Pulp began to dominate the music scene, while Suede became more experimental and introverted. Tensions grew worse during the recording of the album when Butler criticised Anderson in a rare interview, claiming that he worked too slowly and that he was too concerned with rock stardom. Of Anderson he said, "He's not a musician at all. It's very difficult for him to get around anything that isn't ABC."


title: Suede (band)

text: Around this time, journalist Neil Strauss wrote that Suede were a band who were "unafraid to be out of step with its peers." The band started to record excessively lengthy songs at the behest of Butler. Osman said that he, Anderson and Gilbert often thought these tracks were the result of Butler trying to wind them up. Anderson recalled that Butler had largely recorded his parts separately from the rest of the band. This was usually done in shifts, with Anderson coming to the studio in the evenings after Butler had recorded his guitar parts during the day. The point at which tensions became unbearable was when Butler clashed with the producer Ed Buller, who he insisted should be sacked as he wanted to produce the record himself. Butler then gave Anderson an ultimatum demanding that the producer be fired or he would leave. "I called his bluff," said Anderson. Days after his wedding, Butler returned to the studio to find he was not being allowed in and his guitars were left out on the street. According to John Harris's Britpop history, "The Last Party", the final words Butler uttered to Anderson were "you're a fucking cunt." Butler left the band with a quarter of the recording still to be finished. In the first interview the band gave as a three-piece, Anderson foresaw the scenario, telling "NME"'s Steve Sutherland: "I saw it coming two years ago. It was no shock, I don't think he ever really wanted to be in the band or anything that goes with it."


title: Suede (band)

text: Led by the single "We Are the Pigs", Suede's second album, "Dog Man Star", finally appeared in October 1994. The album was very well received by critics in the UK who wrote favourably of the band's new experimental direction. It entered the UK Albums Chart at number three, but slid quickly down the charts. The singles from the album charted poorly, though they are still regarded as Suede's best output, especially "The Wild Ones", which is considered by some to be Suede's best single. Reviews in the US were more mixed, with some critics comparing it unfavourably to the singles from the first album; and several labelling it as pretentious and other synonyms to that effect. "Rolling Stone" would describe it as "one of the most pretentious albums ever released by a major label." Nevertheless, despite not gaining mass exposure at the time, it steadily garnered a legacy throughout the decade and beyond as one of rock music's great albums. In September 1994, Suede announced that 17-year-old Richard Oakes was to be the new guitarist. After reading about Butler's departure, he had sent a demo tape to the band's fanclub. When Gilbert heard Anderson playing back the tape whilst going through audition tapes, he mistakenly believed it to be an early Suede demo. Oakes' first official duty as a member of Suede was an appearance in the "We Are the Pigs" video. He then co-wrote his first music with Suede, the B-sides for the "New Generation" single, "Together" and "Bentswood Boys". Suede embarked on a long international tour during late 1994 and spring 1995, before disappearing to work on their third album. In 1995, the band contributed a track to "The Help Album" charity compilation, covering Elvis Costello's "Shipbuilding".


title: Suede (band)

text: In the autumn of 1995, the band was joined by new member Neil Codling, a cousin of Gilbert who played keyboards and second guitar. His first appearance was at a fanclub gig at the Hanover Grand on 27 January 1996, which turned out to be one of Suede's most important gigs. A short set devoid of Butler songs was well received by critics, "A set that says. 'No Need'," observed Steve Sutherland in "NME". Even before "Dog Man Star" was released, bassist Mat Osman told "Select" magazine in September 1994 that he wanted to move on from the regimented recording process and expansive multi-layered guitar sounds of that era and focus on more radio-friendly pop music; citing "Losing My Religion" by R.E.M. as a song that "doesn't show off in the slightest and is still brilliant." Anderson had a similar outlook, saying that in contrast to the band's previous albums, which he felt "suffered at certain times from being quite obscure," he intended the forthcoming album to be "almost like a 'greatest hits'." Suede's third album, "Coming Up", was released September 1996 and was preceded by the successful lead single, "Trash" in July. The single was popular and tied with "Stay Together" as the band's highest-charting UK single, reaching number three. The album would become the band's biggest mainstream success, earning the band five straight top-10 singles and becoming a hit throughout Europe, Asia and Canada. "Coming Up" never did win an audience in America, partially because it appeared nearly a year after its initial release and partially because Suede only supported it with a three-city tour. The tour was not helped by problems in Boston, Massachusetts, in which the band's music equipment was stolen, leaving them to play remaining shows with acoustic guitars. Nevertheless, the album topped the UK chart and became the band's biggest-selling release, setting expectations high for the follow-up. With the success of the album, Suede secured top billing at the 1997 Reading Festival. Suede's next release was "Sci-Fi Lullabies", a collection of B-sides, which reached number nine on the UK Album Chart. The compilation was well-received, with disc one of two being described by critics as the band's strongest collection of songs.


title: Suede (band)

text: By the time the compilation was released in 1997, the Britpop movement was noticeably waning in popularity, and the band had decided to split with their long-time producer Ed Buller before commencing work on the follow-up to "Coming Up". Before focusing work on their next album, the band recorded a version of "Poor Little Rich Girl" for the "" in 1998. Despite being backed by their second-highest-charting single, "Electricity", Suede's fourth album, "Head Music", did not evoke the critical and listener enthusiasm that previous records did, though it once again took the band to number one on the UK Albums Chart. A synthesiser-infused album that focused less on guitar riffs and more on keyboards, it was produced by Steve Osborne, who had worked with Happy Mondays and New Order. While the record was heavily promoted with some strong financial backing, and received almost widespread critical enthusiasm from the UK music press, the consensus with people close to the band was a feeling that things were not quite right. Richard Oakes was aware of the fans' disapproval of the album, as well as Anderson's more gaunt-like appearance and Oakes' own admission of spending two years "being pissed out [his] face and being out of shape." Moreover, many critics felt the record's lyrics were too shallow and lacking in substance. Though others praised the album, feeling that the band were again taking a different direction and charting new territory.


title: Suede (band)

text: The next three singles released from the album failed to enter the top 10, breaking a run stretching back to the 1996 single "Trash". Anderson also attracted more criticism from fans for his frequent use of redundant vocabulary and limited lyrical themes. The track which received the most attention and criticism was "Savoir Faire". Some critics felt that the album's lyricism could be linked to Anderson's heavy drug use at the time, especially when he later admitted that he "was a crack addict for ages". Speaking of his addiction, which plagued him for two and a half years, Anderson said, "Anyone who has ever tried crack will know exactly why I took it. It's the scariest drug in the world because the hit you get from it is so, so seductive. I wanted to experience that, and I did – repeatedly." Suede headlined the Roskilde and V Festivals in July and August 1999 respectively. During 2000, there was press speculation that Suede were on the verge of disbanding, which was not helped by Codling's absence from some European gigs. Anderson denied these claims and insisted that Codling was healthy and that they were keen to record the next album. For the whole of 2000, Suede retreated from the public and played only one gig, in Reykjavik, Iceland. The band premiered several new songs that eventually appeared on the final album.


title: Suede (band)

text: Not long after the release of "Head Music", Nude Records effectively ceased to exist. Like many of their labelmates, Suede ended up signing to Nude's parent company/distributor Sony to record the band's fifth album, "A New Morning". Between the release of "Head Music" and "A New Morning", Suede wrote and recorded "Simon" as the title theme for the film "Far From China". The long and troubled gestation of the new album saw the keyboard player, Codling, leave the band, citing chronic fatigue syndrome, to be replaced by Alex Lee, formerly of Strangelove. In concert, Lee played keyboards, second guitar, backing vocals and occasionally harmonica. The album title, according to Anderson, referred to "a fresh start, a new band and a new fresh outlook" – the singer had been addicted to heroin and crack cocaine, which was having an increasingly deleterious effect on his health. Anderson claimed that "A New Morning" "was the first ever Suede record that wasn't influenced in its making by drugs".


title: Suede (band)

text: Although the band began work with Tony Hoffer producing, the album was produced by Stephen Street (The Smiths, Blur). Overall, seven different recording studios and four producers were used during the two years spent recording "A New Morning", with costs estimated at £1 million. The album was a commercial disappointment which failed to enter the top 20 and it was never released in the US. "A New Morning" sharply divided fans of the band even more so than "Head Music" and critical reaction was decidedly lukewarm. Furthermore, the mainstream public interest had long disappeared. Only two singles, "Positivity" and "Obsessions", were released, the fewest singles taken from any of the band's albums, and neither charted particularly well. Anderson has since stressed his disappointment with Suede's final album, stating "We made one Suede album too many. 'A New Morning' is the only one I don't believe in as much as the other Suede records and I totally believed in the first four, even 'Head Music' which divided the fans." Mat Osman told journalist Jon Cronshaw in October 2013 that: "It sounded like a Suede album that had been made by a committee – it was quite bland. We're all quite ashamed of it". Anderson went further in his criticism in 2016, saying: "It's a poor record and we should never have released it."


title: Suede (band)

text: In September 2003, Suede played five nights at the Institute of Contemporary Arts in London, dedicating each night to one of their five albums and playing through an entire album a night in chronological order, with B-sides and rarities as encores. In October 2003, Suede released a second compilation album "Singles", and an accompanying single "Attitude", which charted at number 14 in the UK. The band had begun working on a follow-up album to "A New Morning", which was planned to be released after the "Singles" compilation. Anderson said that, "Most of the new material is more aggressive and less song based than "A New Morning"." He added, "We're spending a lot of time working on tracks that sound nothing like traditional Suede." The planned album was never released.


title: Suede (band)

text: On 28 October 2003, Anderson made the decision to call it a day. The same day Suede were booked to perform "Beautiful Ones" on "V Graham Norton" to promote the "Singles" compilation. Jeremy Allen was the last person to interview the band just before the Norton appearance. Allen would see the band again some six weeks later at the aftershow party following the final gig at the London Astoria in December. At the aftershow event, Osman revealed to Allen that they decided to call it quits less than a minute after their last interview. As they were walking along the corridor to the studio set, Anderson whispered into Osman's ear: "Let's not do this anymore." Less than a week after the decision to call an end to Suede, the band's biography, "Love and Poison" was released on 3 November. On 5 November, the band announced that there would be no more projects under the Suede name for the foreseeable future – effectively announcing the end of the band, as they stated on their website: "There will not be a new studio album until the band feel that the moment is artistically right to make one." Anderson also made a personal statement saying: "There has been speculation about record sales and chart positions, but the bottom line is I need to do whatever it takes to get my demon back." Suede's last concert at the London Astoria on 13 December 2003 was a two-and-a-half-hour marathon show, split into two parts plus encore. Anderson made an announcement, saying, "I just want you to know. There will be another Suede record. But not yet."


title: Suede (band)

text: Following persistent rumours, Saul Galpern, the boss of the band's former label, Nude Records, officially announced on 15 January 2010 that Suede would be playing together again. "It's a one-off gig," he explained of the show, which featured the band's second incarnation. The band played at the Royal Albert Hall in London as part of the 2010 Teenage Cancer Trust shows on 24 March 2010. Anderson described the comeback show as his favourite gig and the pinnacle of his 20-year career. Despite the gig initially being billed as a one night only reformation, when questioned on the German radio station MotorFM in early February, Anderson refused to confirm that the band would not continue. The band subsequently announced two UK 'warm up' gigs prior to the Royal Albert Hall show, at the 100 Club in London and The Ritz in Manchester. The three gigs were well received by critics from various newspapers.


title: Suede (band)

text: In August, the band played at the Skanderborg Festival in Denmark and Parkenfestivalen in Bodø, Norway. In September, the band announced that they would release "The Best of Suede" on 1 November 2010. The two-disc compilation, put together by Anderson, consisted of 18 of the band's 20 singles on disc one; and a mixture of album tracks and popular B-sides on disc two. Shortly after the release, Suede made a short European tour from late November into December covering Spain, France, Belgium, Sweden, the Netherlands and Germany. The band concluded the tour on 7 December at the O2 Arena in London.


title: Suede (band)

text: After their biggest show ever at the O2 Arena in London, Brett confirmed that Suede were in the mood for more shows. 2011 would see the band perform at several festivals around the world. In January, they announced their first festival appearance of that year, playing at the SOS 4.8 Festival in Murcia, Spain in May. Other festivals included Blackberry's Live & Rockin' Festival at the Jakarta International Expo, Indonesia in March 2011; and the Coachella Valley Music and Arts Festival in April 2011. This marked the group's first live American show since 1997. Suede played at the Latitude Festival in Suffolk on 17 July 2011. The final performance was at the Berlin Festival on 9 September 2011, directly following the Asian tour in August. In June 2011, following the success of the compilation album, the band released remastered and expanded editions of all five studio albums. They also performed the albums "Suede", "Dog Man Star" and "Coming Up" at the O2 Brixton Academy in London over three nights on 19, 20 and 21 May 2011, and at the Olympia Theatre, Dublin, on 24, 25 and 26 May.


title: Suede (band)

text: Suede embarked on a full Asian tour, which began in late July in Jisan, South Korea, and finished at the Summer Sonic festival in Tokyo, Japan, on 14 August 2011. Suede performed in Athens on 11 September 2011, and ended the band's touring commitments in Russia on 16 and 18 December 2011 where they showcased the new songs "Falling Planes", "The Only", "Someone Better", "I Don't Know Why", "Cold War", "Future Nightmare" and "Sabotage". Suede began recording a new album with Ed Buller in 2012 and Brett Anderson stated that of the songs showcased in Russia, only "Sabotage" was thus far in contention. On 7 January 2013, the band announced that the sixth studio album, "Bloodsports", would be released in March. The announcement was accompanied by "Barriers", a song from the album, as a free download. They released their first single in a decade "It Starts and Ends with You" on 4 February. "Bloodsports" was well received by critics and has been their best reviewed album since the band's 1996 album "Coming Up". On 12 April, Suede announced on their website the dates for their forthcoming European tour. The tour began on 26 October 2013 at the Leeds O2 Academy and finished on 23 November at the Paradiso in Amsterdam. Suede subsequently added a further three shows to the beginning of the tour. They played additional shows in Southampton, Southend and Bristol on 22, 23 and 24 October.


title: Suede (band)

text: In late January 2014, Anderson announced that Suede were working on a new album, he estimated the album would be released in 2015 as the band are in the writing stage for the album. On 7 September 2015, the band announced that their new album, "Night Thoughts", was to be released on 22 January 2016, alongside a feature film directed by photographer Roger Sargent. On 24 September, the first single from the album "Outsiders" was released. The band performed the album in full on 13 and 14 November at the London Roundhouse. The album was released as a standalone CD issue, as a doublepack with the movie on DVD and as a limited numbered issue with CD, DVD and book. Anderson felt that unlike previous albums, for the first time the band had the freedom to do their own thing. Without the pressure to aim for the mainstream, the band deliberately eschewed from writing any radio hits. "Night Thoughts" was very well received by both fans and critics, receiving widespread press coverage on its release. Following on from the success of "Bloodsports", "Night Thoughts" charted at no. 6 in the UK. A series of concert dates in the UK and Europe to support the release followed. The first half of each show consisted of the band playing the album tracks in sequence, while onstage behind a gauze screen with the movie projected onto it. The second half consisted of a mix of back catalogue material, including a number of b-sides and obscure songs. The band also did a number of instore acoustic appearances in HMV stores to promote the release, including Q&A sessions and movie screenings.


title: Suede (band)

text: During the period were the band wrote and toured "Night Thoughts", they also commemorated some of their earlier releases. Once again the band performed as part of the Teenage Cancer Trust charity at the Royal Albert Hall on 30 March 2014. This time, the band performed "Dog Man Star" in full to mark its 20th anniversary. The set was followed by b-sides from that era, and then a greatest hits finale, which included new song "I Don't Know How to Reach You". Furthermore, to celebrate the actual 20th anniversary release of the album, Suede released a limited edition box set in October 2014. A similar 20th anniversary reissue was released for "Coming Up" in September 2016.


title: Suede (band)

text: On 28 April 2018, Suede announced their upcoming eighth studio album. On 30 April 2018, they officially revealed the name "The Blue Hour" as its title, which would later release on 21 September 2018. On 4 May 2018, Suede announced the dates for the European tour which were scheduled to start shortly after the launch of the album. The tour began on 29 September in Berlin, Colombiahalle and finished 13 October at the Eventim Apollo in London. A final show was added to the tour on 14 October at the Bord Gáis Energy Theatre in Dublin. On 5 June 2018, the band shared their first single from the album, "The Invisibles", with an accompanying video. Five singles were released from the album, matching the number of singles from "Night Thoughts", with latest single "Wastelands" released 29 October. The album was released to a generally favourable reception and became their highest-charting album since "Head Music" in 1999. Suede announced their first 2019 show, as Friday night headliners at Pennfest, Penn, Buckinghamshire. In November 2018, the band released a documentary entitled "Suede - The Insatiable Ones" directed by Mike Christie. The feature-length documentary explores the highs and lows of Suede's career, with unprecedented access, new interviews and unseen footage from the band's archive. It was shown as part of a 'Suede Night' 24 November on Sky Arts, along with the band's 2010 comeback gig at the Royal Albert Hall. On 10 December, the band announced new dates as part of a 2019 UK tour. The tour began at Newcastle's O2 Academy on 15 April and concluded on 28 April at the Corn Exchange in Cambridge.


title: Suede (band)

text: In November 2020 an announcement on the official Suede Facebook page stated that a new album was currently being recorded. The same post also asked for fans to contribute some vocals for some as-yet-untitled tracks. In a BBC interview Anderson suggested that the record would be "nasty, brutish and short." On 9 July 2021, "Music Week" revealed that Suede had signed to the BMG label for the release of their next album, though no release date had been confirmed.


title: Suede (band)

text: On 23 May 2022, eighteen months after the band announced that they were recording a new album, Suede revealed the title of their ninth studio album as "Autofiction", which was released via BMG 16 September. On the same day, the band revealed the name of their lead single as "She Still Leads Me On", which was premiered that day at a concert at the Cirque Royal in Brussels. The song is inspired by Anderson's late mother. Speaking about the new album, Anderson said: ""Autofiction" is our punk record. No whistles and bells. Just the five of us in a room with all the glitches and fuck-ups revealed; the band themselves exposed in all their primal mess". Speaking to "Billboard", Anderson further explained: "our intention was also to recover certain aesthetic lines in the sound ... [the] post punk sound is back very strongly in the limelight".


title: Suede (band)

text: Two more singles, "15 Again" and "That Boy on the Stage" were released before the album. According to Anderson the former is "a song about falling in love with life for the first time," and the latter "[is] about persona. It’s about the people we become." On 12 September, the band announced the dates of a March 2023 UK tour. The 2023 tour is due to begin at Bath's Forum on 3 March, closing at O2 Academy Brixton on 25 March, 30 years after the band made their debut performance at the London venue in May 1993. On 13 September, the band announced its first United States concert tour since 1997, a co-headlining North American tour with Manic Street Preachers. Both bands will play ten shows in the US and two shows in Canada throughout November. Suede was one of the bands performing at the 2022 Formula 1 Singapore Grand Prix.


title: Suede (band)

text: A significant part of Suede's legacy consists in having kickstarted the Britpop scene which eventually overshadowed the band's own achievements in the public mind. Alexis Petridis wrote in 2005, "These days, rock historians tend to depict Suede's success as a kind of amuse bouche (appetizer) before the earth-shattering arrival of Britpop's main course". In an article about the British music press's "ferocious one-upmanship campaign" of the mid-1990s, Caroline Sullivan, writing for "The Guardian" in February 1996, noted Suede's appearance as an unsigned band on the cover of "Melody Maker" as a pivotal moment in the history of Britpop:


title: Suede (band)

text: Suede appeared on Melody Maker's cover before they had a record out... The exposure got them a record deal, brought a bunch of like-minded acts to the public's attention, and helped create Britpop. It was the best thing to happen to music in years, and it mightn't have happened without that Suede cover.


title: Suede (band)

text: The year following the "Melody Maker" cover saw Suede captivate a pop phenomenon of critical praise and hype. Not since the dawn of the Smiths had a British band caused such excitement with the release of just a few singles. A March 1993 article in "The Independent" wrote that "Suede have had more hype than anybody since the Smiths, or possibly even the Sex Pistols. The reviews are florid, poetic, half-crazed; they express the almost lascivious delight of journalists hungry for something to pin their hopes on." Suede are regarded by many as the first British band to break into the mainstream from the new wave of alternative rock in the '90s. With their glam rock style and musical references of urban Britain, Suede paved the way for acts such as Oasis, Blur and Pulp to enter the British mainstream. They were influential in returning some of the creative impetus to English guitar music in a scene increasingly dominated by Madchester, grunge and shoegaze. Even beyond their own shores, American heavy metal personality Eric Greif declared that Suede "reinvented and repackaged glam in a creative way, and how refreshing that was as a counterpoint to the drab grunge of the time."


title: Suede (band)

text: Suede's laurels would remain intact through their early career until Butler's departure, which the press signalled as the end of Suede. As new rock bands were arriving on the scene, British pop culture was in the midst of a shift towards lad culture and the same critics who championed Suede were now plotting to extinguish them. In February 1995, music critic J.D. Considine said the band "quickly fell victim to the build-'em-up-then-knock-'em-down mentality of the English music press." On the eve of the release of "Coming Up", Neil McCormick of "The Telegraph" wrote: "Cast in the classic mould of the androgynous rock star, Anderson appears curiously anachronistic in a British rock scene polarised between the laddishness of Oasis and the suburbiana of Blur and Pulp." In a 2007 article in "The Telegraph", Bernadette McNulty wrote that while the frontmen of those bands "are all being bestowed with reverential status, Brett Anderson has become the lost boy of Britpop". Since the Britpop movement ceased to exist, like many bands associated with it, Suede's popularity sharply declined. As one writer put it at the end of Suede's career, "Suede slid from zeitgeist into a smaller, pocket-sized cult band." In the same article, Anderson spoke about their legacy:


title: Suede (band)

text: "It's not in my nature to be bitter. We may have been overlooked somewhat, but all you need to do is listen to the music. Our legacy speaks for itself." He added, "...Fate dealt us this card, and I don't think we've done particularly badly with it. Music today seems so very worthy, so very dull. Nobody wants to stick their neck out any more, and I think that is a great pity. We did, and we left our mark."


title: Suede (band)

text: "Still one of the great British bands of the '90s," David Bowie told "Select" in 1996. "They have the enviable knack of taking the rather pathetic fumble of a quick fuck under the pier and extracting those few golden moments that many years later convince oneself that, for one brief flickering moment, one was as inspired as Romeo or, in some cases, Juliet. The poor things are bound to be an institution by the year 2000. Dame Brett, anybody?"


title: Suede (band)

text: At the 2010 Q Awards, Suede were honoured with the "Inspiration Award". Suede were honoured with the "Godlike Genius Award" at the 2015 NME Awards. New Order frontman Bernard Sumner presented it to the band, following a video introduction of the "fantastic" and "brilliant" Suede by comedian and Suede fan Ricky Gervais.


title: Suede (band)

text: Multiple artists have cited the band as an influence. Kele Okereke, lead singer of London band Bloc Party, said that he started making music because of Suede's "Dog Man Star", and called it "the first record [he] fell in love with". Kate Jackson, lead singer of English indie rock band The Long Blondes has said in interviews of her love for Suede. In 2007, she admitted that Suede got her into music, saying: "Suede's debut album was unlike anything I'd heard before. It was the opposite of grunge, which I hated, and my escape from Bury St Edmunds." Christopher Owens of the Californian indie pop group Girls named Suede as one of his major influences, and his vocal style has been compared to that of Anderson. The band have also served as an influence on acts such as Sons and Daughters, Dum Dum Girls, and Drowners, who took their name from the similarly titled Suede song. Canadian rock band Destroyer named their 2017 album "ken" after the original title for "The Wild Ones".


title: Suede (band)

text: Additionally, Suede's songs have been covered by artists. "My Insatiable One" was performed by Morrissey during his "Your Arsenal" tour in 1992. "The Drowners" was recorded by the Manic Street Preachers as a b-side. "Animal Nitrate" was covered by the Libertines in concert during their tour reunion in 2015: a cover version of the same song was also recorded by Basement for the "Further Sky" EP. "Beautiful Ones" was recorded by Kim Wilde on her cover album "Snapshots" in 2011. Apoptygma Berzerk recorded a cover version of "Trash" on their "Rocket Science" album.


title: Nana (manga)

text: Nana (stylized as NANA) is a Japanese manga series written and illustrated by Ai Yazawa. It was serialized in the monthly manga magazine "Cookie" from May 2000 to May 2009 before entering a hiatus. The series is centered on Nana Osaki and Nana Komatsu, two women who move to Tokyo at the age of 20, with the story focused on Nana O.'s pursuit for fame and Nana K.'s pursuit for romance, all while struggling to maintain their friendship.


title: Nana (manga)

text: The manga was adapted into a live-action film in 2005, with a sequel released in 2006. An anime television series adaptation by Madhouse directed by Morio Asaka aired on Nippon TV between April 2006 and March 2007. All "Nana" media has been licensed for English language release in North America by Viz Media, which serialized the manga in their "Shojo Beat" magazine until the August 2007 issue, while also publishing it in the "tankōbon" format. They released both films in 2008, and their English dub of the anime was broadcast on the Funimation Channel beginning in September 2009.


title: Nana (manga)

text: In 2002, "Nana" won the 48th Shogakukan Manga Award for "shōjo" category. As of September 2019, the manga had over 50 million copies in circulation, making it one of the best-selling manga series.


title: Nana (manga)

text: On March 5, 2001, Nana Osaki and Nana Komatsu (nicknamed Hachi) cross paths when they both move to Tokyo after turning 20 years old: Nana O. to pursue a professional music career with her band, Black Stones, on her own merit; and Nana K. to join her friends and move in with her boyfriend. Despite having different personalities and ambitions, the two women find commonalities with each other and, by coincidence, move into the same apartment. However, as they follow their dreams, troubles of fame and love begin to test their friendship.


title: Nana (manga)

text: As the two women continue their lives in Tokyo, Nana K. breaks up with her boyfriend after he cheats on her, while Nana O. reunites with her ex-boyfriend Ren, the guitarist of Japan's current top band, Trapnest. Nana O.'s relationship with Ren eventually leads Nana K. into starting an on-and-off relationship with Trapnest's bassist, Takumi, causing her friendship with Nana O. to become awkward, while falling in love with Black Stones' guitarist, Nobu, at the same time. Ultimately, when Nana K. becomes pregnant, she chooses to marry Takumi instead. Nana O. begins to suffer from panic attacks at the thought of losing Nana K., but she later resolves to win her back from Trapnest by using the popularity and success of Black Stones.


title: Nana (manga)

text: When a tabloid magazine exposes Nana O. and Ren's relationship, this causes Black Stones to skyrocket in popularity and formally debut. Nana O. and Ren, however, start facing troubles in their relationship due to Nana O.'s jealousy of Trapnest and Ren's drug addiction, even as they become engaged. As the tabloids continue to target Black Stones and Trapnest, Nana K. begins to learn secrets behind Nana O.'s family history, including her birth mother. Shortly before Black Stones begin their first tour, their bassist, Shin, is arrested, causing Nana O. to embark on a solo career in the meantime. As she begins to make a name for herself, Ren dies in a car accident. While recovering from his death, Nana O. begins to question her dependency on Nana K. as well as the change in their relationship.


title: Nana (manga)

text: Starting with volume 12, scenes that take place years later are interspersed in the series, showing that in the present, Nana O. is rumored to have died, but Nana K. and her friends learn that she fled to England and try to find her.


title: Nana (manga)

text: Written and illustrated by Ai Yazawa, "Nana" first appeared as a one-shot in 1999 in Vol. 1 and Vol. 2 of Shueisha's "Cookie", a sister magazine of "Ribon". "Nana" was later serialized in "Cookie", starting in the July 2000 issue (published on May 26), when it was relaunched as a monthly magazine. "Nana" ran in the magazine for 84 chapters, until the July 2009 issue (published on May 26), and the series was put on hiatus in June of the same year due to Yazawa falling ill. Yazawa returned from the hospital in early April 2010, but it was not specified when or if she would resume the manga. The individual chapters of "Nana" have been collected by Shueisha into twenty-one "tankōbon" volumes, published under the Ribon Mascot Comics Cookie imprint, between May 15, 2000 and March 13, 2009. Its latest four chapters have not been published in a "tankōbon" volume.


title: Nana (manga)

text: "Nana" is licensed for English-language release in North America by Viz Media. It was serialized in Viz's manga anthology "Shojo Beat", premiering in the July 2005 debut issue and continuing until the August 2007 issue. They published all 21 collected volumes as of July 6, 2010.


title: Nana (manga)

text: Two live-action film adaptations have been made for "Nana". The first, "Nana", was released on September 3, 2005. The film stars Mika Nakashima as the punk star Nana Oosaki, Aoi Miyazaki as Hachi (Nana Komatsu), Ryuhei Matsuda as Ren Honjou, Tetsuji Tamayama as Takumi Ichinose, Hiroki Narimiya as Nobuo Terashima, and Kenichi Matsuyama as Shinichi Okazaki. The DVD edition was released on March 3, 2006. The film did quite well at the Japanese box office, grossing more than 4 billion yen, and staying in the top 10 for several weeks.


title: Nana (manga)

text: A sequel, "Nana 2", was announced right after the first film debuted. However, on August 4, 2006, Toho stated that shooting would begin mid-September and that the film was to be released on December 9, 2006. Miyazaki, Matsuda and Matsuyama would not be reprising their respective roles as Hachi, Ren and Shin; as such, their roles were assigned to Yui Ichikawa, Nobuo Kyo and Kanata Hongō, respectively. Some locations from the manga had been changed for the film, and many plot differences were introduced as well.


title: Nana (manga)

text: An animated adaptation of "Nana" was produced by Nippon Television, VAP, Shueisha and Madhouse and directed by Morio Asaka, with Tomoko Konparu handling series composition, Kunihiko Hamada designing the characters and Tomoki Hasegawa composing the music. The series aired from April 5, 2006 to March 27, 2007. The first and third openings and third ending songs are sung by Anna Tsuchiya, who provides the singing voice for Nana Osaki, while the second opening and first and second endings were sung by Olivia Lufkin, who provides the singing voice for Reira Serizawa. The series was published and distributed on 17 DVD volumes by VAP from July 7, 2006 to November 21, 2007. The highest average TV ratings for the series was 6.3% in the Kanto region, which was unusually high for a late night anime. In 2007, Viz Media licensed the anime for release in North America and released it on four DVD box sets between September 2009 and April 2010, including an English dub. Funimation acquired the broadcast rights to Viz Media's dub and it premiered on the Funimation Channel on September 19, 2009. After Viz Media lost the rights, Sentai Filmworks re-licensed the series in 2021 and premiered on its HIDIVE service on April 22 that same year.


title: Nana (manga)

text: The anime was intended to be equal to the manga, and adapted up to the first chapter of volume 12 to avoid filler. In April 2007, when asked about a continuation of the anime, Junko Koseki (editor of "Nana" in Shueisha) and Masao Maruyama (former managing director of Madhouse) stated that they had decided to wait until the manga ends before producing more material.


title: Nana (manga)

text: "Nana" has inspired several image and tribute albums, including "Punk Night: From Nana" and "Nana's Song is My Song" in 2003. "Love for Nana: Only 1 Tribute", an album released by EMI Music Japan on March 16, 2005. Several famous artists contributed to it, including English musician Glen Matlock of the Sex Pistols, Canadian singer-songwriter Skye Sweetnam, and various Japanese artists.


title: Nana (manga)

text: A "Nana" video game for the PlayStation 2 platform was produced by Konami and released on March 17, 2005. A PlayStation Portable game, was released on July 6, 2006. A Nintendo DS game, was released by Konami in June 2007. The voice actors for the PS2 game did not return to reprise their roles for the PSP and DS games, which instead feature the anime's cast.


title: Nana (manga)

text: Along with "Kaze Hikaru", "Nana" won the 48th Shogakukan Manga Award in the "shōjo" category in 2003; and was also nominated for the 10th Osamu Tezuka Cultural Award. The Young Adult Library Services Association in the United States listed the series in its "Great Graphic Novels for Teens" in 2007. Deb Aoki of About.com ranked "Nana" as the fifth "Must-Read" shōjo manga series in its "Top shojo Manga Must-Reads" list, with Aoki stating the manga is "a beautifully-drawn series that is filled with heartfelt drama, big city glamor, fabulous fashion, rock and roll sass and many unexpected twists." She also ranked the manga in its "50 Essential Manga for Libraries" list, noting its mature themes and "demonstrates the need for an adult collection." In a survey conducted by "Goo" in 2012 among 1,939 people, "Nana" was among the top favorite manga for women.


title: Nana (manga)

text: The first twelve volumes of the manga series have cumulatively sold over 22 million copies. As of September 2019, the manga had over 50 million copies in circulation.


title: Nana (manga)

text: "Nana" was the top favorite shōjo manga for Oricon Style in 2005. Volume 18 was the second highest selling manga series of 2007. During 2008, volume 19 was the third highest-selling manga and volume 20 was the fifth highest-selling manga in Japan, selling 1,645,128 and 1,431,335 copies respectively. By the end of the year, "Nana" was the sixth best selling manga with 3,122,146 copies sold. As of 2008, the manga series has sold over 43.6 million copies. In the first half of 2009, Volume 21 ranked as the third best selling manga, having sold 1.4 million copies. In the United States, volume twenty-one debuted at number 9 on the "New York Times" Graphic Books list for the week of July 10.


title: Boolean algebra

text: In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values "true" and "false", usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction ("and") denoted as ∧, disjunction ("or") denoted as ∨, and the negation ("not") denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations.


title: Boolean algebra

text: Boolean algebra was introduced by George Boole in his first book "The Mathematical Analysis of Logic" (1847), and set forth more fully in his "An Investigation of the Laws of Thought" (1854).


title: Boolean algebra

text: According to Huntington, the term "Boolean algebra" was first suggested by Sheffer in 1913, although Charles Sanders Peirce gave the title "A Boolean Algebra with One Constant" to the first chapter of his "The Simplest Mathematics" in 1880.


title: Boolean algebra

text: Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.


title: Boolean algebra

text: A precursor of Boolean algebra was Gottfried Wilhelm Leibniz's algebra of concepts. Leibniz's algebra of concepts is deductively equivalent to the Boolean algebra of sets.


title: Boolean algebra

text: Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. In an abstract setting, Boolean algebra was perfected in the late 19th century by Jevons, Schröder, Huntington and others, until it reached the modern conception of an (abstract) mathematical structure. For example, the empirical observation that one can manipulate expressions in the algebra of sets, by translating them into expressions in Boole's algebra, is explained in modern terms by saying that the algebra of sets is "a" Boolean algebra (note the indefinite article). In fact, M. H. Stone proved in 1936 that every Boolean algebra is isomorphic to a field of sets.


title: Boolean algebra

text: In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra in this setting, and he introduced switching algebra as a way to analyze and design circuits by algebraic means in terms of logic gates. Shannon already had at his disposal the abstract mathematical apparatus, thus he cast his switching algebra as the two-element Boolean algebra. In modern circuit engineering settings, there is little need to consider other Boolean algebras, thus "switching algebra" and "Boolean algebra" are often used interchangeably.


title: Boolean algebra

text: Efficient implementation of Boolean functions is a fundamental problem in the design of combinational logic circuits. Modern electronic design automation tools for VLSI circuits often rely on an efficient representation of Boolean functions known as (reduced ordered) binary decision diagrams (BDD) for logic synthesis and formal verification.


title: Boolean algebra

text: Logic sentences that can be expressed in classical propositional calculus have an equivalent expression in Boolean algebra. Thus, Boolean logic is sometimes used to denote propositional calculus performed in this way. Boolean algebra is not sufficient to capture logic formulas using quantifiers, like those from first order logic.


title: Boolean algebra

text: Although the development of mathematical logic did not follow Boole's program, the connection between his algebra and logic was later put on firm ground in the setting of algebraic logic, which also studies the algebraic systems of many other logics. The problem of determining whether the variables of a given Boolean (propositional) formula can be assigned in such a way as to make the formula evaluate to true is called the Boolean satisfiability problem (SAT), and is of importance to theoretical computer science, being the first problem shown to be NP-complete. The closely related model of computation known as a Boolean circuit relates time complexity (of an algorithm) to circuit complexity.


title: Boolean algebra

text: Whereas expressions denote mainly numbers in elementary algebra, in Boolean algebra, they denote the truth values "false" and "true". These values are represented with the bits (or binary digits), namely 0 and 1. They do not behave like the integers 0 and 1, for which , but may be identified with the elements of the two-element field GF(2), that is, integer arithmetic modulo 2, for which . Addition and multiplication then play the Boolean roles of XOR (exclusive-or) and AND (conjunction), respectively, with disjunction (inclusive-or) definable as and negation as . In GF(2), may be replaced by , since they denote the same operation; however this way of writing Boolean operations allows applying the usual arithmetic operations of integers (this may be useful when using a programming language in which GF(2) is not implemented).


title: Boolean algebra

text: A sequence of bits is a commonly used for such functions. Another common example is the subsets of a set "E": to a subset "F" of "E", one can define the indicator function that takes the value 1 on "F", and 0 outside "F". The most general example is the elements of a Boolean algebra, with all of the foregoing being instances thereof.


title: Boolean algebra

text: As with elementary algebra, the purely equational part of the theory may be developed, without considering explicit values for the variables.


title: Boolean algebra

text: The basic operations of Boolean algebra are conjunction, disjunction, and negation. These Boolean operations are expressed with the corresponding binary operators AND, and OR and the unary operator NOT, collectively referred to as Boolean operators.


title: Boolean algebra

text: Alternatively the values of "x"∧"y", "x"∨"y", and ¬"x" can be expressed by tabulating their values with truth tables as follows:


title: Boolean algebra

text: If the truth values 0 and 1 are interpreted as integers, these operations may be expressed with the ordinary operations of arithmetic (where "x" + "y" uses addition and "xy" uses multiplication), or by the minimum/maximum functions:


title: Boolean algebra

text: One might consider that only negation and one of the two other operations are basic, because of the following identities that allow one to define conjunction in terms of negation and the disjunction, and vice versa (De Morgan's laws):


title: Boolean algebra

text: The three Boolean operations described above are referred to as basic, meaning that they can be taken as a basis for other Boolean operations that can be built up from them by composition, the manner in which operations are combined or compounded. Operations composed from the basic operations include the following examples:


title: Boolean algebra

text: These definitions give rise to the following truth tables giving the values of these operations for all four possible inputs.


title: Boolean algebra

text: Given two operands, each with two possible values, there are 2 = 4 possible combinations of inputs. Because each output can have two possible values, there are a total of 2 = 16 possible binary Boolean operations. Any such operation or function (as well as any Boolean function with more inputs) can be expressed with the basic operations from above. Hence the basic operations are functionally complete.


title: Boolean algebra

text: A law of Boolean algebra is an identity such as between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡, but such extensions are unnecessary for the purposes to which the laws are put. Such purposes include the definition of a Boolean algebra as any model of the Boolean laws, and as a means for deriving new laws from old as in the derivation of from (as treated in "").


title: Boolean algebra

text: Boolean algebra satisfies many of the same laws as ordinary algebra when one matches up ∨ with addition and ∧ with multiplication. In particular the following laws are common to both kinds of algebra:


title: Boolean algebra

text: Taking in the third law above shows that it is not an ordinary algebra law, since . The remaining five laws can be falsified in ordinary algebra by taking all variables to be 1. For example, in Absorption Law 1, the left hand side would be , while the right hand side would be 1 (and so on).


title: Boolean algebra

text: All of the laws treated thus far have been for conjunction and disjunction. These operations have the property that changing either argument either leaves the output unchanged, or the output changes in the same way as the input. Equivalently, changing any variable from 0 to 1 never results in the output changing from 1 to 0. Operations with this property are said to be monotone. Thus the axioms thus far have all been for monotonic Boolean logic. Nonmonotonicity enters via complement ¬ as follows.


title: Boolean algebra

text: In both ordinary and Boolean algebra, negation works by exchanging pairs of elements, whence in both algebras it satisfies the double negation law (also called involution law)


title: Boolean algebra

text: The laws listed above define Boolean algebra, in the sense that they entail the rest of the subject. The laws "Complementation" 1 and 2, together with the monotone laws, suffice for this purpose and can therefore be taken as one possible "complete" set of laws or axiomatization of Boolean algebra. Every law of Boolean algebra follows logically from these axioms. Furthermore, Boolean algebras can then be defined as the models of these axioms as treated in "".


title: Boolean algebra

text: To clarify, writing down further laws of Boolean algebra cannot give rise to any new consequences of these axioms, nor can it rule out any model of them. In contrast, in a list of some but not all of the same laws, there could have been Boolean laws that did not follow from those on the list, and moreover there would have been models of the listed laws that were not Boolean algebras.


title: Boolean algebra

text: This axiomatization is by no means the only one, or even necessarily the most natural given that we did not pay attention to whether some of the axioms followed from others but simply chose to stop when we noticed we had enough laws, treated further in '. Or the intermediate notion of axiom can be sidestepped altogether by defining a Boolean law directly as any tautology, understood as an equation that holds for all values of its variables over 0 and 1. All these definitions of Boolean algebra can be shown to be equivalent.


title: Boolean algebra

text: There is nothing magical about the choice of symbols for the values of Boolean algebra. We could rename 0 and 1 to say "α" and "β", and as long as we did so consistently throughout it would still be Boolean algebra, albeit with some obvious cosmetic differences.


title: Boolean algebra

text: But suppose we rename 0 and 1 to 1 and 0 respectively. Then it would still be Boolean algebra, and moreover operating on the same values. However it would not be identical to our original Boolean algebra because now we find ∨ behaving the way ∧ used to do and vice versa. So there are still some cosmetic differences to show that we've been fiddling with the notation, despite the fact that we're still using 0s and 1s.


title: Boolean algebra

text: But if in addition to interchanging the names of the values we also interchange the names of the two binary operations, "now" there is no trace of what we have done. The end product is completely indistinguishable from what we started with. We might notice that the columns for and in the truth tables had changed places, but that switch is immaterial.


title: Boolean algebra

text: When values and operations can be paired up in a way that leaves everything important unchanged when all pairs are switched simultaneously, we call the members of each pair dual to each other. Thus 0 and 1 are dual, and ∧ and ∨ are dual. The Duality Principle, also called De Morgan duality, asserts that Boolean algebra is unchanged when all dual pairs are interchanged.


title: Boolean algebra

text: One change we did not need to make as part of this interchange was to complement. We say that complement is a self-dual operation. The identity or do-nothing operation "x" (copy the input to the output) is also self-dual. A more complicated example of a self-dual operation is . There is no self-dual binary operation that depends on both its arguments. A composition of self-dual operations is a self-dual operation. For example, if , then is a self-dual operation of four arguments "x", "y", "z", "t".


title: Boolean algebra

text: The principle of duality can be explained from a group theory perspective by the fact that there are exactly four functions that are one-to-one mappings (automorphisms) of the set of Boolean polynomials back to itself: the identity function, the complement function, the dual function and the contradual function (complemented dual). These four functions form a group under function composition, isomorphic to the Klein four-group, acting on the set of Boolean polynomials. Walter Gottschalk remarked that consequently a more appropriate name for the phenomenon would be the "principle" (or "square") "of quaternality".


title: Boolean algebra

text: A Venn diagram can be used as a representation of a Boolean operation using shaded overlapping regions. There is one region for each variable, all circular in the examples here. The interior and exterior of region "x" corresponds respectively to the values 1 (true) and 0 (false) for variable "x". The shading indicates the value of the operation for each combination of regions, with dark denoting 1 and light 0 (some authors use the opposite convention).


title: Boolean algebra

text: The three Venn diagrams in the figure below represent respectively conjunction "x"∧"y", disjunction "x"∨"y", and complement ¬"x".


title: Boolean algebra

text: For conjunction, the region inside both circles is shaded to indicate that "x"∧"y" is 1 when both variables are 1. The other regions are left unshaded to indicate that "x"∧"y" is 0 for the other three combinations.