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Talk:Santa Claus parade

Comments
I need information on how far around the world the Santa Claus Parade tradition extends. silsor 02:00, Nov 21, 2003 (UTC)

Kennedy assassination
The article says: "the assassination of President Kennedy a few weeks previously". Surely this should be "days", not "weeks"? Kennedy was assassinated on November 22, which is less than a week before Thanksgiving Day. — Preceding unsigned comment added by Ajd (talk • contribs) 17:20, 18 July 2004 (UTC)

Christmas Pageants?
Aren't Christmas Pageants the things in churches with people acting as Mary and Joseph and so forth? As in this? IMFromKathlene 05:09, 8 December 2006 (UTC)
 * Not under the common use of kthe term. See Adelaide Christmas Pageant.--cj | talk 10:50, 8 December 2006 (UTC)
 * But look here, here, here, and on Wikipedia Mr. Hankey, the Christmas Poo (South Park episode) and A Very Special Family Guy Freakin' Christmas. All are showing use of "Christmas Pageant" as a play about the nativity with large casts and churches. It seems every Children's book about Christmas used that term as well, at least they did when I was growing up. People looking for a Christmas Pageant and the description of what that is are going to come to this page and be kind of confused and/or alienated. I can't find anything on Wikipedia describing the kind of play I am thinking of and it seems widespread enough to deserve its own entry. It may be the area I live in (New Mexico, USA) but the common use I'm familiar with is that of the nativity play at churches and schools and the like-- Jesus instead of Santa. IMFromKathlene 21:34, 9 December 2006 (UTC)
 * It seems there are in fact two uses of the word. The Best Christmas Pageant Ever convinced me. I'm not sure if it is a language difference (between British/Commonwealth/Australian and American English) or whether one of the uses is a corruption/derivation of the original. I know that the meaning you describe is what I would usually call a nativity play. I'm not sure how to proceed, but one possible option is to turn Christmas pageant into disamiguation page directing readers to both here and the as yet uncreated article nativity play. A note could also be placed at the beginning of this article to inform users of the alternate usage. Thoughts?--cj | talk 18:02, 17 December 2006 (UTC)
 * As a minimum we need a note. It's not just a Commonwealth vs. American English question either; in Canada, a Christmas pageant is a form of Nativity play. What this page describes is called a Santa Claus parade. - Eron Talk 03:57, 18 December 2006 (UTC)
 * I turned it into a disambig page, but it's the first time I've made one so I'm not sure if it's totally correct. Feel free to edit it. IMFromKathlene 00:24, 24 December 2006 (UTC)

Santa Claus Parade?
Where is it called a Santa Claus Parade? I've never heard that term. I've always heard Christmas Parade. Is this political correctness? CsikosLo (talk) 15:47, 17 May 2019 (UTC)
 * I've started a move request -- 65.92.246.43 (talk) 22:05, 23 November 2021 (UTC)

Requested move 23 November 2021

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Not moved. Sceptre (talk) 09:04, 8 December 2021 (UTC)

Santa Claus parade → Christmas parade – such parades do not need, and do not always have a Santa. Santa may also not be called Santa either (ie. Father Winter, Father Christmas, etc). Or Black Peter without Santa, a parade with Elves or Mrs. Claus without Santa, etc. -- 65.92.246.43 (talk) 22:04, 23 November 2021 (UTC) — Relisting. Extraordinary Writ (talk) 04:17, 1 December 2021 (UTC)
 * Oppose. The first sentence of the article is in direct contradiction to the nom: the parades "celebrate the official opening of the Christmas season with the arrival of Santa Claus who always appears in the last float." Station1 (talk) 05:36, 2 December 2021 (UTC)
 * redirects here. Then, "Christmas parade" should not redirect here, and should be deleted, since "Santa Claus parade" certainly doesn't cover all of them. Or we could just modify the intro section. Santa is certainly not on the last float in all Santa parades, either, just many of them, so that statement is inaccurate. Sometimes he's even on one of the first floats. -- 65.92.246.43 (talk) 00:45, 3 December 2021 (UTC)
 * Support. I believe that a Santa Claus parade is a subset of a Christmas parade — specifically, one in which there is someone dressed as Santa Claus. I think the article should be moved to Christmas parade, and the article's text should be updated accordingly, so that it still mentions Santa Claus parades. Tol  (talk | contribs) @
 * Oppose This article really isn't even about general Christmas parades. It's about parades celebrating the arrival of Santa as described in the first sentence. This article should maybe be changed to be about general Christmas parades though, or Christmas parade should be it's own separate article. Iamreallygoodatcheckers (talk) 06:19, 3 December 2021 (UTC)

"Christmas parade" listed at Redirects for discussion
A discussion is taking place to address the redirect Christmas parade. The discussion will occur at Redirects for discussion/Log/2021 December 9 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 65.92.246.43 (talk) 03:38, 9 December 2021 (UTC)

title: Talk:Santa Claus parade


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Ergine

Ergine, also known as d-lysergic acid amide (LSA) and d-lysergamide, is an ergoline alkaloid that occurs in various species of vines of the Convolvulaceae and some species of fungi. The psychedelic properties in the seeds of ololiuhqui, Hawaiian baby woodrose and morning glories have been linked to ergine and/or isoergine, its epimer, as it is an alkaloid present in the seeds.

Occurrence in nature
Ergine has been found in high concentrations of 20 μg/g dry weight in the sleepygrass infected with an Acremonium endophytic fungus together with other ergot alkaloids.

Ergine is a component of the alkaloids contained in the ergot fungus, which grows on the heads of infected rye grasses.

It is also found in the seeds of several varieties of morning glories in concentrations of approximately 10 μg per seed, as well as Hawaiian baby woodrose seeds, at a concentration of around 0.13% of dry weight.

History
Ololiuhqui was used by South American healers in shamanic healing ceremonies. Similarly, ingestion of morning glory seeds by Mazatec tribes to "commune with their gods" was reported by Richard Schultes in 1941 and is still practiced today.

Sewell RA. Entheogen Rev. 2008;16:117-25.

Additional reports of the use of ergine were made by Don Thomes MacDougall. He reported that the seeds of Ipomoea violacea were used as sacraments by certain Zapotecs, sometimes in conjunction with the seeds of Rivea corymbosa, another species which has a similar chemical composition, with lysergol instead of ergometrine.

Ergine was assayed for human activity by Albert Hofmann in self-trials in 1947, well before it was known to be a natural compound. Intramuscular administration of a 500 microgram dose led to a tired, dreamy state, with an inability to maintain clear thoughts. After a short period of sleep the effects were gone, and normal baseline was recovered within five hours.

In 1956, the Central Intelligence Agency conducted research on the psychedelic properties of the ergine in the seeds of Rivea corymbosa, as Subproject 22 of MKULTRA.

In 1959, Hofmann was the first to isolate chemically pure ergine from the seeds of Turbina corymbosa, determining that it, and other alkaloids, were acting as the main active components in the seeds. Twenty years prior to its isolation, ergine was first chemically defined by English chemists S. Smith and G. M. Timmis as the cleavage product of ergot alkaloids. Additionally, Guarin and Youngkin reportedly isolated the crude alkaloid in 1964 from morning glory seeds.

Ingestion
Like other psychedelics, ergine is not considered to be addictive. Additionally, there are no known deaths directly associated with pharmacological effects of ergine consumption. All associated deaths are due to indirect causes, such as self-harm, impaired judgement, and adverse drug interactions. One known case involved a suicide that was reported in 1964 after ingestion of morning glory seeds. Another instance is a death due to falling off of a building after ingestion of Hawaiian baby woodrose seeds and alcohol.

Physiological effects
While its physiological effects vary from person to person, the following symptoms have been attributed to the consumption of ergine or ergine containing seeds:

 * Sedation
 * Visual and auditory hallucinations
 * Euphoria
 * Loss of motor control
 * Nausea
 * Vasoconstriction
 * Delusion
 * Anxiety
 * Paranoia
 * Irregular heartbeat
 * Sexual arousal
 * Tachycardia
 * Mydriasis
 * Hypertonia
 * Respiratory disturbances
 * Cramps

One study found that 2 of 4 human subjects experienced cardiovascular dysregulation and the study had to be halted, concluding that the ingestion of seeds containing ergine was less safe then commonly believed. Importantly this may have been a product of other substances within the seeds. The same study also observed that reactions were highly differing in type and intensity between different subjects. Another study in mice found that the drug had aphrodisiac properties, inducing increased sexual behavior.

A study gave mice 3000 mg/kg with no lethal effects.

Psychedelic component
Ergine is thought to be a serotonergic psychedelic and its psychedelic effects are thought to be due to it being a partial agonist of the 5-HT2A receptor. Though, the reason as to why this may be hallucinogenic remains elusive.

The idea that ergine is the main psychedelic component in ergine containing seeds (morning glory, Hawaiian baby woodrose) is well debated, as the effects of isolated synthetic ergine are reported to be only mildly psychedelic. Thus, the overall psychedelic experience after consumption of such seeds has been proposed to be due to a mixture of ergoline alkaloids.

Pharmacodynamics
Ergine interacts with serotonin, dopamine, and adrenergic receptors similarly to but with lower affinity than lysergic acid diethylamide (LSD). The psychedelic effects of ergine can be attributed to activation of serotonin 5-HT2A receptors.

Biosynthesis

The biosynthetic pathway to ergine starts like most other ergoline alkaloid- with the formation of the ergoline scaffold. This synthesis starts with the prenylation of L-tryptophan in an SN1 fashion with dimethylallyl diphosphate (DMAPP) as the prenyl donor and catalyzed by prenyltransferase 4-dimethylallyltryptophan synthase (DMATS), to form 4-L-dimethylallyltryptophan (4-L-DMAT). The DMAPP is derived from mevalonic acid. A three strep mechanism is proposed to form 4-L-DMAT: the formation of an allylic carbocation, a nucleophilic attack of the indole nucleus to the cation, followed by deprotonation to restore aromaticity and to generate 4-L-DMAT. 4-Dimethylallyltyptophan N-methyltransferase (EasF) catalyzes the N-methylation of 4-L-DMAT at the amino of the tryptophan backbone, using S-Adenosyl methionine (SAM) as the methyl source, to form 4-dimethylallyl-L-abrine (4-DMA-L-abrine). The conversion of 4-DMA-L-abrine to chanoclavine-I is thought to occur through a decarboxylation and two oxidation steps, catalyzed by the FAD dependent oxidoreductase, EasE, and the catalase, EasC. The chanoclavine intermediate is then oxidized to chanoclavine-l-aldehyde, catalyzed by the short-chain dehydrogenase/reductase (SDR), EasD.

From here, the biosynthesis diverges and the products formed are plant and fungus-specific. The biosynthesis of ergine in Claviceps purpurea will be exemplified, in which agroclavine is produced following the formation of chanoclavine-l-aldehyde, catalyzed by EasA through a keto-enol tautomerization to facilitate rotation about the C-C bond, followed by tautomerization back to the aldehyde and condensation with the proximal secondary amine to form an iminium species, which is subsequently reduced to the tertiary amine and yielding argoclavine. Cytochrome P450 monooxygenases (CYP450) are then thought to catalyze the formation of elymoclavine from argoclavine via a 2 electron oxidation. This is further converted to paspalic acid via a 4 electron oxidation, catalyzed by cloA, a CYP450 monooxygenase. Paspalic acid then undergoes isomerization of the C-C double bond in conjugation with the acid to form D-lysergic acid. While the specifics of the formation of ergine from D-lysergic acid are not known, it is proposed to occur through a nonribosomal peptide synthase (NRPS) with two enzymes primarily involve: D-lysergyl peptide synthase (LPS) 1 and 2.

Legal status
The legality of consuming, cultivating, and possessing ergine varies depending on the country.

There are no laws against possession of ergine-containing seeds in the United States. However, possession of the pure compound without a prescription or a DEA license would be prosecuted, as ergine, under the name "lysergic acid amide", is listed under Schedule III of the Controlled Substances Act. Similarly, ergine is considered a Class A substance in the United Kingdom, categorized as a precursor to LSD.

In most Australian states, the consumption of ergine containing materials is prohibited under state legislation.

In Canada, ergine is not illegal to possess as it is not listed under Canada's Controlled Drugs and Substances Act, though it is likely illegal to sell for human consumption.

In New Zealand, ergine is a controlled drug, however the plants and seeds of the morning glory species are legal to possess, cultivate, buy, and distribute.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Ergine


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Apocalypse (character)

Apocalypse (En Sabah Nur) is a supervillain appearing in American comic books published by Marvel Comics. He is one of the world's first mutants, and was a principal villain for the original X-Factor team and later the X-Men and related spin-off teams. Created by writer Louise Simonson and artist Jackson Guice, Apocalypse first appeared in X-Factor #5 (June 1986). Apocalypse is one of the most powerful beings in the Marvel Universe where he is the husband of Genesis and the father of the original incarnation of the Horsemen of Apocalypse.

Since his introduction, the character has appeared in a number of X-Men titles, including spin-offs and several limited series. Apocalypse has also been featured in various forms of media. Oscar Isaac portrayed the character in X-Men: Apocalypse.

Conception and creation
While writing the first five issues of X-Factor, Bob Layton dropped hints of a villain operating behind the scenes and leading the Alliance of Evil (mentioned in X-Factor #4, May 1986). Layton intended to reveal this character to be the Daredevil villain the Owl on the final page of X-Factor #5. However, Layton left the book after writing this issue and was replaced by writer Louise Simonson. Editor Bob Harras said that the character arose because of storytelling needs: "All I had communicated to Louise was my desire that an A-level, first class character be introduced. I wanted a Magneto-level villain who would up the stakes and give the X-Factor team reason to exist."

In a 2011 interview with The Philadelphia Inquirer, Simonson explained that when the X-Factor series was created, the original five X-Men were pulled out of the purview of Chris Claremont, who was writing The Uncanny X-Men. However, Simonson felt that the series needed an archenemy, or what Simonson called "a big, bad villain", and conceived of Apocalypse. Simonson described the character thus:

"When X-Factor was created, it caused a split in the 'Mutant World' [and] several seminal characters were pulled out of [writer] Chris Claremont's X-Men. Apocalypse is the first mutant – a brilliant shape-shifter who is virtually immortal – and sees himself as the father of mutantkind. In his early years, which I covered in the X-Factor Forever miniseries... Apocalypse encountered the Celestials and realized there was a time when humanity might be judged unworthy and destroyed. Consequently, he's been using Darwinian principles – survival of the fittest – to kill off the weak and force the survivors to grow stronger, to push humanity to get better and more powerful. He considers himself the Apocalypse of modern man and the father of what humanity will come next – Mutantkind. Where Magneto sees mutants as the next step of evolution and strives to protect all mutants, Apocalypse believes in absolute survival of the fittest – so if the Hulk, for example, is stronger than [the X-Men's] Colossus... well, in Apocalypse's world he would say, 'Bye, bye, comrade.'"

Harras also commented, "As soon as I saw the sketch by Walter [Simonson] and heard Louise's take on him, I knew we had the character I wanted. Jackson [Guice] redrew the page, patching in the shadowy Apocalypse where the Owl had been. But the genesis was clearly Walt and Weezie's." Guice admitted to difficulty recalling the details behind redrawing the last page of issue #5: "The best I can remember now is putting his look together pretty much right on the pencil page—just adding bits of costuming business which hinted toward his true appearance when we'd eventually see him in full reveal. I don't believe there was even a character sketch done for him at that point—I planned on making sense of it all later on, but by then I was gone and others had that concern." Apocalypse's silhouette in issue #5 does not match up with his full appearance in issue #6, suggesting the possibility that Guice was using Simonson's sketch as a reference for issue #6 but did not have access to it earlier, necessitating that he come up with his own design for issue #5. Walter Simonson himself has downplayed his role in the character's creation, saying that Guice was responsible for creating the design and that he, Simonson, merely modified it later: "I did not co-create Apocalypse. However, I wish I had. Louise Simonson and Jackson Guice created him. He appeared in a few panels at the end of one of Jackson’s last X-FACTORs, so I am the first artist to use him extensively in stories. And I kind of juiced up his physique a bit."

Bob Harras said on the character of Apocalypse:

"He looked fantastic. Also, the name is dynamic. It tells you right off this character means trouble. And he came with a clear-cut agenda: 'survival of the fittest.' He didn't care if you were a mutant—if you were weak, you would be destroyed. He was merciless, but his philosophy was easy to grasp and it fit in with the harder edge of evolution which is part and parcel of the mutant story. Isn't that what humans fear about mutants? That they are the next step? Now, we had given mutants something new to fear: a character who would judge them on their genetic worthiness. [...] To his own mind he wasn't evil (despite his leadership of the Alliance of Evil, which I think we dropped pretty soon after Apocalypse's introduction); he believed he was doing the right thing. He was ensuring evolution. To me, he was the perfect next step in the mutant story."

Although the character first appeared in 1986, he was retroactively said to have been present during previously published stories. The unnamed benefactor of the Living Monolith in Marvel Graphic Novel #17 (1985) was later identified as Apocalypse in disguise. Classic X-Men #25 revealed that years earlier, Apocalypse encountered the terrorist Moses Magnum and granted him superhuman power.

During his run on Cable, Robert Weinberg planned a story to reveal that Apocalypse was the third Summers brother, a mysterious sibling to the mutants Cyclops and Havok. But Weinberg left the book before he could go along with his plan and the third Summers brother was revealed to be the mutant Gabriel Summers, a.k.a. Vulcan.

Apocalypse was the principal adversary in the mid-1980s X-Men spin-off series X-Factor (1986–91) until being apparently killed at the climax of issue #68 (July 1991). Since then, the character has died and been resurrected several times thanks to his power and advanced alien technology. His name En Sabah Nur was revealed in Cable #6 (December 1993) and his birthplace (Egypt) and the origin of his technology, were revealed in X-Force #37 (August 1994). According to Marvel, the name translates from Arabic as "The First One" (although, in reality, the translation is considered grammatically incorrect, as it means "The First/Morning Light" [En-("The") + Sabah- ("Morning") + Nur- ("Light")] ). It is later revealed in the origin story Rise of Apocalypse that he is possibly the first mutant (meaning, in this case, a human being born with the X-gene), born 5,000 years ago. The character gained greater popularity in 1995 when the storyline "Age of Apocalypse" featured an alternate timeline in which Apocalypse has conquered much of planet Earth. The character was reincarnated in the pages of Uncanny X-Force #1 as a small boy with no memory of his previous incarnation. The boy was named Evan Sabahnur. In 2012 the adult, villainous version of Apocalypse returned in the series Uncanny Avengers. His origins are further explored in the storyline "Apocalypse Wars".

In 2019, writers Jonathan Hickman and Tini Howard expanded upon Apocalypse's origin and agenda in the Excalibur series and the X of Swords event. Apocalypse's 'survival of the fittest' mentality was revealed to have had the aim of preparing the mutant population for a dangerous reunion with the long-lost mutants of Arakko, which included his wife and four children, the original Horsemen of Apocalypse.

Rise of Apocalypse
The being who would later be called Apocalypse is born with the mutant X-gene thousands of years ago in Aqaba. Because of his grey skin and blue lips, his people abandon him as an infant. He is rescued by Baal of the Sandstormers who sees the child's potential power and will to survive. Baal names him En Sabah Nur, which Marvel translates as "The First One". The Sandstormers live by the credo of survival of the fittest, believing that only those who are strong enough to survive hardship and direct conflict are worthy of life. It is also revealed during the Apocalypse Wars that, as a young boy, En Sabah Nur is very generous and selfless, to the chagrin of Baal. A time-displaced Evan Sabah Nur and All-New X-Men Beast try to save En Sabah Nur, but he allows himself to be captured to help them escape.

Around this time, the time-traveller Kang the Conqueror arrives in Egypt and assumes the identity of Pharaoh Rama-Tut. Knowing who En Sabah Nur is fated to become and where he is, Rama-Tut sends his General Ozymandias and an army to destroy the Sandstormers and find the young Apocalypse. En Sabah Nur and Baal are injured and seek refuge in a cave. Before he dies, Baal reveals advanced alien technology hidden in the cave, left behind by the deity-like aliens known as Celestials. Vowing revenge on Rama-Tut, En Sabah Nur enters the Pharaoh's city posing as a slave and draws the romantic attention of Ozymandias's sister, Nephri. On seeing the mutant's true appearance, Nephri rejects him and turns to her brother for protection. The heartbroken En Sabah Nur's rage causes his mutant abilities to fully emerge. Rampaging, he renames himself Apocalypse. Rama-Tut flees and En Sabah Nur uses the Celestial technology to transform his former tormentor Ozymandias into a blind clairvoyant made of living stone, now enslaved to Apocalypse. As the years pass, Apocalypse finds he no longer aged. Around this time he founded the Coven Akkaba, an order of human sorcerers, in order to exploring the field of magic. The human mages believed that their magic would make them equal to mutants in Apocalypse's eyes. They were wrong and when they realized their patron considered them disposable as non-mutants, however, Akkaba broke from Apocalypse and nursed a centuries-long grudge.

It is revealed in the series S.H.I.E.L.D. that Apocalypse, at some point in the days of ancient Egypt, joined forces with the Brotherhood of the Shield to successfully fend off a Brood invasion. Also present were Imhotep and a man who was either the moon god called Khonshu or his first Moon Knight avatar/champion.

Early history
As the millennia pass, Apocalypse travels around planet Earth, convincing civilizations that he is a deity (inspiring different myths as a result) and manipulating them into fighting wars. He justifies that this encourages "growth, judgment, and destruction". Apocalypse's progeny become the Clan Akkaba. Apocalypse encounters the near-immortal human offshoot race known as Eternals, primarily the members Ikaris and Sersi, who refer to him as their "Ancient Nemesis". At different points, Apocalypse uses his Celestial technology to enter periods of suspended animation, leaving Clan Akkaba and Ozymandias to act in his stead.

In AD 1013, Apocalypse seeks to destroy the Asgardian Thor, who he knows will cause him trouble in the future, according to information obtained from Rama-Tut, yet the plans are foiled by Odin. In the 12th century, Apocalypse encounters the Eternal Sersi again while awakening latent mutant powers in a crusader named Bennet du Paris, also known as Exodus. In 1459, Apocalypse defeats Vlad Tepes (Vlad the Impaler) in Romania, who later becomes the vampire more popularly known as Count Dracula.

In 1859, Apocalypse encounters British scientist Nathaniel Essex and learns more about the nature of mutants. Apocalypse uses his Celestial technology to transform Essex into the superhuman being Mister Sinister. He then coerces Sinister and the Hellfire Club into aiding his plans for global conquest, but Sinister concludes that these plans are madness and betrays Apocalypse, forcing him back into hibernation.

In 1897, Count Dracula attacks the Clan Akkaba in revenge for his defeat at Apocalypse's hands, forcing the Clan to revive their master from suspended animation. Apocalypse defeats the vampire again, this time with help from Abraham Van Helsing. Eventually, Apocalypse enters hibernation again, expecting to remain so for possibly two centuries, by which point mutants should be more common on Earth.

Modern era
After many years of suspended animation, Apocalypse awakens nearly a century earlier than planned due to the arrival of the time-traveling mutant Cable (ironically, Cable had traveled to this point in time hoping to prevent the ancient mutant from awakening). Apocalypse decides the Earth is ready for further examination and testing. He grants superhuman powers to the terrorist known as Moses Magnum, who then tests the X-Men and the Avengers. Apocalypse later briefly employs the Alliance of Evil to capture the mutant Michael Nowlan, who can boost the power of other mutants. This plan brings Apocalypse into direct conflict with the first incarnation of X-Factor, when the team comprised the original X-Men.

Apocalypse then recruits mutants to serve as his personal guard, known as the Four Horsemen. Among them is Angel, AKA Warren Worthington III, whom Apocalypse has corrupted and turned into a cyborg called Death. Warren Worthington regains his identity and helps his friends defeat Apocalypse, adopting the new codename Archangel. Apocalypse escapes with his new recruit, the Morlock called Caliban, while X-Factor then takes his Celestial spaceship as a base.

During The Evolutionary War, the High Evolutionary plans to rid the Earth of those he feels are preventing evolution. Believing this disrupts the natural order and his own plans, Apocalypse battles the High Evolutionary.

Following the genetic manipulation of Caliban, Apocalypse declines an alliance with the Asgardian villain Loki and other villains conspiring to unleash the "Acts of Vengeance". This results in a brief fight between Apocalypse and Loki.

Sins of the Futures
Apocalypse learns of Sinister's intention to create an adversary powerful enough to destroy him: Nathan Christopher Charles Summers, the son of Scott Summers and Madelyne Pryor. Apocalypse, viewing him as a threat and realizing that Nathan's energy is the very energy that awoke him all those months earlier, sends his newly formed group, the Riders of the Storm, to abduct the Summers child. Apocalypse at this time had conquered the city of Attilan, home of the Inhumans, as well as enslaved part of its population. X-Factor, alongside the Inhuman Royal Family, attacks Apocalypse's lunar stronghold. Although Apocalypse is severely defeated, the young Nathan is infected with a techno-organic virus and is sent to the future with a woman named Askani to be cured.

In the future, Apocalypse has conquered the Earth and ruled until the 39th century. By this time, Apocalypse's body had grown feeble: he becomes aware of the young Nathan's presence in this time, but only succeeds in kidnapping a clone of the child which Askani created. Apocalypse plans to transfer his consciousness and power into the clone's stronger body, but perishes in combat with the (real) teenage Nathan. Nathan grows up to become the warrior Cable (while his clone grows up to become the mutant terrorist known as Stryfe) and travels back to the past to prevent Apocalypse's future domination of the planet.

In the present, Apocalypse is prematurely awoken from his regeneration chamber by his Riders (now calling themselves The Dark Riders), who inform their master that his Horsemen have kidnapped Cyclops and Jean Grey, supposedly under his instructions (in actuality, Mister Sinister, who was posing as Apocalypse). When attempting to rejuvenate himself again, Apocalypse is nearly killed by Stryfe who had arrived in the past to take revenge on Apocalypse. After a battle on the Moon with his former servants, the Dark Riders (who had joined Stryfe), Apocalypse is left for dead by Archangel.

The Dark Riders' new leader, Genesis (the adopted son of Cable, who had traveled to the present to ensure Apocalypse's rise and exact revenge on his father), plans to resurrect Apocalypse by sacrificing the lives of the people in villages neighboring Akkaba. During this time, Wolverine is held captive by Genesis, who attempts to restore Wolverine's lost adamantium skeleton and turn him into a Horseman as a gift for Apocalypse. Wolverine breaks free and kills Genesis along with nearly all of the Dark Riders. Genesis had built a sarcophagus with Apocalypse's likeness (which is empty, since Apocalypse had already revived ).

Further schemes
After a long healing slumber, Apocalypse, fully restored, awakens with Ozymandias at his side and quickly learns of the present danger: Onslaught. He observes the conflict between the psionic entity and Earth's heroes with Uatu the Watcher, who suggests to Apocalypse a course of action: an alliance with the one who hated him the most, Cable. Apocalypse surmises that Onslaught will be most vulnerable through the astral plane and that he needs Cable for actual physical transportation to this realm. Once on the astral plane, Apocalypse removes the captive Franklin Richards, greatly weakening Onslaught. The plan succeeds, but is interrupted by the Invisible Woman, who had invisibly accompanied the pair, having suspected Apocalypse's motive in wanting to actually kill her son. However, the reprieve in battle gave Onslaught the time to escape, prolonging the conflict.

Following the events of the Onslaught saga, the gamma-spawned powerhouse, the Hulk and his human alter ego, Banner, are split into two separate entities: Hulk now draws upon energy derived from Franklin Richards' pocket universe. Apocalypse recruits the Hulk to become his Horseman, War, with intentions of using the Hulk's nexus-energy to overcome the Celestials. To test this newest recruit, Apocalypse set War against the New World Order, a shadow cabinet organization that intends to conquer the planet. The New World Order in turn set the Juggernaut and the Absorbing Man against War, but both are easily defeated. Hulk comes to his senses after injuring his friend, Rick Jones. Despite this apparent setback, the incident was still a victory for Apocalypse as it was a successful testing of newly understood Celestial technology. Apocalypse activates the self-destruct mechanism on the sword of War, which the New World Order had obtained, destroying their headquarters.

The Hellfire Club later awakens Apocalypse's long-hidden Harbinger from its deep sleep: originally a normal man, whom Apocalypse in the 19th century once left to incubate for 100 years. Apocalypse releases his Horseman (Caliban) and his scribe Ozymandias from his possession, to fend for themselves, if they were to survive the coming events. Cable with the Avengers battles the Harbinger, but are unable to stop it. Apocalypse then appears, activating a bomb inside the Harbinger intended to destroy all of New York, but Cable manages to prevent this disaster.

When Magneto is disrupting Earth's magnetic field, Apocalypse sends a Skrull impersonating the mutant Astra (having dealt with the original Astra) to stop the Master of Magnetism.

Intending to start an all-out war between the humans and the subterranean-dwelling Deviants as part of his plan to test the strong, Apocalypse sets off nuclear warheads at Lemuria, causing the Deviants to further mutate (which also restores Ikaris' father Virako to life). Apocalypse launches an attack at San Francisco, using a mentally controlled Deviant, Karkas, now a gigantic monster, that the Eternals are forced to battle. Apocalypse is confronted by his centuries-old foe, Ikaris, who now is a Prime Eternal. Although Apocalypse defeats Ikaris, the Eternal still succeeds in destroying his ship and thwarting his plan.

The Twelve
Supposedly lost diaries of the mutant seer Destiny surfaced, telling of twelve beings that could defeat Apocalypse once and for all. Various mutants, all listed in the prophecy, are abducted by Apocalypse's Horsemen including a faction of the Skrulls. The Twelve legend was in fact a ruse, orchestrated by Apocalypse himself: once the Twelve are assembled, Apocalypse intended to use them to transform himself into a deity-like entity beyond the Celestials. It is revealed at the end of this story arc that Apocalypse's physical form has been burned out due to the vast amount of energies he has under his control, forcing him to wear a bio-armor (like his future counterpart) and now plans to use Nate Grey as a host body for him to move his energy and consciousness into. The X-Men confront Apocalypse as he is close to merging with Nate, but are unable to stop him. Cyclops pushes Nate Grey out of the way, merging with Apocalypse instead. While the merge is successful, Apocalypse's aim for unlimited power is not and he attempts to complete the transformation by warping reality into various scenarios (see Ages of Apocalypse). Apocalypse hoped to lure the Twelve into empowering him with their energy, but eventually, the mutants realize their true predicament and Apocalypse teleports away.

An amnesiac and powerless cyborg Cyclops regains control of the merged form, but Apocalypse begins to re-emerge. Jean and Cable are alerted to his location in Egypt, where Jean in the end manages to free Cyclops by telepathically tearing out Apocalypse's essence from her husband's body, rendering Apocalypse in an incorporeal astral form, which Cable apparently destroys using his psimitar.

2000s
In the aftermath of the 2005 "Decimation" storyline, in which most of the mutants lost their powers, Apocalypse was revealed to be alive and well. The techno-organic virus, with which he long ago infected Cable, was revealed to be the means by which Apocalypse's spirit reconstituted itself. With only a drop of his blood into a vat of organs and blood, the virus rewrote the genetic code of the material within to form a body for Apocalypse. Apocalypse awakes from a slumber in a tomb in Akkaba, recalling:

"Across the world—helpless mutants slaughtered. Pogroms. Horror. ...Something has woken me from my slumber. Once, a sudden surge in worldwide mutant power stirred me from a similar sleep. Now—a plummet in global mutant capacity—has opened my eyes."

Apocalypse finds himself on a planet with its mutant population reduced to a fraction of what it had been, only a few hundred remaining out of the millions who populated earth prior to his demise at Cable's hands. Reappearing inside a Sphinx-shaped ship, Apocalypse confronts the X-Men with his newly assembled cadre of Horsemen on the front lawn of the X-Mansion. The Horseman Famine uses his powers to cause an intense feeling of hunger and weakness in the mutants and humans on the institute grounds. Apocalypse offers the mutants an elixir: his own blood, provided they join his side. Bent on becoming the new messiah for mutant-kind, Apocalypse approaches the Earth leaders at the United Nations in New York and issues an ultimatum: humanity would destroy ninety percent of its own population, putting man and mutant on level ground in anticipation of the final conflict when the worthy alone would survive – or Apocalypse would unleash his meta-plague on the planet and obliterate all humanity.

In the end, Apocalypse's horsemen are lost, Ozymandias betrays him, and he is forced to retreat by a combined assault of the X-Men and the Avengers. Ultimately, it is discovered that the Celestials lent their technology to Apocalypse, requiring as payment greater sufferings later. He attempts to embrace death as an escape from his lifelong pact, only to find himself instantly resurrected and hearing a voice: "We cannot let you die. Not yet. It is time Apocalypse… it is time".

During the "Dark Reign" storyline, Quasimodo researched Apocalypse for Norman Osborn and states that he would be unsuitable for Osborn to use in any long term plans.

2010s
Apocalypse's followers, the Clan Akkaba, manage to bring about Apocalypse's return, albeit in the form of a child they will indoctrinate. Upon learning of Apocalypse's return, X-Force seeks to kill him, but when they discover he is a child, Psylocke decides to protect him, believing they can rehabilitate him and train him as a force for good. To the shock of the rest of the team, Fantomex fatally shoots the child.

In a 2011 storyline, as X-Force succeed in stopping the Deathloks inside the World, the home of all Weapon projects, it is revealed that Ultimaton, guardian of the World, is keeping watch over an incubating young boy labeled En Sabah Nur, aged 847 days.

During the 2012 storyline "Dark Angel Saga", it is revealed that Apocalypse had fathered a son with Autumn Rolfson and she kept this a secret from Apocalypse out of fear of what he would do to him. At the end of the storyline, it is revealed that Fantomex creates a clone Apocalypse which he helps raise to the age of a teenager in an artificial world, where the clone knows Fantomex as the kindly "Uncle Cluster" who taught him to use his abilities for good. The boy, code-named Genesis, helps X-force fight Archangel and when the battle is over, Fantomex enrolls him in the Jean Grey School for Higher Learning.

Evan Sabahnur
In Wolverine & the X-Men #4 (March 2012), Evan Sabahnur a.k.a. Genesis is admitted as a student to the Jean Grey School of Higher Learning, where his classmates notice his resemblance to Apocalypse. En is worried when a visiting Deathlok, who reveals to the students their likely futures, shows reluctance to do so with Evan. When Evan presses him, Deathlok informs him that this is what Evan is at the school to discover. Deathlok then tells Wolverine that Evan has great potential and may be a great savior, or a conqueror.

After being called Kid Apocalypse by Kid Omega, Evan begins learning about Apocalypse and is saddened that he himself looks like the villain, raising the possibility of a future that Evan rejects. After saving Angel and discovering that he possesses the ability to see the essence of those he looks upon, Evan asks him to tell him what he sees when he looks at him. Angel tells Evan he sees only goodness inside him, which makes Evan happy, so he thanks Angel for being a good friend. In fact, Angel lied, as the only thing he could see was the dark image of Apocalypse.

A new Brotherhood of Evil Mutants, led by Wolverine's son Daken, kidnaps Evan during a field trip to Genosha's remains. Hoping to sway the boy into becoming Apocalypse, the Brotherhood reveals to him that he is a clone and tells him of X-Force's assassination of the child En Sabah Nur from which he was cloned and the falsehood of his life under the tutelage of Fantomex. After the Brotherhood reveals that they have killed Fantomex and further tortures Evan, Daken tells En that he has a choice: either immediately ascend as Apocalypse and kill the Brotherhood as revenge for the death of "Uncle Cluster", or let the rest of X-Force die at the Brotherhood's hands to avenge the death of the original boy En Sabah Nur and to prevent X-Force from killing Evan the way they killed Apocalypse and Archangel.

Daken offers Evan a suit of Apocalypse's Celestial armor to do with what he will, secretly planning to control the new Apocalypse through the psychic abilities of the Shadow King. After Deadpool's failed attempt to rescue Evan, the boy dons the Celestial armor to prevent Wolverine's death at Daken's hands and nearly kills Brotherhood members Sabretooth and Mystique. Enraged by the lies he has been told and filled with new-found power from Apocalypse's armor, Evan prepares to attack Wolverine himself, but Wolverine convinces him of the ultimate futility of revenge. Evan is later visited by Deadpool at the Jean Grey School for Higher Learning. Deadpool tells Evan he is not Apocalypse and that Deadpool will always be there for him when he needs him.

Later Deadpool enlists Evan and Quentin's help to help him saving his daughter Eleanor Camacho from the Flag-Smasher, with Evan promising Quentin a bloodbath and some action to motivate him. He manages to save Ellie's life and proposes Deadpool to let Quentin erase from the girl's mind every memory of the ordeal. Deadpool loudly refuses and to Evan's surprise, he hugs him and tells him to stay in school.

During the 2014 "AXIS" storyline, Evan is one of many mutants captured by the Red Skull on the island of Genosha. During a fierce battle between the Avengers, the united X-Men, as well as a group of villains who all attempt to defeat the Red Onslaught, Evan assists Kid Omega in preventing Red Onslaught's telepathy from affecting the combined combatants. In the energy released when the Scarlet Witch and Doctor Doom use the combined power of order and chaos spells to suppress the Red Skull's personality in favor of the sliver of Professor X's that still exists in his brain, Evan ascends to adulthood, stepping out of the rubble with a looming, muscular body and the presence and appearance of Apocalypse. Deadpool even comments on how changed Evan is. When Havok and Cyclops argue with Steve Rogers and the new Captain America over who should take custody of the body of Red Skull, Evan convinces the Summers brothers that Professor X is dead and they have other problems to deal with. Acting as Apocalypse, 'En' vows to lead the mutants in an uprising, rallying the converted X-Men into helping him take Avengers Tower—now disregarded by the inverted Avengers after they captured almost all other heroes using Pym particles—to use as the site where he will detonate a Celestial-based 'gene-bomb' to wipe out all humans not carrying the X-gene. With only the inverted villains present at the original confrontation to oppose the inverted X-Men and Avengers, the gene bomb is nearly detonated, but is contained thanks to the sacrifice of Carnage. As Apocalypse broods on his failure, the decapitated Deadpool—converted to a peaceful version of himself called Zenpool by the inversion—convinces Apocalypse that now is the time to be heroic, proclaiming that nobody liked En Sabah Nur but everyone appreciated Evan, as he represented the hope that nurture could beat nature. Inspired by Deadpool's words, Apocalypse turns on the X-Men and the Avengers, allowing the Astonishing Avengers (along with non-inverted heroes Steve Rogers and Spider-Man) to retrieve the White Skull and undo the inversion. At the conclusion of the storyline, Evan is shown on the run with Deadpool.

Apocalypse Wars
During the "Apocalypse Wars" storyline, the Extraordinary X-Men travel thousands of years into Earth's future in order to rescue Colossus and his team of young mutants after they were investigating the sudden appearance of six hundred new mutant signatures in Tokyo. Arriving into Earth's future, the X-Men found themselves in a destroyed New York City and soon discovered that at some point Apocalypse had risen and what remained of Earth after his ascension became the Omega World, a huge structure composed of bubble worlds. The ones who survived the Great Trials lived on Omega World under Apocalypse's rule as he functioned as the Omega World's heart, keeping it alive, while his Horsemen functioned as its antibodies, cleansing the structure of anything that could harm their master. Omega World crumbled as the result of Apocalypse being fatally wounded by Nightcrawler. Storm was forced to take Apocalypse back to the present with them so they could undo the transformation of Colossus, who was turned into a Horseman, however, before he could restore Colossus back to normal, Apocalypse instead teleported him away, sending him to Clan Akkaba. It's left unknown if this Apocalypse was actually a future version of Evan or Apocalypse himself using a new host body. Apocalypse was kept at X-Haven, inside a cell specially built to contain him by Forge, and later after again retrieving Colossus, Forge tried to find a way to cure him by reverse engineering Apocalypse's powers but failed. During the World-Eater's attack on Limbo, Nightcrawler agreed to free Apocalypse in exchange for a cure for his friend. After returning Colossus to his normal self, Nightcrawler indeed released Apocalypse from his prison, however what Apocalypse did not expect was that Nightcrawler would throw him into the vortex created by the World-Eater to consume Limbo, seemingly killing him in the process.

Degeneration
Apocalypse is later revealed to be back on Earth, no details about what the Celestials did to him were revealed, and is shown performing experiments to create an immortal vessel which he can then use as a host for his vast power and consciousness by utilizing a modified ancient Celestial technology known as the Finch, which can repair genetic decay. His efforts are not in vain, as he begins to impose his own consciousness onto a human test subject, the fourth attempt, lending it his own regenerative powers to withstand the assault. However, the test subject resists the process, causing a massive chain reaction that bathes Apocalypse and the subject in a wave of energy. Apocalypse's mind and body are torn apart. He finds his mind wandering to that of his birth before his being is fused, mixed, and exploded along with this human form. Once the wave subsides, Apocalypse finds himself in a strange new land that he deduces was the result of the explosion within the Celestial machine that must have caused a dimensional rift which threw him into another dimension. He also discovers that his body has changed as well. Not only does he discover that he can bleed, something that should be impossible with his injury-resistant mutant physiology, but after a fight against a resident of the twisted dimension, which he was able to defeat, Apocalypse learns that his body is actively refusing physiological mutation. Needing to breathe air for the first time in centuries, he comes to a shocking truth as he watches his hand turn from its usual mutated appearance back to a human form: he's becoming human.

After degenerating into an ape form, he is taken out by his previous human test subjects who, unlike him, have ascended in form after being empowered by Apocalypse's own DNA. He and other apes are tortured with the Finch, which was recovered and repaired by the human test subjects. When test subject D experiments on Apocalypse, he uses the last of his mutant power to try to transfer his mind into D and is finally able to possess him, which restores Apocalypse to his former glory and realizes that he had not been transported to another planet, rather the earlier explosion from the Finch had simply evolved his entire South American island, infusing his superior genetics into everything the blast wave struck, transforming it into the tribulation which he had been forced to endure. Apocalypse then gave his perfect host body a trial run as he killed the remaining test subjects, while reducing the entire island to rubble that was reclaimed by the sea.

Apocalypse was soon afterward captured by some mysterious force - later to be revealed as X-Man, Nate Grey - and was being held captive along with Kitty Pryde and anti-mutant senator Ashton Allen.

Dawn of X
During Dawn of X, Apocalypse accepts Xavier's invite to enter Krakoa and even is among the Quiet Council, a group of fourteen powerful and experienced mutants who serve as the island's lawgivers. He takes up learning magic and acts as an advisor to the new Excalibur team. Mutants who lost their powers after M-Day can regain them by dying and undergoing Krakoan resurrection. In order to prevent mass suicide by depowered mutants in order to regain their powers, the Quiet Council of Krakoa devised the Crucible, a trial by combat where a depowered mutant must endure gruelling physical and psychological attacks from Apocalypse before they can die and be resurrected.

Its also revealed that at an uncertain point in the distant past apparently before En Sabah Nur merged himself with the Celestial technology, he met and married his wife Genesis. Together with Genesis' sister Isca, they found and populated a living island known as Okkara. As time passed he and Genesis conceived four children, two sons and two daughters who eventually became their First Horsemen when the island was split by a force wielding the Twilight Sword. The mutant population were then led by Apocalypse and his family to fight the invading Daemons coming from the hellish reality of Amenth. During the war, the enemies' leader Annihilation tried to make a peace treaty with the mutants by offering a gift to them, but only if they would pass a test first. Genesis seemed to easily pass the test, but the gift Annihilation whispered to Genesis was not revealed. In the end, Genesis, the Horsemen, and Arakko decided to move to Amenth in order to hold off the Amenthi forces and deny Annihilation access to Earth by sealing the chasm, while leaving Apocalypse behind, since he wasn't strong enough, much to his and Krakoa's sorrow. However, before Genesis went to Amenth, she made Apocalypse promise to find and judge the succeeding mutants in following years in order to help them fight the threat.

Powers and abilities
Apocalypse is an ancient mutant who further augmented himself after merging with Celestial technology gaining in the process a variety of superhuman abilities. He is also among the rare subspecies of mutants that possess the additional gift of immortality. He has total control over the molecules of his body which enables him to alter his form as it suits him, such as allowing his body to become extremely malleable and flexible, enhance his physical abilities, transform his limbs into weapons, wings, or jets, regenerate from fatal injuries, generate a wide range of powers at will, and adapt his body to apparently any disease or hostile environment. He can also project and absorb energy and is capable of technopathy, being able to directly interface with the various technologies he has at his disposal. Thanks to the aid of his mutant abilities allowing him complete control over his body, special "regeneration" chambers, Celestial technology, and changing bodies, Apocalypse has further enhanced his abilities and now he can generate almost any mutant power at his will.

Aside from his superhuman powers, Apocalypse is extraordinarily intelligent and a scientific genius with knowledge in various areas of science and technology including physics, engineering, genetics, and biology, all of which are more advanced than conventional science. Apocalypse has knowledge of Celestial technology that he uses for his own applications, such as altering mutants or humans. Apocalypse is also a skilled demagogue and a master strategist.

Apocalypse's blood can heal other mutants, but is fatal for humans. Apocalypse's blood can also restore his de-powered mutant descendants as is seen when a large dose of Apocalypse's blood regenerates the lost body part of Chamber and gave him a look similar to Apocalypse.

Reception

 * In 2017, WhatCulture ranked Apocalypse 1st in their "10 Most Evil X-Men Villains" list.
 * In 2018, CBR.com ranked Apocalypse 1st in their "Age Of Apocalypse: The 30 Strongest Characters In Marvel's Coolest Alternate World" list.
 * In 2018, CBR.com ranked Apocalypse second in their "20 Most Powerful Mutants From The '80s" list.

Age of Apocalypse
In the Age of Apocalypse storyline, Apocalypse awakens ten years before Cable would arrive, witnessing the accidental death of Charles Xavier by his son, attacks humanity and conquers much of the Earth. In this universe, his son is alleged to be Holocaust/Nemesis.

Heroic Age
In the 2010 "Heroic Age" storyline, versions of Apocalypse and his Horsemen from a possible future appear in the Avengers Tower after Kang breaks time itself. After a fight with the Avengers, he and his Horsemen disappear.

House of M
In the House of M universe created by Scarlet Witch, Apocalypse was installed as the ruler of North Africa by Magneto. He was apparently killed by Black Bolt after a failed attempt to assassinate King T'Challa at Magneto's behest.

Messiah War
In a future timeline seen in the 2009 storyline "Messiah War", a greatly weakened Apocalypse is attacked by Stryfe and Bishop, but he survives the attack. Afterward, Apocalypse contacts Archangel in the future and begs him to kill him. Archangel refuses and instead hands over some of his techno organic wing blades to him, telling Apocalypse he no longer holds any control over him. Coming into contact with the blades rejuvenates Apocalypse and he offers to join forces with Archangel to kill Stryfe who is on the verge of killing X-Force, Cable, Bishop, as well as Hope Summers. Archangel takes Apocalypse to a Celestial ship, where Apocalypse is then fully restored and wants to avenge what Stryfe did to him. Just as Stryfe is on the verge of taking Hope for himself, Apocalypse and Archangel confront and defeat Stryfe. Apocalypse releases Hope into Cable's care, but says that he will return for her eventually. Apocalypse then drags Stryfe away, intending to use him as a new host body. Stryfe manages to escape and travels back in time to the present.

Mutant X
In the Mutant X universe, Apocalypse is an ally of the X-Men.

Ultimate Marvel
The Ultimate Marvel imprint title features an alternate version of Apocalypse who is an entity worshiped by Sinister. After completing a series of murders, Sinister is transformed into Apocalypse who intends to conquer the planet. The heroes are unable to defeat him until the Phoenix Force appears and destroys him. Although his abilities are never directly stated in total, he is shown to be capable of negating other mutant powers, adapting mutant powers into his own by exposure to them and "evolving" as he is fought. Following a heavy assault by the X-Men, Fantastic Four, and S.H.I.E.L.D. forces, he emerges from an explosion in a red and silver version of his traditional blue cybernetic battle armor. He is also capable of adapting to and overcoming Professor Xavier's psychic assault despite his training during his time in the future with Cable. Cable makes the most concrete implication that evolving is the major element of his powers when he remarks that Xavier must kill Apocalypse quickly before he adapts to his attacks and becomes immune to the telepathy. Apocalypse is finally dispelled by Phoenix while leaving an alive Mister Sinister.

His actual nature is unknown: he proclaims himself to be the first mutant (like in the mainstream series) and Phoenix readings portray him as an ancient being, but this is later contradicted by Nick Fury's revelation in Ultimatum, that explains mutants are a recent creation of the humans. However he later appears again as part of Sinister's psychosis.

What If...?
The character appears in a number of What If...? issues.

title: Apocalypse (character)


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Emergency Vets

Emergency Vets is a reality television series that aired on Animal Planet. First aired in 1998, it depicts the working and outside lives of the veterinarians at Alameda East Veterinary Hospital in Denver, Colorado, plus the animals that they treat. At its peak of popularity, Emergency Vets alternated with The Crocodile Hunter as Animal Planet's most popular show.

The show stopped first-run production because Alameda East was occupied with building and eventually moving into a new facility in Denver. In 2004, a new documentary called E-Vets: The Cutting Edge aired on Animal Planet, showing the changes in Alameda East Veterinary Hospital since the show's final episode. The documentary scored good ratings and has been rerun several times as part of the ''Whoa! Sunday'' umbrella anthology show on Animal Planet, as well as inspiring a follow-up episode first aired in 2005 that took viewers on a tour of the new Alameda East facility while showing cases of animals receiving cutting-edge treatment at the new hospital. Another documentary, Emergency Vets 20 Most Unusual Cases, aired on ''Whoa! Sunday'' in 2006, featuring 20 cases from the series including follow-ups with the families and interviews with the doctors involved.

In 2007, Animal Planet announced that the real-life drama at Alameda East would return to prime-time airwaves under a new title, E-Vet Interns. The new series features six new veterinary interns during their first year of residency practice at the new Alameda East hospital, as well as familiar faces Dr. Robert Taylor, Dr. Kevin Fitzgerald, Dr. Preston Stubbs, and Dr. Holly Knor. In preparation for the new show's debut on January 22, 2007, Animal Planet aired a new E-Vets special, E-Vets: Things Pets Swallow, featuring memorable cases from the Emergency Vets years dealing with dramatic objects that animals have ingested.

Staff
Emergency Vets features a mix of surgeons, general practitioners, specialists, veterinary technicians, and Alameda East's annual class of 4–6 interns per year. Among the staff members featured regularly:

Surgeons

 * Dr. Robert A. Taylor, founder of Alameda East, who specializes in orthopedic surgery
 * Dr. Steve Petersen, surgeon and director of Alameda East's intern program who left the hospital and the show in 1999
 * Dr. Mark Albrecht, surgeon who replaced Petersen in the 2000 season; departed the hospital before the start of the 2001 season
 * Dr. Preston Stubbs, surgeon who replaced Albrecht after his departure in the 2001 season

General Practitioners

 * Dr. Kevin Fitzgerald, general practitioner who specializes in treating exotic animals, especially reptiles
 * Dr. Holly Knor, general practitioner specializing in animal pregnancies and associated issues
 * Dr. Andrea Oncken, general practitioner who left the hospital and the show in 1998
 * Dr. Jeff Steen, graduate of the Alameda East intern program who joined the staff as a general practitioner in 2000; specializes in dental issues
 * Dr. Ted Owen, DVM, Western Carolina Regional Animal Hospital
 * Dr. Fred Rosen, DVM, Western Carolina Regional Animal Hospital
 * Dr. Michelle L. Foot, DVM, Western Carolina Regional Animal Hospital
 * Dr. Brandon T. Hughes, DVM, Western Carolina Regional Animal Hospital
 * Dr. Bill Gibson, DVM, Western Carolina Regional Animal Hospital

Specialists

 * Caroline Adamson (now Adrian), head of Alameda East's physical therapy department
 * Dr. Dan Steinheimer, chief of radiology; director of Alameda East's intern program after Petersen's departure
 * Dr. David Panciera, internal medicine specialist who left the hospital and the show in 1998 to take a professorship at Virginia Tech in Blacksburg, Virginia
 * Dr. Doug Santen, internal medicine specialist
 * Dr. Lauren Prause, internal medicine specialist who replaced Panciera in 1998 and left the show in 2000
 * Dr. Etta Wertz, chief of anesthesiology who left the show in 2000
 * Dr. James Bailey, consulting veterinary anesthesiologist
 * Dr. Ric Olsen, human dentist who serves as an associate dentist at Alameda East

Veterinary Technicians

 * Rebecca Barwick, vet tech who adopts an owner-surrendered German Shepherd in the episode "Perfectly Imperfect"
 * Dr. John Fiddler, vet tech who returned to Alameda East after graduating from veterinary school to become an intern veterinarian, leaving the show in 2000
 * Ray Parham, CVT Sr. vet tech specializing in radiology procedures
 * Jackie Steinheimer (née Lenz), Sr. vet tech who later married Dan Steinheimer and now runs Alameda East's Associate Staff program
 * Jean Wilbert, vet tech often featured giving chemotherapy to animals undergoing cancer treatments
 * Laura Maez, vet tech during the ringworm episode, now works at another Denver Area ER clinic

Special Years Movie

 * Dog
 * Squirrel
 * Ostrich
 * Horse
 * Rabbit
 * Panda
 * Mouse
 * Camel
 * Raccoon

The farm animals

 * Pig
 * Cow
 * Sheep
 * Cat
 * Pony
 * Rooster
 * Duck

The Wild Animals

 * Elephant
 * Frog
 * Zebra
 * Hippo
 * Lion
 * Penguin
 * Tiger
 * Polar Bear
 * Giraffe
 * Brown Bear
 * Chimpanzee
 * Red Fox
 * Owl
 * Coyote
 * Wolf

Interns

 * Dr. Rani Pheneger (now Reyter), graduate of the Alameda East intern program who left the hospital and the show in 1998
 * Dr. Juli White, graduate of the Alameda East intern program who left the hospital and the show in 1998
 * Dr. Karin Cannizzo, graduate of the Alameda East intern program who left the hospital and the show in 1998
 * Dr. Dennis Crow, graduate of the Alameda East intern program who left the hospital and the show in 1998
 * Dr. Craig Webb, graduate of the Alameda East intern program who stayed an extra six months after his internship on a special assignment before leaving the hospital and the show in 1999
 * Dr. Milan Hess, graduate of the Alameda East intern program who left the hospital and the show in 1999
 * Dr. Sandy Wang, graduate of the Alameda East intern program who left the hospital and the show in 1999
 * Dr. Laura Peycke, graduate of the Alameda East intern program who left the hospital and the show in 1999
 * Dr. Amy Estrada, graduate of the Alameda East intern program who left the hospital and the show in 1999
 * Dr. Katie Miller, graduate of the Alameda East intern program who left the hospital and the show in 1999
 * Dr. Corey Wall, graduate of the Alameda East intern program who left the hospital and the show in 2000
 * Dr. Jason Wheeler, graduate of the Alameda East intern program who left the hospital and the show in 2000 to work alongside Dr. Steve Petersen at another Denver-area animal hospital. Then in 2012 moved to Virginia to open a veterinary referral practice.
 * Dr. Carrie Stephaniak, graduate of the Alameda East intern program who left the hospital and the show in 2000

E-Vet Interns
E-Vet Interns is a reality television series about veterinary interns working at Alameda East Veterinary Hospital in Denver, Colorado. It is a spinoff of Emergency Vets. E-Vet Interns began airing on January 22, 2007, also on Animal Planet.

title: Emergency Vets


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Gibbs phenomenon

In mathematics, the Gibbs phenomenon is the oscillatory behavior of the Fourier series of a piecewise continuously differentiable periodic function around a jump discontinuity. The $N$ th partial Fourier series of the function (formed by summing the $N$ lowest constituent sinusoids of the Fourier series of the function) produces large peaks around the jump which overshoot and undershoot the function values. As more sinusoids are used, this approximation error approaches a limit of about 9% of the jump, though the infinite Fourier series sum does eventually converge almost everywhere (pointwise convergence on continuous points) except points of discontinuity.

The Gibbs phenomenon was observed by experimental physicists and was believed to be due to imperfections in the measuring apparatus, but it is in fact a mathematical result. It is one cause of ringing artifacts in signal processing. It is named after Josiah Willard Gibbs.

Description

The Gibbs phenomenon is a behavior of the Fourier series of a function with a jump discontinuity and is described as the following:"As more Fourier series constituents or components are taken, the Fourier series shows the first overshoot in the oscillatory behavior around the jump point approaching ~ 9% of the (full) jump and this oscillation does not disappear but gets closer to the point so that the integral of the oscillation approaches zero."At the jump point, the Fourier series gives the average of the function's both side limits toward the point.

Square wave example
The three pictures on the right demonstrate the Gibbs phenomenon for a square wave (with peak-to-peak amplitude of $c$ from $-c/2$  to $c/2$  and the periodicity $L$ ) whose $N$ th partial Fourier series is $$ \frac{2c}{\pi}\left ( \sin(\omega x) + \frac{1}{3} \sin(3\omega x) + \cdots + \frac{1}{2N-1} \sin((2N-1)\omega x) \right )$$

where $\omega = 2\pi/L$. More precisely, this square wave is the function $f(x)$ which equals $$\tfrac{c}{2}$$ between $2n(L/2)$  and $(2n+1)(L/2)$  and $-\tfrac{c}{2}$  between $(2n+1)(L/2)$  and $(2n+2)(L/2)$  for every integer $n$ ; thus, this square wave has a jump discontinuity of peak-to-peak height $c$  at every integer multiple of $L/2$.

As more sinusoidal terms are added (i.e., increasing $N$ ), the error of the partial Fourier series converges to a fixed height. But because the width of the error continues to narrow, the area of the error – and hence the energy of the error – converges to 0. The square wave analysis reveals that the error exceeds the height (from zero) $$\tfrac{c}{2}$$ of the square wave by $$\frac{c}{\pi} \int_0^\pi \frac{\sin(t)}{t}\ dt - \frac{c}{2} = c \cdot (0.089489872236\dots).$$

or about 9% of the full jump $c$. More generally, at any discontinuity of a piecewise continuously differentiable function with a jump of $c$, the $N$ th partial Fourier series of the function will (for a very large $N$ value) overshoot this jump by an error approaching $c \cdot (0.089489872236\dots)$  at one end and undershoot it by the same amount at the other end; thus the "full jump" in the partial Fourier series will be about 18% larger than the full jump in the original function. At the discontinuity, the partial Fourier series will converge to the midpoint of the jump (regardless of the actual value of the original function at the discontinuity) as a consequence of Dirichlet's theorem. The quantity $$\int_0^\pi \frac{\sin t}{t}\ dt = (1.851937051982\dots) = \frac{\pi}{2} + \pi \cdot (0.089489872236\dots)$$ is sometimes known as the Wilbraham–Gibbs constant.

History
The Gibbs phenomenon was first noticed and analyzed by Henry Wilbraham in an 1848 paper. The paper attracted little attention until 1914 when it was mentioned in Heinrich Burkhardt's review of mathematical analysis in Klein's encyclopedia. In 1898, Albert A. Michelson developed a device that could compute and re-synthesize the Fourier series. A widespread myth says that when the Fourier coefficients for a square wave were input to the machine, the graph would oscillate at the discontinuities, and that because it was a physical device subject to manufacturing flaws, Michelson was convinced that the overshoot was caused by errors in the machine. In fact the graphs produced by the machine were not good enough to exhibit the Gibbs phenomenon clearly, and Michelson may not have noticed it as he made no mention of this effect in his paper about his machine or his later letters to Nature.

Inspired by correspondence in Nature between Michelson and A. E. H. Love about the convergence of the Fourier series of the square wave function, J. Willard Gibbs published a note in 1898 pointing out the important distinction between the limit of the graphs of the partial sums of the Fourier series of a sawtooth wave and the graph of the limit of those partial sums. In his first letter Gibbs failed to notice the Gibbs phenomenon, and the limit that he described for the graphs of the partial sums was inaccurate. In 1899 he published a correction in which he described the overshoot at the point of discontinuity (Nature, April 27, 1899, p. 606). In 1906, Maxime Bôcher gave a detailed mathematical analysis of that overshoot, coining the term "Gibbs phenomenon" and bringing it into widespread use.

After the existence of Henry Wilbraham's paper became widely known, in 1925 Horatio Scott Carslaw remarked, "We may still call this property of Fourier's series (and certain other series) Gibbs's phenomenon; but we must no longer claim that the property was first discovered by Gibbs."

Explanation
Informally, the Gibbs phenomenon reflects the difficulty inherent in approximating a discontinuous function by a finite series of continuous sinusoidal waves. It is important to put emphasis on the word finite, because even though every partial sum of the Fourier series overshoots around each discontinuity it is approximating, the limit of summing an infinite number of sinusoidal waves does not. The overshoot peaks moves closer and closer to the discontinuity as more terms are summed, so convergence is possible.

There is no contradiction (between the overshoot error converging to a non-zero height even though the infinite sum has no overshoot), because the overshoot peaks move toward the discontinuity. The Gibbs phenomenon thus exhibits pointwise convergence, but not uniform convergence. For a piecewise continuously differentiable (class C1) function, the Fourier series converges to the function at every point except at jump discontinuities. At jump discontinuities, the infinite sum will converge to the jump discontinuity's midpoint (i.e. the average of the values of the function on either side of the jump), as a consequence of Dirichlet's theorem.

The Gibbs phenomenon is closely related to the principle that the smoothness of a function controls the decay rate of its Fourier coefficients. Fourier coefficients of smoother functions will more rapidly decay (resulting in faster convergence), whereas Fourier coefficients of discontinuous functions will slowly decay (resulting in slower convergence). For example, the discontinuous square wave has Fourier coefficients $$(\tfrac{1}{1},{\scriptstyle\text{0}},\tfrac{1}{3},{\scriptstyle\text{0}},\tfrac{1}{5},{\scriptstyle\text{0}},\tfrac{1}{7},{\scriptstyle\text{0}},\tfrac{1}{9},{\scriptstyle\text{0}},\dots)$$ that decay only at the rate of $$\tfrac{1}{n}$$, while the continuous triangle wave has Fourier coefficients $$(\tfrac{1}{1^2},{\scriptstyle\text{0}},\tfrac{-1}{3^2},{\scriptstyle\text{0}},\tfrac{1}{5^2},{\scriptstyle\text{0}},\tfrac{-1}{7^2},{\scriptstyle\text{0}},\tfrac{1}{9^2},{\scriptstyle\text{0}},\dots)$$ that decay at a much faster rate of $$\tfrac{1}{n^2}$$.

This only provides a partial explanation of the Gibbs phenomenon, since Fourier series with absolutely convergent Fourier coefficients would be uniformly convergent by the Weierstrass M-test and would thus be unable to exhibit the above oscillatory behavior. By the same token, it is impossible for a discontinuous function to have absolutely convergent Fourier coefficients, since the function would thus be the uniform limit of continuous functions and therefore be continuous, a contradiction. See.

Solutions
Since the Gibbs phenomenon comes from undershooting, it may be eliminated by using kernels that are never negative, such as the Fejér kernel.

In practice, the difficulties associated with the Gibbs phenomenon can be ameliorated by using a smoother method of Fourier series summation, such as Fejér summation or Riesz summation, or by using sigma-approximation. Using a continuous wavelet transform, the wavelet Gibbs phenomenon never exceeds the Fourier Gibbs phenomenon. Also, using the discrete wavelet transform with Haar basis functions, the Gibbs phenomenon does not occur at all in the case of continuous data at jump discontinuities, and is minimal in the discrete case at large change points. In wavelet analysis, this is commonly referred to as the Longo phenomenon. In the polynomial interpolation setting, the Gibbs phenomenon can be mitigated using the S-Gibbs algorithm.

Formal mathematical description of the Gibbs phenomenon
Let $f: {\mathbb R} \to {\mathbb R}$ be a piecewise continuously differentiable function which is periodic with some period $L > 0$. Suppose that at some point $x_0$, the left limit $f(x_0^-)$ and right limit $f(x_0^+)$  of the function $f$  differ by a non-zero jump of $c$ : $$ f(x_0^+) - f(x_0^-) = c \neq 0.$$

For each positive integer $N$ ≥ 1, let $ S_N f(x)$  be the $N$ th partial Fourier series ($S_N$  can be treated as a mathematical operator on functions.) $$ S_N f(x) := \sum_{-N \leq n \leq N} \widehat f(n) e^{\frac{i2\pi n x}{L}} = \frac{1}{2} a_0 + \sum_{n=1}^N \left( a_n \cos\left(\frac{2\pi nx}{L}\right) + b_n \sin\left(\frac{2\pi nx}{L}\right) \right),$$

where the Fourier coefficients $\widehat f(n), a_n, b_n$ for integers $n$  are given by the usual formulae $$ \widehat f(n) := \frac{1}{L} \int_0^L f(x) e^{-\frac{i2\pi nx}{L}}\, dx$$ $$ a_0 := \frac{1}{L} \int_0^L f(x)\ dx$$ $$ a_n := \frac{2}{L} \int_0^L f(x) \cos\left(\frac{2\pi nx}{L}\right)\, dx$$ $$ b_n := \frac{2}{L} \int_0^L f(x) \sin\left(\frac{2\pi nx}{L}\right)\, dx.$$

Then we have $$ \lim_{N \to \infty} S_N f\left(x_0 + \frac{L}{2N}\right) = f(x_0^+) + c\cdot (0.089489872236\dots)$$ and $$ \lim_{N \to \infty} S_N f\left(x_0 - \frac{L}{2N}\right) = f(x_0^-) - c\cdot (0.089489872236\dots)$$ but $$ \lim_{N \to \infty} S_N f(x_0) = \frac{f(x_0^-) + f(x_0^+)}{2}.$$

More generally, if $x_N$ is any sequence of real numbers which converges to $x_0$  as $N \to \infty$, and if the jump of $a$  is positive then $$ \limsup_{N \to \infty} S_N f(x_N) \leq f(x_0^+) + c\cdot (0.089489872236\dots)$$ and $$ \liminf_{N \to \infty} S_N f(x_N) \geq f(x_0^-) - c\cdot (0.089489872236\dots).$$

If instead the jump of $c$ is negative, one needs to interchange limit superior ($ \limsup$ ) with limit inferior ($ \liminf$ ), and also interchange the $\leq$  and $\ge$  signs, in the above two inequalities.

Proof of the Gibbs phenomenon in a general case
Stated again, let $f: {\mathbb R} \to {\mathbb R}$ be a piecewise continuously differentiable function which is periodic with some period $L > 0$, and this function has multiple jump discontinuity points denoted $x_i$  where $i = 0, 1, 2, $  and so on. At each discontinuity, the amount of the vertical full jump is $c_i$.

Then, $f$ can be expressed as the sum of a continuous function $f_c$  and a multi-step function $f_s $  which is the sum of step functions such as

$$f = f_c + f_s,$$$$f_s = f_{s_1} + f_{s_2} + f_{s_3} + \cdots,$$$$f_{s_i}(x) = \begin{cases} 0 & \text{if } x \leq x_i, \\ c_i, & \text{if } x > x_i. \end{cases} $$

$ S_N f(x)$ as the $N $ th partial Fourier series of $f = f_c + f_s = f_c + \left ( f_{s_1} + f_{s_2} + f_{s_3} + \ldots \right )  $  will converge well at all $x  $  points except points near discontinuities $x_i$. Around each discontinuity point $x_i$, $f_{s_i} $  will only have the Gibbs phenomenon of its own (the maximum oscillatory convergence error of ~ 9% of the jump $$c_i  $$, as shown in the square wave analysis) because other functions are continuous ($$f_c$$) or flat zero ($$f_{s_j}$$ where $$j \neq i$$) around that point. This proves how the Gibbs phenomenon occurs at every discontinuity.

Signal processing explanation
From a signal processing point of view, the Gibbs phenomenon is the step response of a low-pass filter, and the oscillations are called ringing or ringing artifacts. Truncating the Fourier transform of a signal on the real line, or the Fourier series of a periodic signal (equivalently, a signal on the circle), corresponds to filtering out the higher frequencies with an ideal (brick-wall) low-pass filter. This can be represented as convolution of the original signal with the impulse response of the filter (also known as the kernel), which is the sinc function. Thus, the Gibbs phenomenon can be seen as the result of convolving a Heaviside step function (if periodicity is not required) or a square wave (if periodic) with a sinc function: the oscillations in the sinc function cause the ripples in the output.

In the case of convolving with a Heaviside step function, the resulting function is exactly the integral of the sinc function, the sine integral; for a square wave the description is not as simply stated. For the step function, the magnitude of the undershoot is thus exactly the integral of the left tail until the first negative zero: for the normalized sinc of unit sampling period, this is $\int_{-\infty}^{-1} \frac{\sin(\pi x)}{\pi x}\,dx.$ The overshoot is accordingly of the same magnitude: the integral of the right tail or (equivalently) the difference between the integral from negative infinity to the first positive zero minus 1 (the non-overshooting value).

The overshoot and undershoot can be understood thus: kernels are generally normalized to have integral 1, so they result in a mapping of constant functions to constant functions – otherwise they have gain. The value of a convolution at a point is a linear combination of the input signal, with coefficients (weights) the values of the kernel.

If a kernel is non-negative, such as for a Gaussian kernel, then the value of the filtered signal will be a convex combination of the input values (the coefficients (the kernel) integrate to 1, and are non-negative), and will thus fall between the minimum and maximum of the input signal – it will not undershoot or overshoot. If, on the other hand, the kernel assumes negative values, such as the sinc function, then the value of the filtered signal will instead be an affine combination of the input values and may fall outside of the minimum and maximum of the input signal, resulting in undershoot and overshoot, as in the Gibbs phenomenon.

Taking a longer expansion – cutting at a higher frequency – corresponds in the frequency domain to widening the brick-wall, which in the time domain corresponds to narrowing the sinc function and increasing its height by the same factor, leaving the integrals between corresponding points unchanged. This is a general feature of the Fourier transform: widening in one domain corresponds to narrowing and increasing height in the other. This results in the oscillations in sinc being narrower and taller, and (in the filtered function after convolution) yields oscillations that are narrower (and thus with smaller area) but which do not have reduced magnitude: cutting off at any finite frequency results in a sinc function, however narrow, with the same tail integrals. This explains the persistence of the overshoot and undershoot.

Thus, the features of the Gibbs phenomenon are interpreted as follows:
 * the undershoot is due to the impulse response having a negative tail integral, which is possible because the function takes negative values;
 * the overshoot offsets this, by symmetry (the overall integral does not change under filtering);
 * the persistence of the oscillations is because increasing the cutoff narrows the impulse response but does not reduce its integral – the oscillations thus move towards the discontinuity, but do not decrease in magnitude.

Square wave analysis

We examine the $N$ th partial Fourier series $ S_N f(x)$ of a square wave $f(x)$  with the periodicity $L$  and a discontinuity of a vertical "full" jump $c$  from $y = y_0$  at $x = x_0$. Because the case of odd $N$ is very similar, let us just deal with the case when $N$  is even:

$$S_N f(x) = \left(y_0 + \frac{c}{2} \right) + \frac{2c}\pi \left ( \sin(\omega (x - x_0) ) + \frac{1}{3} \sin(3\omega (x - x_0)) + \cdots + \frac{1}{N-1} \sin((N-1)\omega (x - x_0)) \right )$$

with $\omega = \frac{2\pi}{L}$. ($N = 2N'$ where $N'$  is the number of non-zero sinusoidal Fourier series components so there are literatures using $N'$  instead of $N$ .) Substituting $x = x_0$  (a point of discontinuity), we obtain $$S_N f(x_0) = \left(y_0 + \frac{c}{2}\right) = \frac{f(0^-) + f(0^+)}{2} = \frac{y_0 + (y_0 + c)}{2}$$ as claimed above. (The first term that only survives is the average of the Fourier series.)

Next, we find the first maximum of the oscillation around the discontinuity $x = x_0$ by checking the first and second derivatives of $ S_N f(x)$. The first condition for the maximum is that the first derivative equals to zero as

$$\frac{d}{dx} S_N f(x) = \frac{2c}{\pi} \left ( \cos(\omega (x - x_0)) + \cos(3\omega (x - x_0)) + \cdots + \cos((N-1)\omega (x - x_0)) \right ) = \frac{c}{\pi} \frac{\sin(N\omega (x - x_0))}{\sin(\omega (x - x_0))} = 0 $$

where the 2nd equality is from one of Lagrange's trigonometric identities. Solving this condition gives $x - x_0 = k\pi / (N\omega) = kL / (2N) $ for integers $k $  excluding multiples of $N\omega  $  to avoid the zero denominator, so $k = 1, 2, \ldots, N\omega - 1, N\omega + 1, \ldots $   and their negatives are allowed.

The second derivative of $ S_N f(x)$ at $x - x_0 = kL / (2N) $  is

$$\frac{d^2}{dx^2} S_N f(x) = \frac{c\omega}{\pi} \left ( \frac{N\cos(N\omega (x - x_0))\sin(\omega (x - x_0)) - \sin(N\omega (x - x_0))\cos(\omega (x - x_0))}{\sin^2(\omega (x - x_0))} \right ), $$$$\left. \frac{d^2}{dx^2} S_N f(x) \right \vert _{x_0 + kL / (2N)} = \begin{cases} \frac{2c}{L} \frac{N }{\sin(k\pi/N)}, & \text{if }k \text{ is even,} \\[4pt] \frac{2c}{L} \frac{-N }{\sin(k\pi/N)}, & \text{if }k \text{ is odd.} \end{cases} $$

Thus, the first maximum occurs at $x = x_0 + L / (2N) $  ($k = 1 $ ) and $ S_N f(x)$  at this $x $  value is $$S_N f\left(x_0 + \frac{L}{2N} \right) = \left(y_0 + \frac{c}{2}\right) + \frac{2c}{\pi} \left ( \sin\left(\frac{\pi}{N}\right) + \frac{1}{3} \sin\left(\frac{3\pi}{N}\right) + \cdots + \frac{1}{N-1} \sin\left( \frac{(N-1)\pi}{N} \right) \right )$$

If we introduce the normalized sinc function $\operatorname{sinc}(x) = \frac{\sin(\pi x)}{\pi x}$ for $x \neq 0$, we can rewrite this as $$S_N f\left(x_0 + \frac{L}{2N} \right) = (y_0 + \frac{c}{2}) + c \left[ \frac{2}{N} \operatorname{sinc}\left(\frac{1}{N}\right) + \frac{2}{N} \operatorname{sinc}\left(\frac{3}{N}\right)+ \cdots + \frac{2}{N} \operatorname{sinc}\left( \frac{(N-1)}{N} \right) \right].$$

For a sufficiently large $N$, the expression in the square brackets is a Riemann sum approximation to the integral $\int_0^1 \operatorname{sinc}(x)\ dx$ (more precisely, it is a midpoint rule approximation with spacing $$\tfrac{2}{N}$$). Since the sinc function is continuous, this approximation converges to the integral as $$N \to \infty$$. Thus, we have

$$ \begin{align} \lim_{N \to \infty} S_N f\left(x_0 + \frac{L}{2N}\right) & = (y_0 + \frac{c}{2}) + c \int_0^1 \operatorname{sinc}(x)\, dx \\[8pt] & = (y_0 + \frac{c}{2}) + \frac{c}{\pi} \int_{x=0}^1 \frac{\sin(\pi x)}{\pi x}\, d(\pi x) \\[8pt] & = (y_0 + \frac{c}{2}) + \frac{c}{\pi} \int_0^\pi \frac{\sin(t)}{t}\ dt \quad = \quad (y_0 + c) + c \cdot (0.089489872236\dots), \end{align} $$

which was claimed in the previous section. A similar computation shows

$$\lim_{N \to \infty} S_N f\left(x_0 -\frac{L}{2N}\right) = -c \int_0^1 \operatorname{sinc}(x)\, dx = y_0 - c \cdot (0.089489872236\dots).$$

Consequences
The Gibbs phenomenon is undesirable because it causes artifacts, namely clipping from the overshoot and undershoot, and ringing artifacts from the oscillations. In the case of low-pass filtering, these can be reduced or eliminated by using different low-pass filters.

In MRI, the Gibbs phenomenon causes artifacts in the presence of adjacent regions of markedly differing signal intensity. This is most commonly encountered in spinal MRIs where the Gibbs phenomenon may simulate the appearance of syringomyelia.

The Gibbs phenomenon manifests as a cross pattern artifact in the discrete Fourier transform of an image, where most images (e.g. micrographs or photographs) have a sharp discontinuity between boundaries at the top / bottom and left / right of an image. When periodic boundary conditions are imposed in the Fourier transform, this jump discontinuity is represented by continuum of frequencies along the axes in reciprocal space (i.e. a cross pattern of intensity in the Fourier transform).

And although this article mainly focused on the difficulty with trying to construct discontinuities without artifacts in the time domain with only a partial Fourier series, it is also important to consider that because the inverse Fourier transform is extremely similar to the Fourier transform, there equivalently is difficulty with trying to construct discontinuities in the frequency domain using only a partial Fourier series. Thus for instance because idealized brick-wall and rectangular filters have discontinuities in the frequency domain, their exact representation in the time domain necessarily requires an infinitely-long sinc filter impulse response, since a finite impulse response will result in Gibbs rippling in the frequency response near cut-off frequencies, though this rippling can be reduced by windowing finite impulse response filters (at the expense of wider transition bands).

title: Gibbs phenomenon


text:
Pro forma

The term pro forma (Latin for "as a matter of form" or "for the sake of form") is most often used to describe a practice or document that is provided as a courtesy or satisfies minimum requirements, conforms to a norm or doctrine, tends to be performed perfunctorily or is considered a formality. The term is used in legal and business fields to refer to various types of documents that are generated as a matter of course.

Accounting
The pro forma accounting is a statement of the company's financial activities while excluding "unusual and nonrecurring transactions" when stating how much money the company actually made. Examples of expenses often excluded from pro forma results are company restructuring costs, a decline in the value of the company's investments, or other accounting charges, such as adjusting the current balance sheet to fix faulty accounting practices in previous years.

There was a boom in the reporting of pro forma results in the US starting in the late 1990s, with many dot-com companies using the technique to recast their losses as profits, or at least to show smaller losses than the US GAAP accounting showed. The U.S. Securities and Exchange Commission requires publicly traded companies in the United States to report US GAAP-based financial results, and has cautioned companies that using pro forma results to obscure US GAAP results would be considered fraud if used to mislead investors.

Financial statements
In business, pro forma financial statements are prepared in advance of a planned transaction, such as a merger, an acquisition, a new capital investment, or a change in capital structure such as incurrence of new debt or issuance of stock.

The pro forma models the anticipated results of the transaction, with particular emphasis on the projected cash flows, net revenues and taxes. Consequently, pro forma statements summarize the projected future status of a company, based on the current financial statements. Pro forma figures should be clearly labeled as such and the reason for any deviation from reported past figures clearly explained.

For example, when a transaction with a material effect on a company's financial condition is contemplated, the finance department will prepare, for management and board review, a business plan containing pro forma financial statements demonstrating the expected effect of the proposed transaction on the company's financial viability. Lenders and investors will require such statements to structure or confirm compliance with debt covenants such as debt service reserve coverage and debt to equity ratios. Similarly, when a new corporation is envisioned, its founders will prepare pro forma financial statements for the information of prospective investors. Also, banks will request pro forma statements in lieu of tax returns for a start up business in order to verify cash flow before issuing a loan or line of credit.

Invoices
In trade transactions, a pro forma invoice is a document that states a commitment from the seller to sell goods to the buyer at specified prices and terms. It is used to declare the value of the trade. It is not a true invoice because it is not used to record accounts receivable for the seller and accounts payable for the buyer.

Simply, a "pro forma invoice" is a "confirmed purchase order" where buyer and supplier agree on detail and cost of the product to be shipped to the buyer. A pro forma invoice is generally raised when the seller is ready for dispatching the material but they want to ensure that the payment is being sent before dispatch. And similarly, the customer also wants to know which components are included in the pro forma invoice to avoid disagreements later.

A sales quote is prepared in the form of a pro forma invoice, which is different from a commercial invoice. It is used to create a sale and is sent in advance of the commercial invoice. The content of a pro forma invoice is almost identical to a commercial invoice and is usually considered a binding agreement, but because a pro forma invoice is not a legally-binding document, the price may change in advance of the final sale.

A pro forma invoice can also be used for shipments containing items that are not being bought or sold, such as gifts, samples and personal belongings, whereas a commercial invoice is used when the commodities shipped are being bought or sold. However, it is best to use a customs invoice or declaration as border officials require values for the export declaration. A Customs Invoice or declaration is commonly used in New Zealand for air parcel post shipments.

International trade
A pro forma invoice is the same as a commercial invoice, which, when used in international trade, represents the details of an international sale to customs authorities. A pro forma invoice is presented in the place of a commercial invoice when there is no sale between the sender and the importer (for example, in the case of an RMA for replacement goods), or if the terms of the sale between the seller and the buyer are such that a commercial invoice is not yet available at the time of the international shipment. A pro forma invoice is required to state the same facts that the commercial invoice would and the content is prescribed by the governments who are a party to the transaction.

In some countries, customs may accept a pro forma invoice (generated by the importer and not the exporter) if the required commercial invoice is not available at the time when filing entry documents at the port of entry to get goods released from customs. The U.S. Customs and Border Protection, for example, uses pro forma invoices to assess duty and examine goods, but the importer on record is required to post a bond and produce a commercial invoice within 120 days from the date of entry. If the required commercial invoice is needed for statistical purposes, the importer has to produce the commercial invoice within 50 days from the date Customs releases the goods to the importer.

Law
In law, pro forma court rulings are intended merely to facilitate the legal process (indeed to move matters along).

Westminster system
In certain Commonwealth nations with a Westminster system, such as the United Kingdom, Canada, and Australia, pro forma bills are introduced immediately before consideration of the speech from the throne. Pro forma bills are incomplete pieces of legislation and undergo only the first reading stage. They symbolize the authority of the parliament to discuss matters other than those specified by the head of state, for which ostensibly parliament was summoned. After first reading, the bill is never considered further. The pro forma bill was first introduced in the House of Commons of England in 1558.

In the Parliament of the United Kingdom, the equivalents are the Outlawries Bill in the House of Commons and the Select Vestries Bill in the House of Lords. In the Parliament of Canada, such bills are titled Bill C-1, An Act respecting the Administration of Oaths of Office, and Bill S-1, An Act relating to Railways in the House of Commons of Canada and Senate of Canada, respectively. In the Australian House of Representatives, a new bill is drafted at the start of each parliamentary term (in the 47th Parliament this was the Customs Amendment Bill 2022) and presented by the Prime Minister. The bill undergoes the first reading, but a second reading is not moved unlike normal bills. However, departing from British and Canadian tradition, the contents of the bills do address the matters referred to in its title, and could theoretically be enacted like any other normal bill. This practice does not extend to the Australian Senate; instead other formal business is conducted (such as question time) before consideration of the governor-general's speech.

United States
In the federal government of the United States, either house of the Congress (the House of Representatives or the Senate) can hold a pro forma session at which no formal business is expected to be conducted. This is usually to fulfill the obligation under the Constitution "that neither chamber can adjourn for more than three days without the consent of the other." Pro forma sessions can also be used to prevent the president from pocket-vetoing bills, or calling the Congress into special session. They have also been used to prevent presidents from making recess appointments.

In 2012 President Barack Obama attempted to make four appointments during a pro forma session, calling the practice of blocking recess appointments into question. However, in 2014 the Supreme Court of the United States in NLRB v. Noel Canning determined that the President had improperly used his presidential power to make these appointments, stating that while the Senate was in recess punctuated by pro forma sessions the period of time between the sessions was not long enough to invoke such power.

In April 2020, President Donald Trump claimed that the president's constitutional power to "convene or adjourn Congress" "on extraordinary occasions", a power that has never been used to adjourn Congress, though it has been used on rare occasions to convene Congress, empowers him to suspend both houses of Congress (overriding the pro forma procedure) and enabling him to make appointments to vacant government positions while Congress is suspended. The suggestion was condemned by Joe Lockhart. In addition, the President's Constitutional power to adjourn either or both houses of Congress is limited to situations in which the "Time of Adjournment" is disagreed upon between the House and Senate creating a "Case of Disagreement", which implicates Article I, Section 5 of the Constitution, which prohibits either house of Congress from adjourning for more than three days without the consent of the other house of Congress. However, the system of pro forma sessions every three days by both houses of Congress would appear to represent an obstacle to finding a Constitutional "Case of Disagreement" between the houses of Congress regarding an adjournment of more than three days if neither house of Congress ever deems itself adjourned for more than three days and therefore never seeks the consent of the other house of Congress to adjourn and therefore never creates a situation in which a "Case of Disagreement" could arise to authorize the President to exercise this power.

Similar practices exist in the state legislatures, and for similar reasons; for example, in Minnesota, legislative bodies have the same every-three-days meeting requirement that Congress has. Pro forma sessions are held to meet this requirement.

title: Pro forma