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Hippolytus of Rome

Hippolytus was one of the most important second-third century Christian theologians, whose provenance and corpus remain elusive to scholars and historians. Suggested communities include Palestine, Anatolia and regions of the mideast; the best historians of literature in the ancient church, including Eusebius of Caesarea and Jerome confess they cannot name where Hippolytus the biblical commentator and theologian served in leadership. They did not possess evidence of his community. Photios I of Constantinople describes him in his Bibliotheca as a disciple of Irenaeus, said to be a disciple of Polycarp, from the context of this passage it is supposed that he suggested that Hippolytus so styled himself; this assertion is doubtful. One older theory asserts he came into conflict with the popes of his time and seems to have headed a schismatic group as a rival to the Bishop of Rome, thus becoming an Antipope. In this view, he opposed the Roman Popes who softened the penitential system to accommodate the large number of new pagan converts.

However, he was reconciled to the Church. Starting in the fourth century, various legends arose about him, identifying him as a priest of the Novatianist schism or as a soldier converted by Saint Lawrence, he has been confused with another martyr of the same name. Pope Pius IV identifies him as "Saint Hippolytus, Bishop of Pontus", martyred in the reign of Severus Alexander through his inscription on a statue found at the Church of Saint Lawrence in Rome and kept at the Vatican as photographed and published in Brunsen. Little is known for certain about his community of origin. One Victorian theory suggested that as a presbyter of the church at Rome under Pope Zephyrinus, Hippolytus was distinguished for his learning and eloquence, it was at this time that Origen a young man, heard him preach. In this view, Hippolytus accused Pope Zephyrinus of modalism, the heresy which held that the names Father and Son are different names for the same subject. Hippolytus championed the Logos doctrine of the Greek apologists, most notably Justin Martyr, which distinguished the Father from the Logos.

An ethical conservative, he was scandalized when Pope Callixtus I extended absolution to Christians who had committed grave sins, such as adultery. Some suggest Hippolytus. At this time, he seems to have allowed himself to be elected as a rival Bishop of Rome, continued to attack Pope Urban I and Pope Pontian. G. Salmon suggests. Allen Brent sees the development of Roman house-churches into something akin to Greek philosophical schools gathered around a compelling teacher. Under this view: during the persecution at the time of Emperor Maximinus Thrax and Pontian were exiled together in 235 to Sardinia dying in the mines, it is quite probable that, before his death there, he was reconciled to the other party at Rome, under Pope Fabian, his body and that of Pontian were brought to Rome. The so-called Chronography of 354 reports that on August 13 in 236, the two bodies were interred in Rome, that of Hippolytus in a cemetery on the Via Tiburtina, his funeral being conducted by Justin the Confessor.

This document indicates that, by about 255, Hippolytus was considered a martyr and gives him the rank of a priest, not of a bishop, an indication that before his death the schismatic was received again into the Church. The name Hippolytus appears in various hagiographical and martyrological sources of the early churches; the facts about the life of the writer Hippolytus, as opposed to other celebrated Christians who bore the name Hippolytus, were lost in the West partly because he wrote in Hellenic Greek. Pope Damasus I dedicated to a Hippolytus one of his famous epigrams, referring to a priest of the Novatianist schism, a view forwarded by Prudentius in the 5th century in his "Passion of St Hippolytus". In the Passionals of the 7th and 8th centuries he is represented as a soldier converted by Saint Lawrence, a legend that long survived in the Roman Breviary, he was confused with a martyr of the same name, buried in Portus, of which city he was believed to have been a bishop, put to death by drowning in a deep well.

According to Prudentius' account, a martyr Hippolytus was dragged to death by wild horses, a striking parallel to the story of the mythological Hippolytus, dragged to death by wild horses at Athens. He described the subterranean tomb of the saint and states that he saw there a picture representing Hippolytus' execution, he confirms August 13 as the date on which a Hippolytus was celebrated but this again refers to the convert of Lawrence, as preserved in the Menaion of the Eastern Orthodox Church. The latter account led to a Hippolytus being considered the patron saint of horses. During the Middle Ages, sick horses were brought to St Ippolyts, England, where a church is dedicated to him. Controversy surrounds the corpus of the writer Hippolytus. In the Victorian Era, scholars claimed his principal work to be the Refutation of all Heresies. Of its ten books, Book I was the most important, it was printed among the works of Origen. Books II and III are lost, Books IV–X were found, without the name of the author, in a monastery of Mount Athos in 1842.

E. Miller published them in 1851 under the title Philosophumena, attributing them to Origen of Alexandria. Recent scholarship prefers to treat the text as the work of an unknown author of Roman o

3-dimensional matching

In the mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching to 3-uniform hypergraphs. Finding a largest 3-dimensional matching is a well-known NP-hard problem in computational complexity theory. Let X, Y, Z be finite, disjoint sets, let T be a subset of X × Y × Z; that is, T consists of triples such that x ∈ X, y ∈ Y, z ∈ Z. Now M ⊆ T is a 3-dimensional matching if the following holds: for any two distinct triples ∈ M and ∈ M, we have x1 ≠ x2, y1 ≠ y2, z1 ≠ z2; the figure on the right illustrates 3-dimensional matchings. The set X is marked with red dots, Y is marked with blue dots, Z is marked with green dots. Figure shows the set T. Figure shows a 3-dimensional matching M with |M| = 2, Figure shows a 3-dimensional matching M with |M| = 3; the matching M illustrated in Figure is a maximum 3-dimensional matching, i.e. it maximises |M|. The matching illustrated in Figures – are maximal 3-dimensional matchings, i.e. they cannot be extended by adding more elements from T.

Here is example interactive visualisation in javascript A 2-dimensional matching can be defined in a analogous manner. Let X and Y be finite, disjoint sets, let T be a subset of X × Y. Now M ⊆ T is a 2-dimensional matching if the following holds: for any two distinct pairs ∈ M and ∈ M, we have x1 ≠ x2 and y1 ≠ y2. In the case of 2-dimensional matching, the set T can be interpreted as the set of edges in a bipartite graph G =. A 2-dimensional matching is a matching in the graph G, that is, a set of pairwise non-adjacent edges. Hence 3-dimensional matchings can be interpreted as a generalization of matchings to hypergraphs: the sets X, Y, Z contain the vertices, each element of T is a hyperedge, the set M consists of pairwise non-adjacent edges. In case of 2-dimensional matching, we have Y = Z. A 3-dimensional matching is a special case of a set packing: we can interpret each element of T as a subset of X ∪ Y ∪ Z. In computational complexity theory, 3-dimensional matching is the name of the following decision problem: given a set T and an integer k, decide whether there exists a 3-dimensional matching M ⊆ T with |M| ≥ k.

This decision problem is known to be NP-complete. There exist; the problem is NP-complete in the special case that k = |X| = |Y| = |Z|. In this case, a 3-dimensional matching is not only a set packing but an exact cover: the set M covers each element of X, Y, Z once. A maximum 3-dimensional matching is a largest 3-dimensional matching. In computational complexity theory, this is the name of the following optimization problem: given a set T, find a 3-dimensional matching M ⊆ T that maximizes |M|. Since the decision problem described above is NP-complete, this optimization problem is NP-hard, hence it seems that there is no polynomial-time algorithm for finding a maximum 3-dimensional matching. However, there are efficient polynomial-time algorithms for finding a maximum bipartite matching, for example, the Hopcroft–Karp algorithm; the problem is APX-complete. However, for any constant ε > 0 there is a polynomial-time -approximation algorithm for 3-dimensional matching. There is a simple polynomial-time 3-approximation algorithm for 3-dimensional matching: find any maximal 3-dimensional matching.

Just like a maximal matching is within factor 2 of a maximum matching, a maximal 3-dimensional matching is within factor 3 of a maximum 3-dimensional matching. List of NP-complete problems Ausiello, Giorgio. Crescenzi, Pierluigi. Garey, Michael R.. Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, ISBN 0-7167-1045-5. Kann, Viggo, "Maximum bounded 3-dimensional matching is MAX SNP-complete", Information Processing Letters, 37: 27–35, doi:10.1016/0020-019090246-E. Karp, Richard M. "Reducibility among combinatorial problems", in Miller, Raymond E.. Karpinski, Marek. Keevash, Peter. Korte, Bernhard. Papadimitriou, Christos H..

North Wind (visual novel)

North Wind is an adult visual novel developed by DreamSoft, a brand of F&C. It first released for Windows on September 24, 2004; the game was ported to the PlayStation 2, released in two separate volumes for the iOS. North Wind follows the player character and protagonist, Makoto Akizuki, a young man, born into a town where every winter, a "Love Letter Festival" is held. Gameplay in North Wind offers branching plot lines, a multi-choice navigation, where the player can attain multiple endings. Media based on the game has been published; this includes audio CDs, art books, a manga adaptation which serialized in ASCII Media Works' Dengeki Daioh magazine. North Wind is a romance visual novel, its gameplay consists of reading and progressing through the story's narrative and dialogue. The game's text is accompanied by character sprites, which represent who Makoto is talking to, appearing on top of background artwork. Throughout the game, the player encounters CG artwork at certain points in the story, which take the place of the regular background art and character sprites.

North Wind follows a branching plot line with nonlinear sequences and multiple endings, where the plot's direction is affected by the player's decisions. Throughout gameplay, the player is given multiple options to choose from, text progression pauses at these points until a decision is made; these decisions determine the sequence in which the story's events will occur, progress the plot toward a specific heroine's ending. In order to view all plot lines in their entirety, the player will have to replay the game multiple times and make different decisions to progress the plot in alternate directions. In the PC version of the game, there are scenes depicting Makoto and a given heroine having sexual intercourse. However, in the PlayStation 2 and iOS versions, these scenes cannot be viewed; the story of North Wind takes place in a small town surrounded by the mountains. Every winter there, a special event called; the idea, is that if you write a letter to the person that you have feelings for, post it at the local shrine on the 26th of December, the day after Christmas you will get to meet that person.

Makoto Akizuki, the main protagonist and player character, has been living in Tokyo for the last three years, is now visiting that town. Makoto Akizuki is the protagonist of the game, he lived in Tokyo for three years before moving to the small town. Makoto is the only character to not be voiced in the game, he is accompanied by a junior at his school, Hakana Fuyutsuta, the main heroine of the game. She is gentle and kind, but has a weak constitution. Another heroine in the game includes Yukika Yanagi, a mysterious girl who has lost her memory, but due to her bright, cheerful personality, she befriends Makoto quickly. Makoto has a childhood friend called Kanon Ayakawa, she grew up with Makoto like a brother and sister since they were both little. Kanon has a honest personality, works part-time in a cafe. An additional heroine called. Other characters include Misumi Komaki, another childhood friend of Makoto, is one year older than him, she is an older sister figure for him. The last heroine is a kind and polite shrine maiden.

Naizumi Mitomi worked as the director for North Wind. Haioku and Torishimo were the character designers for the game; the main scenario writers were Mugetsu Tomoe, Rōnin Moto, Sakana Hiromori, Sakana worked as the producer. The executive producer was Hiromitsu Sasaoka. Mikano took charge of the graphic progression supervision, the graphics were handled by Miwaza Kamino, Hinata Mutsuki, Hoka. KANZO handled the programming. On September 24, 2004, DreamSoft released North Wind for the PC for both first press edition and regular edition, both rated 18 prohibited. Datam Polystar released the game on April 28, 2005, as a PlayStation 2 port, entitled North Wind ~Eien no Yakusoku~, again for both first press limited and regular editions. However, sexual content was removed and the age rating fell to 15+. On June 11, 2010, an iOS version was released for North Wind, this time all ages, entitled North Wind First Volume. Two months on August 11, 2010, there was another iOS release, entitled North Wind Second Volume.

The iOS versions are only complete. A short-lived manga adaptation of North Wind was serialized in ASCII Media Works' Dengeki Daioh magazine between September 2004 to October 2004 issues. Chinji Yaoroosu illustrated the manga; the manga was serialized in the same month of the game's first initial release. A 127-page fan book titled North Wind Fan Book was published by Ichijinsha on February 22, 2005, it contains a visual gallery, interviews with production staff, a large number of unpublished images, includes comments from the voice cast. The North Wind first press limited edition comes bundled with an art book entitled North Wind Extra Art Book, which contains various illustrations, a preview at the manga. An OP single consisting of one disc entitled North Wind — Last Letter / have eyes only for you… was published on September 3, 2004; the CD contains the two main opening songs, as well as their instrumentals. North Wind's first opening song is "Last Letter" by Kiriko, five minutes and nine seconds long.

The game's second opening song is "Have eyes only for you..." by Kiriko, is five min