title: William Hogarth

text: Later prints of significance include his pictorial warning of the consequences of alcoholism in "Beer Street" and "Gin Lane" (1751). Hogarth engraved "Beer Street" to show a happy city drinking the 'good' beverage, English beer, in contrast to "Gin Lane", in which the effects of drinking gin are shown – as a more potent liquor, gin caused more problems for society. There had been a sharp increase in the popularity of gin at this time, which was called the 'Gin Craze.' It started in the early 18th century, after a series of legislative actions in the late 17th century impacted the importation and manufacturing of alcohol in London. Among these, were the Prohibition of 1678, which barred popular French brandy imports, and the forced disbandment, in 1690, of the London Guild of Distillers, whose members had previously been the only legal manufacturers of alcohol, leading to an increase in the production and then consumption of domestic gin.


title: William Hogarth

text: In "Beer Street", people are shown as healthy, happy and prosperous, while in "Gin Lane", they are scrawny, lazy and careless. The woman at the front of "Gin Lane", who lets her baby fall to its death, echoes the tale of Judith Dufour, who strangled her baby so she could sell its clothes for gin money. The prints were published in support of the Gin Act 1751.


title: William Hogarth

text: Hogarth's friend, the magistrate Henry Fielding, may have enlisted Hogarth to help with propaganda for the Gin Act; "Beer Street" and "Gin Lane" were issued shortly after his work "An Enquiry into the Causes of the Late Increase of Robbers, and Related Writings", and addressed the same issues.


title: William Hogarth

text: Other prints were his outcry against inhumanity in "The Four Stages of Cruelty" (published 21 February 1751), in which Hogarth depicts the cruel treatment of animals which he saw around him and suggests what will happen to people who carry on in this manner. In the first print, there are scenes of boys torturing dogs, cats and other animals. It centers around a poorly dressed boy committing a violent act of torture upon a dog, while being pleaded with to stop, and offered food, by another well-dressed boy. A boy behind them has graffitied a hanged stickman figure upon a wall, with the name "Tom Nero" underneath, and is pointing to this dog torturer.


title: William Hogarth

text: The second shows Tom Nero has grown up to become a Hackney coach driver. His coach has overturned with a heavy load and his horse is lying on the ground, having broken its leg. He is beating it with the handle of his whip; its eye severely wounded. Other people around him are seen abusing their work animals and livestock, and a child is being run over by the wheel of a dray, as the drayman dozes off on the job.


title: William Hogarth

text: In the third print, Tom is shown to be a murderer, surrounded by a mob of accusers. The woman he has apparently killed is lying on the ground, brutally slain, with a trunk and sack of stolen goods near by. One of the accusers holds a letter from the woman to Tom, speaking of how wronging her mistress upsets her conscience, but that she is resolved to do as he would have her, closing with: "I remain yours till death."


title: William Hogarth

text: The fourth, titled "The Reward of Cruelty", shows Tom's withering corpse being publicly dissected by scientists after his execution by hanging; a noose still around his neck. The dissection reflects the Murder Act 1751, which allowed for the public dissection of criminals who had been hanged for murder.


title: William Hogarth

text: Hogarth was also popular portrait painter. In 1745, he painted actor David Garrick as Richard III, for which he was paid £200, "which was more", he wrote, "than any English artist ever received for a single portrait." In 1746, a sketch of Simon Fraser, 11th Lord Lovat, afterwards beheaded on Tower Hill, had an exceptional success.


title: William Hogarth

text: In 1740, he created a truthful, vivid full-length portrait of his friend, the philanthropic Captain Coram, for the Thomas Coram Foundation for Children, now in the Foundling Museum. This portrait, and his unfinished oil sketch of a young fishwoman, entitled "The Shrimp Girl" (National Gallery, London), may be called masterpieces of British painting. There are also portraits of his wife, his two sisters, and of many other people; among them Bishop Hoadly and Bishop Herring.


title: William Hogarth

text: For a long period, during the mid-18th century, Hogarth tried to achieve the status of a history painter, but did not earn much respect in this field. The painter, and later founder of the Royal Academy of Arts, Joshua Reynolds, was highly critical of Hogarth's style and work. According to art historian David Bindman, in Dr Johnson's serial of essays for London's "Universal Chronicle", "The Idler", the three essays written by Reynolds for the months of September through November 1759 are directed at Hogarth. In them, Reynolds argues that this "connoisseur" has a "servile attention to minute exactness" and questions their idea of the imitation of nature as "the obvious sense, that objects are represented naturally when they have such relief that they seem real." Reynolds rejected "this kind of imitation", favouring the "grand style of painting" which avoids "minute attention" to the visible world. In Reynolds' "Discourse XIV", he grants Hogarth has "extraordinary talents", but reproaches him for "very imprudently, or rather presumptuously, attempt[ing] the great historical style."


title: William Hogarth

text: Writer, art historian and politician, Horace Walpole, was also critical of Hogarth as a history painter, but did find value in his satirical prints.


title: William Hogarth

text: Hogarth's history pictures include "The Pool of Bethesda" and "The Good Samaritan", executed in 1736–1737 for St Bartholomew's Hospital; "Moses brought before Pharaoh's Daughter", painted for the Foundling Hospital (1747, formerly at the Thomas Coram Foundation for Children, now in the Foundling Museum); "Paul before Felix" (1748) at Lincoln's Inn; and his altarpiece for St. Mary Redcliffe, Bristol (1755–56).


title: William Hogarth

text: "The Gate of Calais" (1748; now in Tate Britain) was produced soon after his return from a visit to France. Horace Walpole wrote that Hogarth had run a great risk to go there since the peace of Aix-la-Chapelle: he went to France, and was so imprudent as to be taking a sketch of the drawbridge at Calais. He was seized and carried to the governor, where he was forced to prove his vocation by producing several caricatures of the French; particularly a scene of the shore, with an immense piece of beef landing for the "Lion d'argent", the English inn at Calais, and several hungry friars following it. They were much diverted with his drawings, and dismissed him.


title: William Hogarth

text: Back home, he immediately executed a painting of the subject in which he unkindly represented his enemies, the Frenchmen, as cringing, emaciated and superstitious people, while an enormous sirloin of beef arrives, destined for the English inn as a symbol of British prosperity and superiority. He claimed to have painted himself into the picture in the left corner sketching the gate, with a "soldier's hand upon my shoulder", running him in.


title: William Hogarth

text: Notable Hogarth engravings in the 1740s include "The Enraged Musician" (1741), the six prints of "Marriage à-la-mode" (1745; executed by French artists under Hogarth's inspection), and "The Stage Coach or The Country Inn Yard" (1747).


title: William Hogarth

text: In 1745, Hogarth painted a self-portrait with his pug dog, Trump (now also in Tate Britain), which shows him as a learned artist supported by volumes of Shakespeare, Milton and Swift. In 1749, he represented the somewhat disorderly English troops on their "March of the Guards to Finchley" (formerly located in Thomas Coram Foundation for Children, now Foundling Museum).


title: William Hogarth

text: Others works included his ingenious "Satire on False Perspective" (1754); his satire on canvassing in his "Election" series (1755–1758; now in Sir John Soane's Museum); his ridicule of the English passion for cockfighting in "The Cockpit" (1759); his attack on Methodism in "Credulity, Superstition, and Fanaticism" (1762); his political anti-war satire in "The Times", plate I (1762); and his pessimistic view of all things in "Tailpiece, or The Bathos" (1764).


title: William Hogarth

text: Hogarth wrote and published his ideas of artistic design in his book "The Analysis of Beauty" (1753). In it, he professes to define the principles of beauty and grace which he, a real child of Rococo, saw realized in serpentine lines (the Line of Beauty). By some of Hogarth's adherents, the book was praised as a fine deliverance upon aesthetics; by his enemies and rivals, its obscurities and minor errors were made the subject of endless ridicule and caricature. For instance, Paul Sandby produced several caricatures against Hogarth's treatise. Hogarth wrote also a manuscript called "Apology for Painters" (c.1761) and unpublished "autobiographical notes".


title: William Hogarth

text: Hogarth lived in an age when artwork became increasingly commercialized, being viewed in shop windows, taverns, and public buildings, and sold in printshops. Old hierarchies broke down, and new forms began to flourish: the ballad opera, the bourgeois tragedy, and especially, a new form of fiction called the novel with which authors such as Henry Fielding had great success. Therefore, by that time, Hogarth hit on a new idea: "painting and engraving modern moral subjects ... to treat my subjects as a dramatic writer; my picture was my stage", as he himself remarked in his manuscript notes.


title: William Hogarth

text: He drew from the highly moralizing Protestant tradition of Dutch genre painting, and the very vigorous satirical traditions of the English broadsheet and other types of popular print. In England the fine arts had little comedy in them before Hogarth. His prints were expensive, and remained so until early 19th-century reprints brought them to a wider audience.


title: William Hogarth

text: When analysing the work of the artist as a whole, Ronald Paulson says, "In "A Harlot's Progress", every single plate but one is based on Dürer's images of the story of the Virgin and the story of the Passion." In other works, he parodies Leonardo da Vinci's Last Supper. According to Paulson, Hogarth is subverting the religious establishment and the orthodox belief in an immanent God who intervenes in the lives of people and produces miracles. Indeed, Hogarth was a Deist, a believer in a God who created the universe but takes no direct hand in the lives of his creations. Thus, as a "comic history painter", he often poked fun at the old-fashioned, "beaten" subjects of religious art in his paintings and prints. Hogarth also rejected Lord Shaftesbury's then-current ideal of the classical Greek male in favour of the living, breathing female. He said, "Who but a bigot, even to the antiques, will say that he has not seen faces and necks, hands and arms in living women, that even the Grecian Venus doth but coarsely imitate."


title: William Hogarth

text: On 23 March 1729, Hogarth eloped with Jane Thornhill at Paddington Church, against the wishes of her father, the artist Sir James Thornhill.


title: William Hogarth

text: Sir James saw the match as unequal, as Hogarth was a rather obscure artist at the time. However, when Hogarth started on his series of moral prints, "A Harlot's Progress", some of the initial paintings were placed either in Sir James' drawing room or dining room, through the conspiring of Jane and her mother, in the hopes of reconciling him with the couple. When he saw them, he inquired as to the artist's name and, upon hearing it, replied: "Very well; the man who can produce such representations as these, can also maintain a wife without a portion." However, he soon after relented, becoming more generous to, and living in harmony with the couple until his death.


title: William Hogarth

text: Hogarth was initiated as a Freemason before 1728 in the Lodge at the Hand and Apple Tree Tavern, Little Queen Street, and later belonged to the Carrier Stone Lodge and the Grand Stewards' Lodge; the latter still possesses the 'Hogarth Jewel' which Hogarth designed for the Lodge's Master to wear. Today the original is in storage and a replica is worn by the Master of the Lodge. Freemasonry was a theme in some of Hogarth's work, most notably 'Night', the fourth in the quartet of paintings (later released as engravings) collectively entitled the "Four Times of the Day".


title: William Hogarth

text: His main home was in Leicester Square (then known as Leicester Fields), but he bought a country retreat in Chiswick in 1749, the house now known as Hogarth's House and preserved as a museum, and spent time there for the rest of his life.


title: William Hogarth

text: The Hogarths had no children, although they fostered foundling children. He was a founding Governor of the Foundling Hospital.


title: William Hogarth

text: Among his friends and acquaintances were many English artists and satirists of the period, such as Francis Hayman, Henry Fielding, and Laurence Sterne.


title: William Hogarth

text: On 25 October 1764, Hogarth was conveyed from his villa in Chiswick to his home in Leicester Fields, in weak condition. He had been in a weakened state for a while by this time, but was said to be in a cheerful mood and was even still working—with some help; doing more retouches on "The Bench" on this same day. On 26 October, he received a letter from Benjamin Franklin and wrote up a rough draught in reply. Before going to bed that evening, he'd boasted about eating a pound of beefsteaks for dinner and reportedly looked more robust than he had in a while at this time. However, when he went to bed, he suddenly began vomiting; something that caused him to ring his bell so forcefully that it broke. Hogarth passed away around two hours later, in the arms of his servant, Mrs Mary Lewis. John Nichols claimed that he died of an aneurysm, which he said took place in the "chest." Horace Walpole claimed that he died of "a dropsy of his breast."


title: William Hogarth

text: Mrs Lewis, who stayed on with Jane Hogarth in Leicester Fields, was the only non-familial person acknowledged financially in Hogarth's will and was left £100 (approximately £18,651.61 in 2020) for her "faithful services."


title: William Hogarth

text: Hogarth was buried at St. Nicholas Church, Chiswick, now in the west of London. His friend, actor David Garrick, composed the following inscription for his tombstone:


title: William Hogarth

text: Hogarth's works were a direct influence on John Collier, who was known as the "Lancashire Hogarth". The spread of Hogarth's prints throughout Europe, together with the depiction of popular scenes from his prints in faked Hogarth prints, influenced Continental book illustration through the 18th and early 19th centuries, especially in Germany and France. He also influenced many caricaturists of the 18th, 19th and 20th centuries. Hogarth's influence lives on today as artists continue to draw inspiration from his work.


title: William Hogarth

text: Hogarth's paintings and prints have provided the subject matter for several other works. For example, Gavin Gordon's 1935 ballet "The Rake's Progress", to choreography by Ninette de Valois, was based directly on Hogarth's series of paintings of that title. Igor Stravinsky's 1951 opera "The Rake's Progress", with libretto by W. H. Auden, was less literally inspired by the same series. Hogarth's engravings also inspired the BBC radio play "The Midnight House" by Jonathan Hall, based on the M. R. James ghost story "The Mezzotint" and first broadcast on BBC Radio 4 in 2006.


title: William Hogarth

text: Russell Banks' short story "Indisposed" is a fictional account of Hogarth's infidelity as told from the viewpoint of his wife, Jane. Hogarth was the lead character in Nick Dear's play "The Art of Success", whilst he is played by Toby Jones in the 2006 television film "A Harlot's Progress".


title: William Hogarth

text: Hogarth's House in Chiswick, west London, is now a museum; the major road junction next to it is named the Hogarth Roundabout. In 2014 both Hogarth's House and the Foundling Museum held special exhibitions to mark the 250th anniversary of his death.


title: William Hogarth

text: In 2019, Sir John Soane's Museum, which owns both "The Rake's Progress" and "The Humours of an Election", held an exhibition which assembled all Hogarth's series of paintings, and his series of engravings, in one place for the first time.


title: William Hogarth

text: Stanley Kubrick based the cinematography of his 1975 period drama film, "Barry Lyndon", on several Hogarth paintings.


title: William Hogarth

text: In Roger Michell's 2003 film "The Mother", starring Anne Reid and Daniel Craig, the protagonists visit Hogarth's tomb during their first outing together. They read aloud the poem inscribed there and their shared admiration of Hogarth helps to affirm their connection with one another.


title: Cassandra Lang

text: Cassandra "Cassie" Lang is a fictional character appearing in American comic books published by Marvel Comics. The daughter of Scott Lang, the character first appeared in "Marvel Premiere" #47 (April 1979) as Cassie Lang, in "Young Avengers" #6 (May 2006) as Stature and in "The Astonishing Ant-Man" #6 (May 2016) as Stinger. A member of the Young Avengers and The Initiative and love interest of Iron Lad, she has the same powers as her father, the ability to shrink and grow in size, although she manifested these powers long after her first exposure to Pym Particles.


title: Cassandra Lang

text: In the Marvel Cinematic Universe (MCU), the character was portrayed by Abby Ryder Fortson as a child in "Ant-Man" (2015) and "Ant-Man and the Wasp" (2018), by Emma Fuhrmann as a teenager in "" (2019), and will be portrayed by Kathryn Newton in "" (2023).


title: Cassandra Lang

text: Created by David Michelinie and John Byrne, Cassie Lang first appeared in "Marvel Premiere" #47 (April 1979). She first appeared as Stature in "Young Avengers" #6 (May 2006), and adopted the identity of Stinger in "The Astonishing Ant-Man" #6 (May 2016).


title: Cassandra Lang

text: Cassie Lang is introduced to the Marvel Universe as the ill daughter of Scott Lang. Her congenital heart condition forces her father to steal Hank Pym's Ant-Man equipment and Pym Particles, which he uses to rescue Doctor Sondheim, the only doctor able to cure Cassie's condition, from Cross Technological Enterprises.


title: Cassandra Lang

text: After the divorce of her parents, Cassie lives for most of her childhood with her father, whom she loves and admires greatly. Although Scott tries his best to keep his superhero life secret, Cassie gradually finds out that he is Ant-Man, and secretly experiments with his Pym Particle supplies on her own. She is fascinated by her father's life as a superhero, and generally has a good relationship with her father's colleagues; when she was younger, she even called Tony Stark "Uncle Tony".


title: Cassandra Lang

text: Scott's time as an engineer for the Fantastic Four brings Cassie to the team's then-headquarters of Four Freedoms Plaza. In the spectacular environment Cassie calls home, she forges a strong friendship with the former ward of Doctor Doom, Kristoff Vernard. During the time they share a home with the Fantastic Four, Cassie helps Kristoff adjust to life outside of Doom's castle, and she develops a crush on him. It is also during this time that she meets her father in his Ant-Man identity, and confesses that she had known about it for a long time.


title: Cassandra Lang

text: After the Fantastic Four go missing and Cassie's father finds himself without a job, Scott takes employment at Oracle, Inc. with the Heroes for Hire (H4H). While working with the Heroes for Hire, Cassie has further adventures, accidentally activating the Super-Adaptoid and receiving horrifying visions of things to come. The H4H easily defeated Super-Adaptoid, and Cassie's participation in these dark events help her father and his allies defeat Master of the World in a battle for the fate of the Earth. All of these adventures give Cassie a taste for the action-filled life of a superhero, but it causes her mother Peggy to take sole custody from Scott.


title: Cassandra Lang

text: As a result of Cassie being kept away from her father Scott, she grows more and more bitter toward her mother, and even more so toward her stepfather Blake Burdick. As a police officer, he cannot stand the world of superheroes the young girl loves, and he unsuccessfully tries to keep Cassie and Scott apart. For years, Cassie visits her father whenever possible, much to her mother and stepfather's chagrin, until the events of "Avengers Disassembled", when Scott is killed due to the actions of an insane Scarlet Witch.


title: Cassandra Lang

text: Cassie retreats into herself, blaming Blake for being unable to understand her as her father always did. Blake tries unsuccessfully to be a caring stepfather, despite being sometimes distant toward her, seeing his stepdaughter as a "less than brilliant" girl. Some time after her father's death, and after another confrontation with her mother and stepfather, Cassie decides to run away to Los Angeles to join the Runaways, but after seeing the "Young Avengers" on television just before leaving, she subsequently changes her plans, as she later tells Jessica Jones.


title: Cassandra Lang

text: Iron Lad, a younger version of classic Avengers foe Kang the Conqueror, desperate for help against his future self after learning what he will become, uses the Vision's database to track and recruit young superpowered individuals connected to the Avengers' history; however, Cassie Lang is not one of the individuals on the list. Wishing to join the Young Avengers, she and Kate Bishop meet the young heroes at the Avengers Mansion; when they refuse to let them join or to let her take her father's gear, she angrily rebukes them, only to discover much to her own shock that by doing so she had increased her size. She later confesses that she had repeatedly stolen Pym particles from her father for years, but until then it seemed they never had any effect on her. Cassie later displays the ability to also shrink.


title: Cassandra Lang

text: Iron Lad assures her that if Vision had known she had developed powers, she would have been part of his plans for the Young Avengers, thus accepting her as a teammate; she then takes part in the battle against Kang, which ends in the villain's defeat. However, as the altered timeline causes several of them to disappear, Iron Lad realizes that he must return to his own time and accept the fact that he will become Kang, much to Cassie's sorrow, as she had fallen in love with him.


title: Cassandra Lang

text: While Captain America and Iron Man order the team to disband, both Cassie and Kate refuse and convince the others to keep the team active; after initially considering Ant-Girl or Giant-Girl, she ultimately adopts the codename Stature, along with a new costume based on her father's. Despite this, she feels guilty when overhearing her mother and stepfather discussing the possibility of her being a member of the team, also showing that rage or guilt make her respectively grow or shrink, metaphorically reflecting her being a "shrinking violet" about her family issues. After deciding to continue her life as a superhero, Cassie overhears her stepfather talking to her mother. They suspect that she is secretly Stature, but refuse to believe it. Later, Jessica Jones talks to Cassie's mother and confirms Cassie's dual identity. Cassie's mother is overwhelmed by this news and begs Jessica not to tell her husband about this due to his hatred of superheroes; she also worries that although Cassie was cured of her heart condition, her heart might not be able to handle the strain of continuous size-changing.


title: Cassandra Lang

text: When Jessica Jones asks Cassie if there isn't even a small part of her wishing for a normal life, Cassie replies, "Ms. Jones, my dad was Ant-Man. I never had a normal life."


title: Cassandra Lang

text: In the "Civil War" limited series, Cassie, along with her fellow Young Avengers, join Captain America's resistance to the Superhero Registration Act; she and the rest of her team stay at a safe house, while Nick Fury arranges new secret identities for them. During this time, she participates in a rescue effort, which turns out to be a trap laid by Iron Man: during the subsequent battle, Goliath is killed by a clone of Thor and her teammate Wiccan is captured. Afterwards, Cassie opts to leave Captain America's side and to register, citing her reasons as wishing to fight villains rather than cops and other heroes.


title: Cassandra Lang

text: Cassie Lang joins the Initiative, as a trainee. Along with fellow Initiative members Dusk, Tigra, Silverclaw, and Araña, she is ensnared by the Puppet Master. Although she (along with the others) is mentally controlled into fighting Ms. Marvel, she is eventually freed from the mind control.


title: Cassandra Lang

text: Her time at Camp Hammond brings her in to contact with her father's successor as Ant-Man: Eric O'Grady. O'Grady makes several disparaging remarks about her father, not realizing that she is within earshot; this causes a literally giant-sized brawl between the two as both grow to their giant forms. After O'Grady picks up a bus and hits Lang with it, Henry Pym intervenes. Taskmaster breaks up the fight by attacking their now giant-sized Achilles tendons, bringing all three crashing to the ground.


title: Cassandra Lang

text: Later, the Vision visits Cassie, disguising himself as Tony Stark in order to take her out on a date. After fighting off an attempt by A.I.M. to steal the Vision, he confesses that because he was programmed based on Iron Lad's mental patterns, he shares Iron Lad's attraction to her, and hopes that she can love him; Cassie is unsure, but does not reject him, telling him to give her time to sort things out.


title: Cassandra Lang

text: Cassie accidentally injures her stepfather Blake while stopping the Growing Man. Her guilt causes her to continue shrinking down, and the other Young Avengers attempt to snap her out of it before she shrinks into non-existence. With the help of Patriot, she comes to terms with the responsibilities and risks of her position as part of the Young Avengers and the Initiative, reasoning that Blake also faces the risks as a policeman.


title: Cassandra Lang

text: Stature fights against the Skrull invasion of Manhattan as part of the Initiative. She grows larger than the Skrull Yellowjacket and punches him out.


title: Cassandra Lang

text: In the aftermath of the Skrull invasion, Cassie Lang leaves the Initiative at the start of the "Dark Reign" storyline and rejoins the Young Avengers. Cassie and Vision (now seemingly in a relationship) fly to the Avengers Mansion ruins, having been summoned by Wiccan with warnings of a great magical threat. After finding their teammates turned to stone, they encounter the Scarlet Witch transporting them away to be a part of the Mighty Avengers, led by Hank Pym. Despite her evident and vocal distrust of Scarlet Witch, whom she holds responsible for her father's death, she remains on the team. During a confrontation with the Fantastic Four for a device of the late Bill Foster, she refuses to participate in the attack and instead warns them about what was really happening, citing her reluctance to fight those she feels are like family to her. Eventually, Cassie's distrust of Scarlet Witch leads her to expose her as Loki in disguise. While part of the team, Lang also fights a demi-god at Mount Wundagore and a homicidal ancient Inhuman.


title: Cassandra Lang

text: Norman Osborn later mounts a full-scale attack on Asgard. Teaming up with the rest of the Mighty Avengers one last time, Cassie and Vision help stop the Thunderbolts from delivering Odin's Spear (an Asgardian weapon of virtually limitless power) to the Iron Patriot; in the battle, she also fights the new Ant-Man again.


title: Cassandra Lang

text: At some point, Cassie applies for a babysitter job with Jessica Jones and Luke Cage, though more in the hope of eventually finding her way into the ranks of the New Avengers rather than any dedication to babysitting itself; she is dismissed in favor of Squirrel Girl.


title: Cassandra Lang

text: When Wiccan's uncontrolled magical energy nearly kills several members of the Sons of the Serpent, the Avengers begin to fear that he might become another Scarlet Witch; they explain to the Young Avengers how the Scarlet Witch went insane after the loss of her twin boys, resulting in the death of the original Vision and Scott Lang, and rendering nearly all of the world's mutants powerless. When Wiccan feels unsure about what to do, Cassie suggests that they try to find the Scarlet Witch, believing that if they can show her that her children are alive, she may be able to reverse everything she has done, including her father's death.


title: Cassandra Lang

text: During the team's search in Latveria, Cassie is reunited with Iron Lad, and, when he takes the team back to the period of Avengers Disassembled, she is able to bring her father forward in time to the present, avoiding his original death from the attack by Jack of Hearts. After she manifests her powers in front of him, Scott tells her he's proud of her.


title: Cassandra Lang

text: After the Scarlet Witch is found, Dr. Doom steals her reality warping powers and fights the combined forces of the Avengers and X-Men. As Doom seemingly kills her father (who actually managed to shrink down and escape with minor wounds), a distraught Cassie charges the super-powered dictator, gaining time for Scarlet Witch and Wiccan to prepare a joint spell to remove his new powers; however, Doom retaliates by blasting Cassie with an explosive spell, killing her. Although Iron Lad offers to take her into the future to save her, his offer is rejected by the other Young Avengers, as it is more in line with what Kang would do than what an Avenger should do. While contemplating rebuilding the Vision (who Iron Lad destroyed in rage when he protested against his plans to save Cassie), the Young Avengers realize that they would have to tell a restored Vision about Cassie's death, and thus decide not to follow through with the rebuilding. Kate expresses her desire to believe that Vision and Cassie are somehow together in the afterlife. The team disbands and a statue of Cassie and the Vision's is built in their honor in the gardens of the mansion.


title: Cassandra Lang

text: Bentley 23 (a clone of Wizard) of the Future Foundation later postulates that, due to the unstable nature of Pym Particles, Cassie's body could conceivably regenerate into an ionic form similar to the resurrection of Wonder Man; he suggests digging up the corpse to check, stating that he is sure his classmates are thinking the same thing.


title: Cassandra Lang

text: During the "AXIS" storyline, Doctor Doom is transformed into a more heroic, altruistic form as a result of the battle with the Red Skull that involved a spell that inverted heroes and villains' personalities. Seeking redemption for his past crimes, but only able to draw on enough power to alter one key event, Doom chooses to use that power to resurrect Cassie. She is then seen tearfully reuniting with her father and his new girlfriend Darla Deering.


title: Cassandra Lang

text: In the "Ant-Man" ongoing series, she is shown living a normal life as a middle-school student. Worried that Scott's lifestyle and actions might attract more danger to her, Cassie's mother decides to relocate to Miami despite Cassie's reluctance. Scott nonetheless decides to relocate there as well to stay near his daughter. She is later kidnapped by Crossfire on behalf of Augustine Cross of Cross Technological Enterprises; Cross believes that Cassie's Pym Particle-irradiated heart can sustain Darren Cross's sickly body. Scott didn't arrive in time to prevent the transplant of Cassie's heart (which caused the revived Darren Cross to shrink uncontrollably) and so Dr. Sondheim was forced to transplant another one in Cassie's body, with Scott slowing down her immune system enough to make sure it is not rejected. While Cassie survived, not knowing herself what had happened to her, Scott was so shaken up by that experience that he decided to leave her, reasoning that he cannot risk to put her in harm's way again and that she deserves a normal and happy life he cannot provide.


title: Cassandra Lang

text: A now depowered Cassie struggles with her everyday activities, while feeling frustrated by her current status; feeling resentful over Scott's seeming disappearance, she is later shocked and outraged to find out that he was secretly following her around, watching over her. One day, she is reunited with Kate, who has found out about her resurrection; despite her lack of powers, she follows her friend to a Secret Empire hideout, but almost gets killed, which further fuels her frustration, despite Kate's assurances that she is still special her own way. However, Cassie ultimately decides to turn to the new Power Broker to regain her powers; although he realizes that she has no intention of actually becoming a supervillain, he tells her about Darren Cross having stolen her heart and that her father hid it from her. Power Broker offers a deal, in which he will grant her wish if she infiltrates Cross' base to shut him down; Cassie accepts, and adopts the new codename Stinger. When Scott learns about her disappearance, he rushes to help her, but ends up captured in her place; however, Cassie manages to get his crew to help him escape. In the end, though, because of Darla's show, they end up discovered by the police; to protect his daughter, Scott takes the blame and claims he kidnapped and forced her to help him. Cassie captures Power Broker shortly after her father's arrest. When Cassie finally confesses to her mother what she did, Peggy takes her to the trial, where Darren Cross in the Yellowjacket suit and his henchmen (Crossfire and Egghead) burst into the courtroom to get revenge on Scott. Cassie rushes to help her father, and the two make amends during the fight, which ends with Cassie defeating Cross. Cassie's mother is called as the final prosecution witness, but surprisingly she declares that Scott was innocent, as he always looked after Cassie and has always been her hero, admitting that he took the blame for what she did; this allowed Scott to be acquitted. Afterward, Cassie finally receives her mother's blessing as a superhero, and joins her father as a new crimefighting duo.


title: Cassandra Lang

text: Cassie Lang has the ability to increase and decrease her size. She can become roughly tall and can shrink to the size of an ant. Her abilities seemed to be fueled by her emotions. She grows when she gets angry and shrinks when she feels guilty. Cassie seems to have become more powerful since first demonstrating her powers, as she has in recent issues surpassed her previous growth limit. At first she struggled to shrink to 6 inches and grow to 10–15 feet. She has been seen growing larger than the Skrull Yellowjacket, who could grow to at least tall. It was established that she and Hank Pym share an upper limit of somewhere around in height, and that, if she keeps her bigger dimensions for too long, Cassie will suffer from strains that will eventually force her to shrink back down.


title: Cassandra Lang

text: As Stinger, she has a helmet similar to that of Ant-Man, which allows her to communicate with and control "over five thousands species of ants and insects"; she also sports a suit with bio-synthetic wings that allow her to fly, and that can fire bio-electric blasts from the wrists.


title: Cassandra Lang

text: In MC2, Cassandra Lang is now a doctor and operates under the name Stinger on the group A-Next. Although she is the oldest member of A-Next, in her mid-20s, and the only one on the original team with a professional life and a scientific background, she is still doted on by her father, who constantly worries about her newfound superhero life. She possesses many abilities originally engineered by Henry Pym, including resizing, flying, communication with insects, and firing bioelectric "stinger" blasts (as well artificial "stingers" sedative darts), all based on her costume and helmet. She does not seem to be capable of increasing her size and strength, unlike her main continuity version.


title: Cassandra Lang

text: In issue 3 of "Avengers Fairy Tales", Cassie Lang is portrayed as Alice of "Alice in Wonderland". She encounters Wonderland versions of the Young Avengers. At first, her emotions cause her to grow and shrink beyond her control. She also meets Wonderland versions of Ant-Man (Scott Lang) and Tigra.


title: Cassandra Lang

text: Cassie Lang, under the codename Stature, went with her team on the search for the Scarlet Witch. In the alternate future timeline glimpsed during the "Children's Crusade", Cassie was shown as a member of the future Avengers under the codename Stinger. It was later revealed that it had been Wiccan, now renamed Sorcerer Supreme, posing as Stinger to get Iron Lad to go back in time.


title: Cassandra Lang

text: The Ultimate Marvel version of Cassie Lang appears in "" initially as Giant-Woman, and later as Stature. A member of the Ultimates Reserves' Giant-Women squad, she was brainwashed by Thor's son Modi to battle Spider-Man but is defeated. Giant-Woman later recovers and rescues the shot down S.H.I.E.L.D. Helicarrier during a skirmish with HYDRA. Monica Chang subsequently offers Giant-Woman a spot on the Ultimates due to the bravery she displayed during the battle with HYDRA. However, Stature later resurfaced as a member of Nick Fury's Howling Commandos, as assistance against the Maker's Dark Ultimates.


title: Cassandra Lang

text: Cassie Lang appears in films set in the Marvel Cinematic Universe. She first appears as a child in the films "Ant-Man" and "Ant-Man and the Wasp", portrayed by Abby Ryder Fortson, before appearing as a teenager in "", portrayed by Emma Fuhrmann, and as an adult in the upcoming film "", portrayed by Kathryn Newton.


title: Cassandra Lang

text: Cassie Lang is referenced in the mc chris song "Nrrrd Grrrl": "Wanna conquer her like Kang, When you kiss like Cassie Lang".


title: Patrick Bergin

text: Patrick Connolly Bergin (born 4 February 1951) is an Irish actor and singer perhaps best known for his leading role opposite Julia Roberts in "Sleeping with the Enemy" (1991), the title character in Robin Hood (1991 film), terrorist Kevin O'Donnell in Patriot Games and for playing the villainous Aidan Maguire in the BBC soap "EastEnders" in 2017–2018.


title: Patrick Bergin

text: Bergin was born in Dublin. His father, Patrick Bergin snr., was a Labour Party politician who once studied to be a priest with the Holy Ghost Fathers in Blackrock, Ireland. Patrick was one of four sons and one daughter (Pearse, Emmet, Patrick, Allen and Siobhan Bergin). He left Dublin for London in 1973, and by the time he was 17 he was in London running a theatre company. He worked on building sites and at a library. He studied at night and completed an education degree from North London Polytechnic. He was an English teacher for several years, then formed his own theatrical company because "no one else would have him".


title: Patrick Bergin

text: In 1980, Bergin decided to pursue acting full-time and found work in repertory theatre. For much of the 1990s it seemed that no one in Hollywood was interested in him. He accepted diverse acting roles, including a trilogy of Yeats plays; "Morphine and Dolly Mixtures", for which he won a BAFTA Cymru Award for Best Actor; "Durango", based on John B Keane's novel; hosting "TnaG's Silín Draíochta"; and narrating "Patrick Cassidy's Famine Concert". After "Sleeping with the Enemy" (1991), he portrayed the title character in "Robin Hood", opposite Uma Thurman as Maid Marian. He describes 1996 as the lowest point in his career, a time when he rarely received any calls for movie roles.


title: Patrick Bergin

text: Internationally, Bergin's best-known role may be that of the menacing husband of Julia Roberts' character in the thriller "Sleeping with the Enemy". He is also known for his role as Irish terrorist Kevin O'Donnell in the film adaptation of Tom Clancy's "Patriot Games". He also appeared as Robin Hood in a 1991 film. In 2013 he appeared in the Scottish film "The Wee Man" playing notorious Glasgow gangster Arthur 'The Godfather' Thompson. He joined the BBC soap "EastEnders" towards the end of 2017, departing in March 2018.


title: Patrick Bergin

text: Bergin currently leads the band Patrick Bergin and the Spirit Merchants. They had a top 10 hit in Ireland with their song "The Knacker", released in 2003, which tells the story of a person who recycles horse carcasses and turns them into glue. As a singer, Bergin collaborated with Vlad DeBriansky and appeared on his album "Jacks Last Dollar".


title: Patrick Bergin

text: Bergin was onstage singing the Leonard Cohen song "Anthem" as Pope Francis, on his visit to Ireland, arrived in Croke Park for the Festival of Families as part of the World Meeting of Families 2018.


title: Patrick Bergin

text: In 1993, Bergin bought an old church in Tipperary and converted it into a poetry centre. He explained: "I've recently come to feel I can encourage children and teenagers with their writing. I'm continually giving groups money to make videos, but I insist that they have a good script. I do it because it makes the difference between them doing a video or not. It doesn't cost a lot, and it gives kids an incredible boost of confidence." In 1998, in response to the murder of a 14-year-old Tallaght boy, Ben Smyth, Bergin helped to establish a special fund to sponsor young children from Tallaght.


title: Patrick Bergin

text: At a wedding in the early 1980s, Bergin met his future wife, Paula Frazier, a British woman of Afro-Caribbean descent. They married in Trinidad and Tobago in 1992. They have a daughter, Tatiana (Tia). After their divorce, Bergin began dating Helen Goldin.


title: BJ's Wholesale Club

text: BJ's Wholesale Club Holdings, Inc., commonly referred as BJ's, is an American membership-only warehouse club chain based in Marlborough, Massachusetts, operating on the East Coast of the United States in addition to Ohio and Michigan, with plans to expand into Indiana.


title: BJ's Wholesale Club

text: The company was started by discount department store chain Zayre in 1984, on the Medford/Malden border in Massachusetts. The company's name was derived from the initials of Beverly Jean Weich, the daughter of Mervyn Weich, the president of the new company. Weich announced his resignation as president in June 1987, and left on August 1. He was replaced by John Levy.


title: BJ's Wholesale Club

text: When Zayre Corporation sold the Zayre nameplate to rival discount chain Ames in October 1988, TJX Companies was formed. In 1989, TJX spun off their warehouse division, consisting of BJ's and now-defunct HomeClub (later known as HomeBase, then House2Home), to form Waban, Inc. In August 1997, Waban spun off BJ's to become an independent company, BJ's Wholesale Club, Inc., headquartered in Natick, Massachusetts, while Waban renamed itself to HomeBase, Inc.


title: BJ's Wholesale Club

text: In 2011, BJ's was acquired by two private equity firms, Leonard Green & Partners and CVC Capital Partners. It returned to being a public company in 2018.


title: BJ's Wholesale Club

text: In 2019, BJ's expanded into Michigan, with a new store in Madison Heights. A second and a third Michigan location have since opened in Taylor and Chesterfield Township, respectively.


title: BJ's Wholesale Club

text: As of summer 2020, BJ's operates 216 BJ's clubs in 17 states and employed approximately 25,000 team members (both full- and part-time). Clubs are found in Maine, New Hampshire, Massachusetts, Delaware, Connecticut, Rhode Island, New York, New Jersey, Pennsylvania, Maryland, Virginia, North Carolina, South Carolina, Georgia, Florida, Ohio, and Michigan. Its major competitors are Costco Wholesale and Sam's Club.


title: BJ's Wholesale Club

text: BJ's offers a variety of special benefits to its members. These include "member pricing", a variety of name-brand products at discount wholesale prices, acceptance of all valid manufacturers coupons, and acceptance of many forms of payment (cash, check, ATM/debit cards, all major credit cards, and EBT SNAP benefits).


title: BJ's Wholesale Club

text: Memberships at BJ's are required for these benefits and are available to individual consumers and businesses. BJ's memberships normally last for twelve months from the date of purchase and must be renewed yearly. , a standard Inner Circle (individual) membership at BJ's cost $55 per year. In addition, BJ's also has a special "Rewards" membership that may be purchased for an additional $55, allowing 2% of most of a member's purchases to be "rewarded" and redeemed for use towards future BJ's purchases (with the exception of alcohol, gas, and tobacco). Business members may apply to purchase BJ's products for resale, and nonprofit organization members may apply for tax-exempt privileges (where applicable). Members with expired memberships (if they choose not to renew), as well as non-members are allowed to shop, but are assessed a 5-20% surcharge (depending on the club and the circumstances) on their total, and are not allowed to pay by check. However, if non-members keep their receipts and decide to renew their membership or open a new membership, they will be refunded the surcharge and applied towards the membership fee, within seven days. To aid in convenience, most BJ's memberships can be renewed at the register during checkout. BJ's Wholesale Club has a 100% Satisfaction Guarantee on their memberships; therefore a membership can be refunded at any time during that membership period without any 90- or 30-day stipulation.


title: BJ's Wholesale Club

text: Many of BJ's clubs offer special services to members, such as car rentals, gas stations, home heating oil, an optical department, propane filling, and vacation packages. These services vary from location to location. , there were 154 clubs with optical departments. BJ's operated 104 gasoline stations at their clubs. In February 2007, BJ's closed all pharmacies in its clubs.


title: BJ's Wholesale Club

text: BJ's Wholesale Club locations frequently stock different varieties of products at different locations. However, all clubs carry the items listed in the coupon book that is published on a monthly basis. However, at certain times, it is not uncommon for a certain club not to carry a new item immediately due to its higher demand.


title: BJ's Wholesale Club

text: In March 2010, BJ's announced they would move their corporate headquarters from Natick to Westborough, Massachusetts in 2011. On January 5, 2011, BJ's announced it would close five underperforming stores in the Southeast, eliminate approximately 100 headquarters jobs by the end of the month, and restructure its home office and some field operations. Its restructuring moves would result in savings of 78 to 82 cents per share for its fiscal fourth quarter.


title: BJ's Wholesale Club

text: On December 19, 2019, BJ's named Lee Delaney as its next CEO starting February 2, 2020. Delaney had been an executive vice president and chief growth officer of the company since 2016. Then CEO Chris Baldwin became executive chairman. Following Delaney's death on April 8, 2021, BJ's financial chief Bob Eddy took over as interim CEO. On April 20, 2021, Bob Eddy’s interim status was removed and he was given the permanent CEO position.


title: BJ's Wholesale Club

text: In November 2021, BJ’s announced plans to expand to La Vergne, Tennessee. The announcement of the club in La Vergne will represent the first BJ’s Club in Tennessee.


title: BJ's Wholesale Club

text: BJ's Wholesale Club regularly markets numerous products under its own private labels—including products by Richelieu Foods.


title: BJ's Wholesale Club

text: Additionally, BJ's carries many organic and natural food brands such as Kerrygold, Amy's Kitchen, Kashi, Newman's Own and American Flatbread.


title: BJ's Wholesale Club

text: BJ's utilizes three cross-dock distribution centers along with third-party warehouse space when extra storage is needed.


title: I Kissed a Girl

text: "I Kissed a Girl" is the debut single of American singer Katy Perry from her second studio album, "One of the Boys" (2008). It was released on April 28, 2008, by Capitol Records as the lead single from the record. Perry co-wrote the song with Max Martin, Cathy Dennis, and its producer Dr. Luke, with additional production from Benny Blanco. "I Kissed a Girl" is a pop-rock, electropop, and disco song with elements of new wave. Perry stated its lyrics are "about the magical beauty of a woman." The song sparked controversy for its handling of bi-curious themes, but in retrospect has been viewed as the beginning of LGBT awareness in pop music.


title: I Kissed a Girl

text: The song topped the US "Billboard" Hot 100 chart for seven consecutive weeks, becoming the 1,000th number-one song of the rock era. The single has sold 6 million units in the US alone. "I Kissed a Girl" is one of eight songs by Perry to sell over 4 million digital copies in the US, the others being "Hot n Cold", "California Gurls", "Teenage Dream", "Firework", "E.T.", "Dark Horse" and "Roar". It also topped the charts in Australia, Austria, Belgium, Canada, the Czech Republic, Denmark, Germany, Hungary, Ireland, Italy, New Zealand, Norway, Scotland, Sweden, Switzerland, and the United Kingdom. It was the bestselling song of 2008 in Finland. The song has been certified multi-platinum in Australia, Canada, Denmark, the UK, and the US.


title: I Kissed a Girl

text: An accompanying music video for the song was released on May 16, 2008. The video, directed by Kinga Burza, features the singer in a setting inspired by burlesque and Moulin Rouge styles. It features appearances from Perry's friends, including actress Shannon Woodward and singer Kesha. The song is recognized as the 10th best-selling single in the 21st century. "I Kissed a Girl" was performed and a nominee at the 51st Grammy Awards (Grammy Award for Best Female Pop Vocal Performance). It was also nominated for Favorite Song at the 2009 Kids' Choice Awards. The song has been performed on all of her tours. It was also included in Perry's performance in Super Bowl XLIX's Pepsi Halftime Show in 2015.


title: I Kissed a Girl

text: According to Perry, "the chorus actually popped into my head when I woke up". Perry also said that it somewhat was from personal experience. "It was one of those moments where you hear artists talking about songs they get in dreams or in the middle of the night. I was like 'wow, what an interesting subject matter to kind of pop into the head' and I didn't do anything with it for about a year-and-a-half. Then all of a sudden at the very, very end of making my album, I literally had two days left in the recording studio with my producer, Dr Luke. We just said, 'we're gonna finish it—it's so catchy because it won't get out of our heads.'"


title: I Kissed a Girl

text: Capitol A&R Chris Anokute told "HitQuarters" that the song and its controversial theme met with strong resistance at the label. "People said, 'This is never going to get played on the radio. How do we sell this? How's this going to be played in the Bible Belt?'" Anokute said that they needed the support of one of the label's radio promoters to convince people to believe in the record. Otherwise, Perry would have likely been dropped again. Dennis Reese, Capitol's senior vice president of promotions, saw the vision and helped push the single on national radio. The first station to pick it up and take a chance was 107.5 The River in Nashville. Rich Davis, then PD, was played the song by Joe Rainey of Capitol Records outside his favorite sushi spot in Nashville and immediately put it on the air. After playing it for three days, they were inundated with enthusiastic calls.


title: I Kissed a Girl

text: "I Kissed a Girl" has a length of three minutes. The song is a pop rock, new wave, electropop, and disco track which runs through a throbbing beat and an organic instrumental thump, according to About.com's Bill Lamb. It features instrumentation provided by drums, guitars, and bass, courtesy of Dr. Luke. The song was produced by Dr. Luke, which was coordinated by Gary 'G' Silver and aided by American producer and songwriter Benny Blanco. There were a number of personnel who engineered the track for the album, including Emily Wright, Sam Holland, Nick Banns, Aniela Gottwald, Mike Caffrey, and Tina Kennedy. Kitty Purty assisted in the engineering while Tim Roberts assisted in the engineering for mix, which was done by John Hanes. The song was mixed by Serban Ghenea at his studio MixStar Studios in Virginia Beach, Virginia. Cathy Dennis was on background vocals while Dr. Luke and Benny Blanco were featured on drums and programming. Steven Wolf provided the live drums on the song while Mike Caffrey recorded and produced the drums at Monster Island in New York City.


title: I Kissed a Girl

text: In an interview for "The New Gay", Perry describes the song to be about girls. She defends the lyrics, saying that "When we're young, we're very touchy-feely. We have slumber party sing-a-longs, we make up dance routines in our pajamas. We're a lot more intimate in a friendship than guys can be. It's not perverse but just sweet..." The song was partially inspired by Scarlett Johansson. Perry also stated that the lyrics were inspired by her friendship with a girl as a teenager, commenting that "I did kiss her. I was totally obsessed with her. She was beautiful — porcelain skin, perfect lips." While Perry has not explicitly revealed the main person behind the inspiration of the song, Miley Cyrus has claimed it was about her.


title: I Kissed a Girl

text: In an interview with the German online web show MalcolmMusic, Macy Gray revealed that "I Kissed a Girl" was initially offered to her before Perry ended up releasing the song.


title: I Kissed a Girl

text: The song is written in the key of A minor in common time with a tempo of 130 beats per minute. It follows a chord progression of Am-[B-C]-Dm-[F-Em] in the verses, Am-C-Dm-[F-Em] in the choruses (except for the Dm chord being major in the third segment), and F-Em-Am-G in the bridge, which ends with an extra-Dm chord. Perry's vocals span from A to E.


title: I Kissed a Girl

text: "Blogcritics" magazine called it "an instantly catchy number." About.com said, "fueled by an instrumental wallop provided courtesy of producer Dr. Luke, 'I Kissed a Girl' is the perfect breakthrough." However, "Rolling Stone" magazine, while giving her album 2/5 stars, described the song as a "new wave-y club single", saying the supposedly rebellious "attention-grabbing" lyrics are "a vanilla recounting of her chick-on-chick exploits" and that this "acting out" is "just to get a dude's attention." AllMusic praises "the stomping Gary Glitter beat" before criticizing the producers for turning it "into a leaden stumble and burying Perry's voice underneath Pro Tools overdubs so it all winds up as a faceless wash of sound designed to be placed in TV shows, movie trailers, and malls."


title: I Kissed a Girl

text: Sal Cinquemani of "Slant Magazine" wrote that Perry's "lead single 'I Kissed a Girl' features a throbbing beat and an infectious, bi-curious hook, but its self-satisfied, in-your-face posturing rings phony in comparison to the expertly constructed ambiguities of 'Justify My Love' or practically anything in the first decade of Ani DiFranco's catalog; it's like a tween version of DiFranco's tortured bisexual confession 'Light of Some Kind'." Hiponline.com wrote that the song is "not nearly as interesting or exciting as you'd expect. It's not even half as good as Jill Sobule's song 'I Kissed a Girl'." "Glitterati Gossip" agreed Sobule's song "was ten times better, because there was actual emotional content to her lyrics."


title: I Kissed a Girl

text: The song received criticism from members of the LGBT community. AllMusic concluded, "the problem is not with Katy's gender-bending, it's that her heart isn't in it; she's just using it to get her places, so she sinks to crass, craven depths." "Slant Magazine" agreed, saying the song "isn't problematic because it promotes homosexuality, but because its appropriation of the gay lifestyle exists for the sole purpose of garnering attention — both from Perry's boyfriend and her audience."


title: I Kissed a Girl

text: Adam Holz of "PluggedinOnline", a division of Focus on the Family, wrote an article entitled "A Tale of Two Katys" about the singer's image transformation from a Contemporary Christian music artist to one of the "girls gone wild." He criticizes the song for being the latest, "high-profile message to young women and men that our sexuality is a malleable commodity that can be reshaped at will." Holz also argues that Perry's message carries with it "no need to worry about who might get used or objectified in the process," causing Perry to live "down to a damaging, demeaning stereotype." After numerous reports that Perry's religious parents were against her music and career, she stated in August 2008, "They love and support me."


title: I Kissed a Girl

text: Though the "Toronto Star" describes it as "a lesbian-friendly tune," whether homophobia fuels negative reactions to the song or the song itself appears to divide critics. "Slant" and other critics suggest that Perry may be homophobic, especially given her single "Ur So Gay", which makes "I Kissed a Girl" seems like "a classic example of the 'Guys kissing is gross, girls kissing is hot' line of thought," which promotes hypersexualization of queer women and demonization of queer men. MomLogic.com writer Vuv-A-Licious agrees, asking "What's the big deal? ... When this tune is playing and my son and daughter are dancing, I will be trying to dance along, or trying to acknowledge that they may one day dance to the beat of a different drummer than me."


title: I Kissed a Girl

text: When asked about her own sexuality, Perry told "Santa Barbara" magazine "I like to kiss boys, but there is no doubt in my mind if Angelina Jolie or Gisele Bündchen came a callin', who wouldn't pucker up?" Perry told "The New Gay" she had never actually kissed a girl and is heterosexual. She is quoted as saying "Yeah, it's fantasy, it's a song about curiosity."


title: I Kissed a Girl

text: At an annual fund-raiser in 2008, she mentioned "I remember having a little crush when I was 15 on this girl who was a little bit older than me. She was my best friend at the time [but] I never kissed her or anything. In retrospect, she was my muse for that song." When asked by "OK!" magazine about kissing a girl, she replied: "Of course. I think I was 19. I kissed a girl and it was great", she also added: "Growing up I had a friend who, looking back, I think I had an obsessive little crush on her. I never kissed her but she was very beautiful and she was like a ballerina and I wanted to copy everything she did. But I think that was kind of the extent of it."


title: I Kissed a Girl

text: In a separate interview in 2010, Perry stated to a female interviewer that she has kissed several girls. Perry later admitted to "Vanity Fair" in early May 2011 that the reason she did not discuss it honestly at first was that a couple of "sleazy" male journalists made her uncomfortable, she stated: "So I said no, I hadn't experienced it, even though I had, because I didn't like where the guys were taking the interviews."


title: I Kissed a Girl

text: In February 2009, Márcio Barros, a substitute English language teacher in a Distrito Federal, Brazil public school was fired after he used the song in a class activity among students aged 12 to 14. He was accused of promoting "homosexualism" and alcoholic beverages through the lyrics. The Secretary of Education supported the decision of the head of the school.


title: I Kissed a Girl

text: In a February 2018 online "Glamour" article, Perry expressed the following about her song:"We've really changed, conversationally, in the past 10 years. We've come a long way. Bisexuality wasn't as talked about back then, or any type of fluidity. If I had to write that song again, I probably would make an edit on it. Lyrically, it has a couple of stereotypes in it. Your mind changes so much in 10 years, and you grow so much. What's true for you can evolve."


title: I Kissed a Girl

text: "I Kissed a Girl" debuted at No. 76 on the "Billboard" Hot 100. After a couple of weeks, the single hit the top five, due to the rising digital downloads and increasing radio airplay. It continued to rise the next week, reaching No. 2, just behind her labelmates, Coldplay. On the chart dated July 5, 2008, the song peaked at the summit of the "Billboard" Hot 100, becoming the 1,000th No. 1 song of the rock era (the 961st No. 1 single on the "Billboard" Hot 100). In addition, the song also gave the Capitol label two consecutive Hot 100 No. 1 singles following Coldplay's "Viva la Vida", making it the first time since 1976 that Capitol had two back-to-back chart-toppers on the Hot 100. The single also crossed over to "Billboard"s sister publication "R&R"'s Rhythmic chart in its July 5 issue, where not only did she have the highest debut ever for a non-rhythmic track, entering at No. 26 with 1,065 spins, she also had the highest debut from a new artist in over five years. The bow is the best for a debut track at Rhythmic since Beyoncé entered at no. 21 with "Crazy in Love" in 2003. It also has become the first song since Gnarls Barkley's "Crazy" to simultaneously appear on the Mainstream Top 40, Rhythmic, Adult Top 40, and Alternative charts. On July 26, 2008, the track also made history by reaching the No. 1 spot on "Billboard"'s Hot Dance Airplay chart by three weeks, a first for a solo act with a debut single. The song topped the Hot 100 for seven weeks in a row before being dethroned by Rihanna's "Disturbia". It was the second longest-running No. 1 on the Hot 100 of 2008 (tied with T.I.'s "Whatever You Like"), with only Flo Rida's "Low" topping the chart for longer. As of August 2020, the song has been certified sextuple platinum by the Recording Industry Association of America (RIAA) and sold 4.8 million copies in the United States.


title: I Kissed a Girl

text: In the United Kingdom, the single debuted at No. 4 on the UK Singles Chart on August 3, 2008, ― for the week ending date August 9, 2008. A week later, it topped the chart, where it remained for five weeks (a feat which would not be matched again until "Someone like You" by Adele in 2011) until it was dethroned by "Sex on Fire" by Kings of Leon. Alongside Basshunter's "Now You're Gone" and "Mercy" by Duffy, "I Kissed a Girl" spent more weeks at No. 1 on the UK Singles Chart than any other single in 2008. According to the Official Charts Company, the single has sold over 635,000 copies in Britain as of June 2010. It is the first Virgin label single to sell more than half a million copies since the Spice Girls' "Goodbye" in 1998. As of March 2012, the single had sold 654,560 copies in the United Kingdom, becoming her fourth best-selling single there behind "Firework", "Roar" and "California Gurls".


title: I Kissed a Girl

text: In Canada, the single debuted at No. 55 on the Canadian Hot 100, later peaking at No. 1, becoming the first country where the song reached the top of the charts.


title: I Kissed a Girl

text: In New Zealand, the song debuted at No. 38 on the New Zealand Singles Chart, the single's first appearance in other countries chart outside North America, moving to No. 3 the following week. The song was certified Gold after seven weeks with sales of over 7,500. On August 11, 2008, eight weeks after debuting on the chart, "I Kissed a Girl" finally made it to No. 1. "I Kissed a Girl" was certified platinum in New Zealand after 20 weeks, selling more than 15,000 copies.


title: I Kissed a Girl

text: In Australia, the song debuted at No. 30 on downloads alone. The next week, it jumped to No. 2, still on downloads alone. It later jumped to No. 1 still solely off downloads, becoming only the second single to do so. On July 21, 2008, after the single's physical release, the track retained its No. 1 position and was certified Gold. The single held the No. 1 position for several weeks and was certified double platinum.


title: I Kissed a Girl

text: According to Perry, the song became a massive hit for being musically "catchy". She told BBC News: "I think that it's one of those subject matters that is, you know, like 'Oh my God I can't believe she said that, that someone came out and said it.' I think that, whenever anyone writes something that is different than, like, your plain peanut butter and jelly song, 'I love you, you love me,' everyone kind of perks up and says 'what's this?'"


title: I Kissed a Girl

text: A music video for the song was released on May 16, 2008, on Perry's personal website and on Myspace. The video was directed by Kinga Burza and features a Moulin Rouge and burlesque-type setting with scenes of Perry, along with many other flamboyantly dressed women dancing to the song. Towards the end of the video, she wakes up next to a male companion, played by DJ Skeet Skeet. Despite the song's title, there is no depiction of same-sex kissing at all. Perry features her real-life friend and DJ, Mia Moretti, Markus Molinari's cat Bella and Kesha in the music video.


title: I Kissed a Girl

text: The song was listed at the ASCAP Pop Music Awards as one of 50 Most Performed Songs of 2008. Other honors given to the song include the following:


title: Aromatic compound

text: Aromatic compounds, also known as "mono- and polycyclic aromatic hydrocarbons", are organic compounds containing one or more aromatic rings. The parent member of aromatic compounds is benzene. The word "aromatic" originates from the past grouping of molecules based on smell, before their general chemical properties are understood. The current definition of aromatic compounds does not have any relation with their smell.


title: Aromatic compound

text: Heteroarenes are closely related, since at least one carbon atom of CH group is replaced by one of the heteroatoms oxygen, nitrogen, or sulfur. Examples of non-benzene compounds with aromatic properties are furan, a heterocyclic compound with a five-membered ring that includes a single oxygen atom, and pyridine, a heterocyclic compound with a six-membered ring containing one nitrogen atom. Hydrocarbons without an aromatic ring are called aliphatic.


title: Aromatic compound

text: Benzene, <chem>C6H6</chem>, is the least complex aromatic hydrocarbon, and it was the first one named as such. The nature of its bonding was first recognized by August Kekulé in the 19th century. Each carbon atom in the hexagonal cycle has four electrons to share. One goes to the hydrogen atom, and one to each of the two neighboring carbons. This leaves one electron to share with one of the two neighboring carbon atoms, thus creating a double bond with one carbon and leaving a single bond with the other, which is why some representations of the benzene molecule portray it as a hexagon with alternating single and double bonds.


title: Aromatic compound

text: Other depictions of the structure portray the hexagon with a circle inside it, to indicate that the six electrons are floating around in delocalized molecular orbitals the size of the ring itself. This represents the equivalent nature of the six carbon-carbon bonds all of bond order 1.5; the equivalency is explained by resonance forms. The electrons are visualized as floating above and below the ring, with the electromagnetic fields they generate acting to keep the ring flat.


title: Aromatic compound

text: The circle symbol for aromaticity was introduced by Sir Robert Robinson and his student James Armit in 1925 and popularized starting in 1959 by the Morrison & Boyd textbook on organic chemistry. The proper use of the symbol is debated: some publications use it to "any" cyclic π system, while others use it only for those π systems that obey Hückel's rule. Jensen argues that, in line with Robinson's original proposal, the use of the circle symbol should be limited to monocyclic 6 π-electron systems. In this way the circle symbol for a six-center six-electron bond can be compared to the Y symbol for a three-center two-electron bond.


title: Aromatic compound

text: In aromatic substitution one substituent on the arene ring, usually hydrogen, is replaced by another substituent. The two main types are electrophilic aromatic substitution, when the active reagent is an electrophile, and nucleophilic aromatic substitution, when the reagent is a nucleophile. In radical-nucleophilic aromatic substitution, the active reagent is a radical. An example of electrophilic aromatic substitution is the nitration of salicylic acid:


title: Aromatic compound

text: In coupling reactions a metal catalyzes a coupling between two formal radical fragments. Common coupling reactions with arenes result in the formation of new carbon–carbon bonds e.g., alkylarenes, vinyl arenes, biraryls, new carbon–nitrogen bonds (anilines) or new carbon–oxygen bonds (aryloxy compounds). An example is a direct arylation of perfluorobenzenes


title: Aromatic compound

text: Hydrogenation of arenes create saturated rings. The compound 1-naphthol is completely reduced to a mixture of decalin-ol isomers.


title: Aromatic compound

text: The compound resorcinol, hydrogenated with Raney nickel in presence of aqueous sodium hydroxide forms an enolate which is alkylated with methyl iodide to 2-methyl-1,3-cyclohexandione:


title: Aromatic compound

text: Cycloaddition reactions are not common. Unusual thermal Diels–Alder reactivity of arenes can be found in the Wagner-Jauregg reaction. Other photochemical cycloaddition reactions with alkenes occur through excimers.


title: Aromatic compound

text: Benzene derivatives have from one to six substituents attached to the central benzene core. Examples of benzene compounds with just one substituent are phenol, which carries a hydroxyl group, and toluene with a methyl group. When there is more than one substituent present on the ring, their spatial relationship becomes important for which the arene substitution patterns "ortho", "meta", and "para" are devised. For example, three isomers exist for cresol because the methyl group and the hydroxyl group can be placed next to each other ("ortho"), one position removed from each other ("meta"), or two positions removed from each other ("para"). Xylenol has two methyl groups in addition to the hydroxyl group, and, for this structure, 6 isomers exist.


title: Aromatic compound

text: The arene ring has the ability to stabilize charges. This is seen in, for example, phenol (CH–OH), which is acidic at the hydroxyl (OH), since a charge on this oxygen (alkoxide –O) is partially delocalized into the benzene ring.


title: Aromatic compound

text: Polynuclear aromatic hydrocarbons (PAHs) are aromatic hydrocarbons that consist of fused aromatic rings and do not contain heteroatoms or carry substituents. Naphthalene is the simplest example of a PAH. PAHs occur in oil, coal, and tar deposits, and are produced as byproducts of fuel burning (whether fossil fuel or biomass). As pollutants, they are of concern because some compounds have been identified as carcinogenic, mutagenic, and teratogenic. PAHs are also found in cooked foods. Studies have shown that high levels of PAHs are found, for example, in meat cooked at high temperatures such as grilling or barbecuing, and in smoked fish.


title: Aromatic compound

text: They are also found in the interstellar medium, in comets, and in meteorites and are a candidate molecule to act as a basis for the earliest forms of life. In graphene the PAH motif is extended to large 2D sheets.


title: Reed–Solomon error correction

text: Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.


title: Reed–Solomon error correction

text: They have many applications, the most prominent of which include consumer technologies such as MiniDiscs, CDs, DVDs, Blu-ray discs, QR codes, data transmission technologies such as DSL and WiMAX, broadcast systems such as satellite communications, DVB and ATSC, and storage systems such as RAID 6.


title: Reed–Solomon error correction

text: Reed–Solomon codes operate on a block of data treated as a set of finite-field elements called symbols. Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding =  −  check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to erroneous symbols, "or" locate and correct up to erroneous symbols at unknown locations. As an erasure code, it can correct up to erasures at locations that are known and provided to the algorithm, or it can detect and correct combinations of errors and erasures. Reed–Solomon codes are also suitable as multiple-burst bit-error correcting codes, since a sequence of consecutive bit errors can affect at most two symbols of size . The choice of is up to the designer of the code and may be selected within wide limits.


title: Reed–Solomon error correction

text: There are two basic types of Reed–Solomon codes original view and BCH view with BCH view being the most common, as BCH view decoders are faster and require less working storage than original view decoders.


title: Reed–Solomon error correction

text: Reed–Solomon codes were developed in 1960 by Irving S. Reed and Gustave Solomon, who were then staff members of MIT Lincoln Laboratory. Their seminal article was titled "Polynomial Codes over Certain Finite Fields". . The original encoding scheme described in the Reed & Solomon article used a variable polynomial based on the message to be encoded where only a fixed set of values (evaluation points) to be encoded are known to encoder and decoder. The original theoretical decoder generated potential polynomials based on subsets of "k" (unencoded message length) out of "n" (encoded message length) values of a received message, choosing the most popular polynomial as the correct one, which was impractical for all but the simplest of cases. This was initially resolved by changing the original scheme to a BCH code like scheme based on a fixed polynomial known to both encoder and decoder, but later, practical decoders based on the original scheme were developed, although slower than the BCH schemes. The result of this is that there are two main types of Reed Solomon codes, ones that use the original encoding scheme, and ones that use the BCH encoding scheme.


title: Reed–Solomon error correction

text: Also in 1960, a practical fixed polynomial decoder for BCH codes developed by Daniel Gorenstein and Neal Zierler was described in an MIT Lincoln Laboratory report by Zierler in January 1960 and later in a paper in June 1961. The Gorenstein–Zierler decoder and the related work on BCH codes are described in a book Error Correcting Codes by W. Wesley Peterson (1961). By 1963 (or possibly earlier), J. J. Stone (and others) recognized that Reed Solomon codes could use the BCH scheme of using a fixed generator polynomial, making such codes a special class of BCH codes, but Reed Solomon codes based on the original encoding scheme, are not a class of BCH codes, and depending on the set of evaluation points, they are not even cyclic codes.


title: Reed–Solomon error correction

text: In 1969, an improved BCH scheme decoder was developed by Elwyn Berlekamp and James Massey, and has since been known as the Berlekamp–Massey decoding algorithm.


title: Reed–Solomon error correction

text: In 1975, another improved BCH scheme decoder was developed by Yasuo Sugiyama, based on the extended Euclidean algorithm.


title: Reed–Solomon error correction

text: In 1977, Reed–Solomon codes were implemented in the Voyager program in the form of concatenated error correction codes. The first commercial application in mass-produced consumer products appeared in 1982 with the compact disc, where two interleaved Reed–Solomon codes are used. Today, Reed–Solomon codes are widely implemented in digital storage devices and digital communication standards, though they are being slowly replaced by Bose–Chaudhuri–Hocquenghem (BCH) codes. For example, Reed–Solomon codes are used in the Digital Video Broadcasting (DVB) standard DVB-S, in conjunction with a convolutional inner code, but BCH codes are used with LDPC in its successor, DVB-S2.


title: Reed–Solomon error correction

text: In 1996, variations of original scheme decoders called list decoders or soft decoders were developed by Madhu Sudan and others, and work continues on these types of decoders – see "Guruswami–Sudan list decoding algorithm".


title: Reed–Solomon error correction

text: In 2002, another original scheme decoder was developed by Shuhong Gao, based on the extended Euclidean algorithm.


title: Reed–Solomon error correction

text: Reed–Solomon coding is a key component of the compact disc. It was the first use of strong error correction coding in a mass-produced consumer product, and DAT and DVD use similar schemes. In the CD, two layers of Reed–Solomon coding separated by a 28-way convolutional interleaver yields a scheme called Cross-Interleaved Reed–Solomon Coding (CIRC). The first element of a CIRC decoder is a relatively weak inner (32,28) Reed–Solomon code, shortened from a (255,251) code with 8-bit symbols. This code can correct up to 2 byte errors per 32-byte block. More importantly, it flags as erasures any uncorrectable blocks, i.e., blocks with more than 2 byte errors. The decoded 28-byte blocks, with erasure indications, are then spread by the deinterleaver to different blocks of the (28,24) outer code. Thanks to the deinterleaving, an erased 28-byte block from the inner code becomes a single erased byte in each of 28 outer code blocks. The outer code easily corrects this, since it can handle up to 4 such erasures per block.


title: Reed–Solomon error correction

text: The result is a CIRC that can completely correct error bursts up to 4000 bits, or about 2.5 mm on the disc surface. This code is so strong that most CD playback errors are almost certainly caused by tracking errors that cause the laser to jump track, not by uncorrectable error bursts.


title: Reed–Solomon error correction

text: DVDs use a similar scheme, but with much larger blocks, a (208,192) inner code, and a (182,172) outer code.


title: Reed–Solomon error correction

text: Reed–Solomon error correction is also used in parchive files which are commonly posted accompanying multimedia files on USENET. The Distributed online storage service Wuala (discontinued in 2015) also used Reed–Solomon when breaking up files.


title: Reed–Solomon error correction

text: Almost all two-dimensional bar codes such as PDF-417, MaxiCode, Datamatrix, QR Code, and Aztec Code use Reed–Solomon error correction to allow correct reading even if a portion of the bar code is damaged. When the bar code scanner cannot recognize a bar code symbol, it will treat it as an erasure.


title: Reed–Solomon error correction

text: Reed–Solomon coding is less common in one-dimensional bar codes, but is used by the PostBar symbology.


title: Reed–Solomon error correction

text: Specialized forms of Reed–Solomon codes, specifically Cauchy-RS and Vandermonde-RS, can be used to overcome the unreliable nature of data transmission over erasure channels. The encoding process assumes a code of RS("N", "K") which results in "N" codewords of length "N" symbols each storing "K" symbols of data, being generated, that are then sent over an erasure channel.


title: Reed–Solomon error correction

text: Any combination of "K" codewords received at the other end is enough to reconstruct all of the "N" codewords. The code rate is generally set to 1/2 unless the channel's erasure likelihood can be adequately modelled and is seen to be less. In conclusion, "N" is usually 2"K", meaning that at least half of all the codewords sent must be received in order to reconstruct all of the codewords sent.


title: Reed–Solomon error correction

text: Reed–Solomon codes are also used in xDSL systems and CCSDS's Space Communications Protocol Specifications as a form of forward error correction.


title: Reed–Solomon error correction

text: One significant application of Reed–Solomon coding was to encode the digital pictures sent back by the Voyager program.


title: Reed–Solomon error correction

text: Voyager introduced Reed–Solomon coding concatenated with convolutional codes, a practice that has since become very widespread in deep space and satellite (e.g., direct digital broadcasting) communications.


title: Reed–Solomon error correction

text: Viterbi decoders tend to produce errors in short bursts. Correcting these burst errors is a job best done by short or simplified Reed–Solomon codes.


title: Reed–Solomon error correction

text: Modern versions of concatenated Reed–Solomon/Viterbi-decoded convolutional coding were and are used on the Mars Pathfinder, Galileo, Mars Exploration Rover and Cassini missions, where they perform within about 1–1.5 dB of the ultimate limit, the Shannon capacity.


title: Reed–Solomon error correction

text: The Reed–Solomon code is actually a family of codes, where every code is characterised by three parameters: an alphabet size "q", a block length "n", and a message length "k," with "k < n ≤ q." The set of alphabet symbols is interpreted as the finite field of order "q", and thus, "q" must be a prime power. In the most useful parameterizations of the Reed–Solomon code, the block length is usually some constant multiple of the message length, that is, the rate is some constant, and furthermore, the block length is equal to or one less than the alphabet size, that is, or .


title: Reed–Solomon error correction

text: There are different encoding procedures for the Reed–Solomon code, and thus, there are different ways to describe the set of all codewords.


title: Reed–Solomon error correction

text: In the original view of , every codeword of the Reed–Solomon code is a sequence of function values of a polynomial of degree less than "k". In order to obtain a codeword of the Reed–Solomon code, the message symbols (each within the q-sized alphabet) are treated as the coefficients of a polynomial "p" of degree less than "k", over the finite field "F" with "q" elements.


title: Reed–Solomon error correction

text: In turn, the polynomial "p" is evaluated at "n" ≤ "q" distinct points formula_1 of the field "F", and the sequence of values is the corresponding codeword. Common choices for a set of evaluation points include {0, 1, 2, ..., "n" − 1}, {0, 1, "α", "α", ..., "α"}, or for "n" < "q", {1, "α", "α", ..., "α"}, ... , where "α" is a primitive element of "F".


title: Reed–Solomon error correction

text: Since any two "distinct" polynomials of degree less than formula_4 agree in at most formula_5 points, this means that any two codewords of the Reed–Solomon code disagree in at least formula_6 positions.


title: Reed–Solomon error correction

text: Furthermore, there are two polynomials that do agree in formula_5 points but are not equal, and thus, the distance of the Reed–Solomon code is exactly formula_8.


title: Reed–Solomon error correction

text: This trade-off between the relative distance and the rate is asymptotically optimal since, by the Singleton bound, "every" code satisfies formula_11.


title: Reed–Solomon error correction

text: Being a code that achieves this optimal trade-off, the Reed–Solomon code belongs to the class of maximum distance separable codes.


title: Reed–Solomon error correction

text: While the number of different polynomials of degree less than "k" and the number of different messages are both equal to formula_12, and thus every message can be uniquely mapped to such a polynomial, there are different ways of doing this encoding.


title: Reed–Solomon error correction

text: The original construction of interprets the message "x" as the "coefficients" of the polynomial "p", whereas subsequent constructions interpret the message as the "values" of the polynomial at the first "k" points formula_13 and obtain the polynomial "p" by interpolating these values with a polynomial of degree less than "k".


title: Reed–Solomon error correction

text: The latter encoding procedure, while being slightly less efficient, has the advantage that it gives rise to a systematic code, that is, the original message is always contained as a subsequence of the codeword.


title: Reed–Solomon error correction

text: The codeword of formula_17 is obtained by evaluating formula_15 at formula_19 different points formula_1 of the field formula_21.


title: Reed–Solomon error correction

text: This function formula_24 is a linear mapping, that is, it satisfies formula_25 for the following formula_26-matrix formula_27 with elements from formula_21:


title: Reed–Solomon error correction

text: This matrix is the transpose of a Vandermonde matrix over formula_21. In other words, the Reed–Solomon code is a linear code, and in the classical encoding procedure, its generator matrix is formula_27.


title: Reed–Solomon error correction

text: There is an alternative encoding procedure that also produces the Reed–Solomon code, but that does so in a systematic way. Here, the mapping from the message formula_17 to the polynomial formula_15 works differently: the polynomial formula_15 is now defined as the unique polynomial of degree less than formula_4 such that


title: Reed–Solomon error correction

text: The alternative encoding function formula_22 for the Reed–Solomon code is then again just the sequence of values:


title: Reed–Solomon error correction

text: Since the first formula_4 entries of each codeword formula_44 coincide with formula_17, this encoding procedure is indeed systematic.


title: Reed–Solomon error correction

text: Since Lagrange interpolation is a linear transformation, formula_46 is a linear mapping. In fact, we have formula_47, where


title: Reed–Solomon error correction

text: A discrete Fourier transform is essentially the same as the encoding procedure; it uses the generator polynomial "p"(x) to map a set of evaluation points into the message values as shown above:


title: Reed–Solomon error correction

text: The inverse Fourier transform could be used to convert an error free set of "n" < "q" message values back into the encoding polynomial of "k" coefficients, with the constraint that in order for this to work, the set of evaluation points used to encode the message must be a set of increasing powers of "α":


title: Reed–Solomon error correction

text: However, Lagrange interpolation performs the same conversion without the constraint on the set of evaluation points or the requirement of an error free set of message values and is used for systematic encoding, and in one of the steps of the Gao decoder.


title: Reed–Solomon error correction

text: In this view, the message is interpreted as the coefficients of a polynomial formula_52. The sender computes a related polynomial formula_53 of degree formula_54 where formula_55 and sends the polynomial formula_53. The polynomial formula_53 is constructed by multiplying the message polynomial formula_52, which has degree formula_5, with a generator polynomial formula_60 of degree formula_61 that is known to both the sender and the receiver. The generator polynomial formula_60 is defined as the polynomial whose roots are sequential powers of the Galois field primitive formula_63


title: Reed–Solomon error correction

text: The encoding procedure for the BCH view of Reed–Solomon codes can be modified to yield a systematic encoding procedure, in which each codeword contains the message as a prefix, and simply appends error correcting symbols as a suffix. Here, instead of sending formula_67, the encoder constructs the transmitted polynomial formula_53 such that the coefficients of the formula_4 largest monomials are equal to the corresponding coefficients of formula_52, and the lower-order coefficients of formula_53 are chosen exactly in such a way that formula_53 becomes divisible by formula_60. Then the coefficients of formula_52 are a subsequence of the coefficients of formula_53. To get a code that is overall systematic, we construct the message polynomial formula_52 by interpreting the message as the sequence of its coefficients.


title: Reed–Solomon error correction

text: Formally, the construction is done by multiplying formula_52 by formula_78 to make room for the formula_79 check symbols, dividing that product by formula_60 to find the remainder, and then compensating for that remainder by subtracting it. The formula_81 check symbols are created by computing the remainder formula_82:


title: Reed–Solomon error correction

text: The remainder has degree at most formula_84, whereas the coefficients of formula_85 in the polynomial formula_86 are zero. Therefore, the following definition of the codeword formula_53 has the property that the first formula_4 coefficients are identical to the coefficients of formula_52:


title: Reed–Solomon error correction

text: As a result, the codewords formula_53 are indeed elements of formula_2, that is, they are divisible by the generator polynomial formula_60:


title: Reed–Solomon error correction

text: The Reed–Solomon code is a ["n", "k", "n" − "k" + 1] code; in other words, it is a linear block code of length "n" (over "F") with dimension "k" and minimum Hamming distance formula_95 The Reed–Solomon code is optimal in the sense that the minimum distance has the maximum value possible for a linear code of size ("n", "k"); this is known as the Singleton bound. Such a code is also called a maximum distance separable (MDS) code.


title: Reed–Solomon error correction

text: The error-correcting ability of a Reed–Solomon code is determined by its minimum distance, or equivalently, by formula_96, the measure of redundancy in the block. If the locations of the error symbols are not known in advance, then a Reed–Solomon code can correct up to formula_97 erroneous symbols, i.e., it can correct half as many errors as there are redundant symbols added to the block. Sometimes error locations are known in advance (e.g., "side information" in demodulator signal-to-noise ratios)—these are called erasures. A Reed–Solomon code (like any MDS code) is able to correct twice as many erasures as errors, and any combination of errors and erasures can be corrected as long as the relation 2"E" + "S" ≤ "n" − "k" is satisfied, where formula_98 is the number of errors and formula_99 is the number of erasures in the block.


title: Reed–Solomon error correction

text: where formula_102, formula_103, formula_104, formula_105 is the symbol error rate in uncoded AWGN case and formula_106 is the modulation order.


title: Reed–Solomon error correction

text: For practical uses of Reed–Solomon codes, it is common to use a finite field formula_21 with formula_108 elements. In this case, each symbol can be represented as an formula_109-bit value.


title: Reed–Solomon error correction

text: The sender sends the data points as encoded blocks, and the number of symbols in the encoded block is formula_110. Thus a Reed–Solomon code operating on 8-bit symbols has formula_111 symbols per block. (This is a very popular value because of the prevalence of byte-oriented computer systems.) The number formula_4, with formula_113, of "data" symbols in the block is a design parameter. A commonly used code encodes formula_114 eight-bit data symbols plus 32 eight-bit parity symbols in an formula_115-symbol block; this is denoted as a formula_116 code, and is capable of correcting up to 16 symbol errors per block.


title: Reed–Solomon error correction

text: The Reed–Solomon code properties discussed above make them especially well-suited to applications where errors occur in bursts. This is because it does not matter to the code how many bits in a symbol are in error — if multiple bits in a symbol are corrupted it only counts as a single error. Conversely, if a data stream is not characterized by error bursts or drop-outs but by random single bit errors, a Reed–Solomon code is usually a poor choice compared to a binary code.


title: Reed–Solomon error correction

text: The Reed–Solomon code, like the convolutional code, is a transparent code. This means that if the channel symbols have been inverted somewhere along the line, the decoders will still operate. The result will be the inversion of the original data. However, the Reed–Solomon code loses its transparency when the code is shortened. The "missing" bits in a shortened code need to be filled by either zeros or ones, depending on whether the data is complemented or not. (To put it another way, if the symbols are inverted, then the zero-fill needs to be inverted to a one-fill.) For this reason it is mandatory that the sense of the data (i.e., true or complemented) be resolved before Reed–Solomon decoding.


title: Reed–Solomon error correction

text: Whether the Reed–Solomon code is cyclic or not depends on subtle details of the construction. In the original view of Reed and Solomon, where the codewords are the values of a polynomial, one can choose the sequence of evaluation points in such a way as to make the code cyclic. In particular, if formula_63 is a primitive root of the field formula_21, then by definition all non-zero elements of formula_21 take the form formula_120 for formula_121, where formula_122. Each polynomial formula_123 over formula_21 gives rise to a codeword formula_125. Since the function formula_126 is also a polynomial of the same degree, this function gives rise to a codeword formula_127; since formula_128 holds, this codeword is the cyclic left-shift of the original codeword derived from formula_123. So choosing a sequence of primitive root powers as the evaluation points makes the original view Reed–Solomon code cyclic. Reed–Solomon codes in the BCH view are always cyclic because BCH codes are cyclic.


title: Reed–Solomon error correction

text: Designers are not required to use the "natural" sizes of Reed–Solomon code blocks. A technique known as "shortening" can produce a smaller code of any desired size from a larger code. For example, the widely used (255,223) code can be converted to a (160,128) code by padding the unused portion of the source block with 95 binary zeroes and not transmitting them. At the decoder, the same portion of the block is loaded locally with binary zeroes. The Delsarte–Goethals–Seidel theorem illustrates an example of an application of shortened Reed–Solomon codes. In parallel to shortening, a technique known as puncturing allows omitting some of the encoded parity symbols.


title: Reed–Solomon error correction

text: The decoders described in this section use the BCH view of a codeword as a sequence of coefficients. They use a fixed generator polynomial known to both encoder and decoder.


title: Reed–Solomon error correction

text: Daniel Gorenstein and Neal Zierler developed a decoder that was described in a MIT Lincoln Laboratory report by Zierler in January 1960 and later in a paper in June 1961. The Gorenstein–Zierler decoder and the related work on BCH codes are described in a book "Error Correcting Codes" by W. Wesley Peterson (1961).


title: Reed–Solomon error correction

text: As a result of the Reed-Solomon encoding procedure, "s"("x") is divisible by the generator polynomial "g"("x"):


title: Reed–Solomon error correction

text: The transmitted polynomial is corrupted in transit by an error polynomial "e"("x") to produce the received polynomial "r"("x").


title: Reed–Solomon error correction

text: Coefficient "e" will be zero if there is no error at that power of "x" and nonzero if there is an error. If there are "ν" errors at distinct powers "i" of "x", then


title: Reed–Solomon error correction

text: The goal of the decoder is to find the number of errors ("ν"), the positions of the errors ("i"), and the error values at those positions ("e"). From those, "e"("x") can be calculated and subtracted from "r"("x") to get the originally sent message "s"("x").


title: Reed–Solomon error correction

text: The decoder starts by evaluating the polynomial as received at points formula_138. We call the results of that evaluation the "syndromes", "S". They are defined as:


title: Reed–Solomon error correction

text: The advantage of looking at the syndromes is that the message polynomial drops out. In other words, the syndromes only relate to the error, and are unaffected by the actual contents of the message being transmitted. If the syndromes are all zero, the algorithm stops here and reports that the message was not corrupted in transit.


title: Reed–Solomon error correction

text: The syndromes give a system of "n" − "k" ≥ 2"ν" equations in 2"ν" unknowns, but that system of equations is nonlinear in the "X" and does not have an obvious solution. However, if the "X" were known (see below), then the syndrome equations provide a linear system of equations that can easily be solved for the "Y" error values.


title: Reed–Solomon error correction

text: Consequently, the problem is finding the "X", because then the leftmost matrix would be known, and both sides of the equation could be multiplied by its inverse, yielding Y""


title: Reed–Solomon error correction

text: In the variant of this algorithm where the locations of the errors are already known (when it is being used as an erasure code), this is the end. The error locations ("X") are already known by some other method (for example, in an FM transmission, the sections where the bitstream was unclear or overcome with interference are probabilistically determinable from frequency analysis). In this scenario, up to formula_61 errors can be corrected.


title: Reed–Solomon error correction

text: The rest of the algorithm serves to locate the errors, and will require syndrome values up to formula_148, instead of just the formula_149 used thus far. This is why 2x as many error correcting symbols need to be added as can be corrected without knowing their locations.


title: Reed–Solomon error correction

text: There is a linear recurrence relation that gives rise to a system of linear equations. Solving those equations identifies those error locations "X".