The tetrad is the four spores of a yeast, other Ascomycota or Chlamydomonas produced after meiosis. After parent haploids mate, they produce diploids. Under appropriate environmental conditions, diploids sporulate and undergo meiosis. The meiotic products, spores, remain packaged in the parental cell body to produce the tetrad. If the two parents have a mutation in two different genes, the tetrad can segregate these genes as the parental ditype (PD), the non-parental ditype (NPD) or as the tetratype (TT).[1]


Tetrad dissection has become a powerful tool of yeast geneticists, and is used in conjunction with the many established procedures utilizing the versatility of yeasts as model organisms. Use of modern microscopy and micromanipulation techniques allows the four haploid spores of a yeast tetrad to be separated and germinated individually to form isolated spore colonies.



Tetrad analysis can be used to confirm whether a phenotype is caused by a specific mutation, construction of strains, and for investigating gene interaction. Since the frequency of tetrad segregation types is influenced by the recombination frequency for the two markers, the segregation data can be used to calculate the genetic distance between the markers if they are close on the same chromosome. Tetrad analyses have also contributed to detection and study of the phenomena of gene conversion and post-meiotic segregation.[2] These studies have proven central to understanding the mechanism of meiotic recombination, which in turn is a key to understanding the adaptive function of sexual reproduction. The use of tetrads in fine-structure genetic analysis is described in the articles Neurospora crassa and Gene conversion.



During his years in Moscow, Ouspensky wrote for several newspapers and was particularly interested in the then-fashionable idea of the fourth dimension.[12] His first published work was titled The Fourth Dimension[13] and he explored the subject along the ideas prevalent at the time in the works of Charles H. Hinton,[14] the fourth dimension being an extension in space.[15][16] Ouspensky treats time as a fourth dimension only indirectly in a novel he wrote titled Strange Life of Ivan Osokin[17] where he also explores the theory of eternal recurrence.


Gurdjieff proposed that there are three ways of self-development generally known in esoteric circles. These are the Way of the Fakir, dealing exclusively with the physical body, the Way of the Monk, dealing with the emotions, and the Way of the Yogi, dealing with the mind. What is common about the three ways is that they demand complete seclusion from the world. According to Gurdjieff, there is a Fourth Way which does not demand its followers to abandon the world. The work of self-development takes place right in the midst of ordinary life. Gurdjieff called his system a school of the Fourth Way where a person learns to work in harmony with his physical body, emotions and mind. Ouspensky picked up this idea and continued his own school along this line.[20]

Ouspensky made the term "Fourth Way" and its use central to his own teaching of the ideas of Gurdjieff. He greatly focused on Fourth Way schools and their existence throughout history.






God is also represented in the Chinese language by the word Shén. This word may be written in two different forms (see to the right and below). The etymology of this image reveals details about God's work in creation. On the left side of the character, we see an image meaning to REVEAL or DECLARE. Over and over in the Biblical creation account, we are told that "...God said..." (Genesis 1:3, 6, 9, 11, 14, 20, 24, 26, NKJV). The Psalmist declared of God's work of creation:

By the word of the LORD the heavens were made, and all the hosts of them by the breath of His mouth ... For He spoke, and it was done; He commanded, and it stood fast. (Psalm 33:6, 9, NKJV)


On the right side of the character, two images are intertwined. There, we find a MAN and a GARDEN. Man, the crowning jewel of God's creation (Genesis 1:26), was placed in the garden of Eden. Moses recorded,

The LORD God planted a garden eastward in Eden, and there He put the man whom He had formed. (Genesis 2:8, NKJV)



Barron has hung the show in three rooms, devoted to eight of Hartley’s geometric riffs on Native American motifs (featuring a network of tepees and various bird and bow-and-arrow abstractions), eight early nature-based abstractions, and ten of the symbol-fraught, Kandinsky-esque “German Paintings.” Among the codes contained therein: the number four (von Freyburg’s military regiment), the Iron Cross (which von Freyburg was awarded shortly before he died), the number 24 (he was 24 when he died), and a black-and-white chessboard (von Freyburg’s favorite game).

The Iron Cross, Marsden Hartley, 1915. Photo courtesy of Mildred Lane Kemper Art Museum, Washington University in St. Louis

Indian Composition, Marsden Hartley, 1914–15. Photo courtesy of the Frances Lehman Loeb Art Center, Vassar College



Four Americans died in the attack: Ambassador J. Christopher Stevens, Information Officer Sean Smith,[105] and two CIA operatives,[106] Glen Doherty and Tyrone Woods,[107] both former Navy SEALs.[108][109] Stevens was the first United States ambassador killed in an attack since Adolph Dubs was killed in Kabul, Afghanistan in 1979.[110]


On September 12, U.S. President Barack Obama condemned "this outrageous attack" on U.S. diplomatic facilities[162] and stated that "since our founding, the United States has been a nation that respects all faiths. We reject all efforts to denigrate the religious beliefs of others."[162] After referring to "the 9/11 attacks", "troops who made the ultimate sacrifice in Iraq and Afghanistan", and "then last night, we learned the news of this attack in Benghazi"[162] the President urged, "As Americans, let us never, ever forget that our freedom is only sustained because there are people who are willing to fight for it, to stand up for it, and in some cases, lay down their lives for it."[162] He then went on to say, "No acts of terror will ever shake the resolve of this great nation, alter that character, or eclipse the light of the values that we stand for. Today we mourn four more Americans who represent the very best of the United States of America. We will not waver in our commitment to see that justice is done for this terrible act. And make no mistake, justice will be done".[162]


On September 20, White House Press Secretary Jay Carney answered a question about an open hearing with the National Counterterrorism Center Director, Matthew G. Olsen, which referenced which extremist groups might have been involved. Carney said, "It is, I think, self-evident that what happened in Benghazi was a terrorist attack. Our embassy was attacked violently, and the result was four deaths of American officials. So, again, that's self-evident."[182] On the same day, during an appearance on Univision, a Spanish-language television network in the United States, President Obama stated, "What we do know is that the natural protests that arose because of the outrage over the video were used as an excuse by extremists to see if they can also directly harm U.S. interests."[183][184][185][186][187]


On January 23, 2013, during testimony at a Senate hearing on Benghazi, Clinton engaged in a heated exchange with Senator Ron Johnson. When Johnson pressed her to explain why, in the immediate aftermath, no one from the State Department had asked American evacuees if there had been a protest before the attack, Clinton replied:


With all due respect, the fact is, we had four dead Americans! Was it because of a protest or was it because of guys out for a walk one night and decided they'd go kill some Americans?! What difference, at this point, does it make?! It is our job to figure out what happened and do everything we can to prevent it from ever happening again, Senator. Now, honestly, I will do my best to answer your questions about this, but the fact is that people were trying in real time to get to the best information. The [Intelligence Community] has a process, I understand, going with the other committees to explain how these talking points came out. But you know, to be clear, it is, from my perspective, less important today looking backwards as to why these militants decided they did it than to find them and bring them to justice, and then maybe we’ll figure out what was going on in the meantime.[209]



Santi Quattro Coronati is an ancient basilica in Rome, Italy. The church dates back to the 4th (or 5th) century, and is devoted to four anonymous saints and martyrs. The complex of the basilica with its two courtyards, the fortified Cardinal Palace with the Saint Silvester Chapel, and the monastery with its cosmatesque cloister is built in a silent and green part of Rome, between the Colosseum and San Giovanni in Laterano, in an out-of-time setting.


"Santi Quattro Coronati" means the Four Holy Crowned Ones [i.e. martyrs], and refers to the fact that the saints' names are not known, and therefore referred to with their number, and that they were martyrs, since the crown, together to the branches of palm, is an ancient symbol of martyrdom. According to the Passion of St. Sebastian, the four saints were soldiers who refused to sacrifice to Aesculapius, and therefore were killed by order of Emperor Diocletian (284-305). The bodies of the martyrs were buried in the cemetery of Santi Marcellino e Pietro, on the fourth mile of via Labicana, by Pope Miltiades and St Sebastian (whose skull is preserved in the church). Miltiades decided that the martyrs should be venerated with the names of Claudius, Nicostratus, Simpronianus and Castorius; these names — together to a fifth, Simplicius — were those of five Pannonian martyr stonemasons. These martyrs were later identified with the four martyrs from Albano, Secundus (or Severus), Severianus, Carpoforus (Carpophorus) and Victorinus (Vittorinus). The bodies of the martyrs are kept in four ancient sarcophagi in the crypt. According to a lapid dated 1123, the head of one of the four martyrs is buried in Santa Maria in Cosmedin.


The apse contains the frescoes (1630) by Giovanni da San Giovanni of the four patron martyr saints, Severo, Severiano, Carpoforo e Vittorino. The altarpiece on the left nave of S.Sebastiano curato da Lucina e Irene was painted by Giovanni Baglione. The second courtyard holds the entrance to the Oratorio di San Silvestro, with frescoes of medieval origin, as well as others by Raffaellino da Reggio.



The designation Four Crowned Martyrs or Four Holy Crowned Ones (Latin, Sancti Quatuor Coronati) refers to nine individuals venerated as martyrs and saints in the Catholic Church. The nine saints are divided into two groups:


Severus (or Secundius), Severian(us), Carpophorus (Carpoforus), Victorinus (Victorius, Vittorinus)

Claudius, Castorius, Symphorian (Simpronian), Nicostratus, and Simplicius

According to the Golden Legend, the names of the members of the first group were not known at the time of their death “but were learned through the Lord’s revelation after many years had passed."[1] They were called the "Four Crowned Martyrs" because their names were unknown ("crown" referring to the crown of martyrdom).


Severus (or Secundius), Severian(us), Carpophorus, and Victorinus were martyred at Rome or Castra Albana, according to Christian tradition.[2]


According to the Passion of St. Sebastian, the four saints were soldiers (specifically cornicularii, or clerks, in charge of all the regiment's records and paperwork) who refused to sacrifice to Aesculapius, and therefore were killed by order of Emperor Diocletian (284-305), two years after the death of the five sculptors, mentioned below. The bodies of the martyrs were buried in the cemetery of Santi Marcellino e Pietro on the fourth mile of the via Labicana by Pope Miltiades and St. Sebastian (whose skull is preserved in the church).


Second group[edit]

The second group, according to Christian tradition, were sculptors from Sirmium who were killed in Pannonia. They refused to fashion a pagan statue for the Emperor Diocletian or to offer sacrifice to the Roman gods. The Emperor ordered them to be placed alive in lead coffins and thrown into the sea in about 287. Simplicius was killed with them.[1] According to the Catholic Encyclopedia,


"[T]he Acts of these martyrs, written by a revenue officer named Porphyrius probably in the fourth century, relates of the five sculptors that, although they raised no objections to executing such profane images as Victoria, Cupid, and the Chariot of the Sun, they refused to make a statue of Æsculapius for a heathen temple. For this they were condemned to death as Christians. They were put into leaden caskets and drowned in the River Save. This happened towards the end of 305."[3]

Joint veneration[edit]

When the names of the first group were learned, it was decreed that they should be commemorated with the second group.[1] The bodies of the first group were interred by St. Sebastian and Pope Melchiades (Miltiades) at the fourth milestone on the Via Labicana, in a sandpit where there rested the remains of other executed Christians.


It is unclear where the names of the second group actually come from. The tradition states that Melchiades asked that the saints be commemorated as Claudius, Nicostratus, Simpronian, and Castorius. These same names actually are identical to names shared by converts of Polycarp the priest, in the legend of St. Sebastian.[4] According to the Catholic Encyclopedia, however, "this report has no historic foundation. It is merely a tentative explanation of the name Quatuor Coronati, a name given to a group of really authenticated martyrs who were buried and venerated in the catatomb of Saint Marcellinus and Pietro, the real origin of which, however, is not known. They were classed with the five martyrs of Pannonia in a purely external relationship."[3]


The bodies of the martyrs are kept in four ancient sarcophagi in the crypt of Santi Marcellino e Pietro. According to a lapid dated 1123, the head of one of the four martyrs is buried in Santa Maria in Cosmedin.


Confusion and conclusions[edit]

The rather confusing story of the four crowned martyrs was well known in Renaissance Florence, principally as told in the thirteenth-century Golden Legend by Jacopo da Voragine. It appears that the original four martyrs were beaten to death by order of the emperor Diocletian (r. AD 284-305). Their story became conflated with that of a group of five stonecarvers, also martyred by Diocletian, in this case because they refused to carve an image of a pagan idol. Due to their profession as sculptors, the five early Christian martyrs were an obvious choice for the guild of stonemasons, but their number seems often to have been understood to be four, as in this case.[5]


Problems arise with determining the historicity of these martyrs because one group contains five names instead of four. Alban Butler believed that the four names of group one, which the Roman Martyrology and the Breviary say were revealed as those of the Four Crowned Martyrs, were borrowed from the martyrology of the Diocese of Albano Laziale, which kept their feast on August 8, not November 8.[4] These four "borrowed" martyrs were not buried in Rome, but in the catacomb of Albano; their feast was celebrated on August 7 or August 8, the date under which is cited in the Roman Calendar of Feasts of 354.[3] The Catholic Encyclopedia wrote that the "martyrs of Albano have no connection with the Roman martyrs".[3]


The double tradition may have arisen because a second passio had to be written. It was written to account for the fact that there were five saints in group two rather than four. Thus, the story concerning group one was simply invented, and the story describes the death of four martyrs, who were soldiers from Rome rather than Pannonian stonemasons. The Bollandist Hippolyte Delehaye calls this invented tradition "l'opprobre de l'hagiographie" (the disgrace of hagiography).[4]


Delehaye, after extensive research, determined that there was actually only one group of martyrs – the stonemasons of group two - whose relics were taken to Rome.[4] One scholar has written that “the latest research tends to agree” with Delehaye's conclusion.[4]


The Roman Martyrology gives the stonemasons Simpronianus, Claudius, Nicostratus, Castorius and Simplicius as the martyrs celebrated on November 8, and the Albano martyrs Secundus, Carpophorus, Victorinus and Severianus as celebrated on August 8.[6]

The Four Crowned Saints, Nanni di BancoOrsanmicheleFlorence, ca. 1415.


quadrilatero in forma scacherii (“rectangle in the form of a chessboard”)- QUAD IS FOUR

Lattice multiplication has been used historically in many different cultures. It is not known where it arose first, nor whether it developed independently within more than one region of the world.[4] The earliest recorded use of lattice multiplication:[5]

  • in Arab mathematics was by Ibn al-Banna' al-Marrakushi in his Talkhīṣ a‘māl al-ḥisāb, in the Maghreb in the late 13th century

  • in European mathematics was by the unknown author of a Latin treatise in England, Tractatus de minutis philosophicis et vulgaribus, c. 1300

  • in Chinese mathematics was by Wu Jing in his Jiuzhang suanfa bilei daquan, completed in 1450.

The mathematician and educator David Eugene Smith asserted that lattice multiplication was brought to Italy from the Middle East.[6] This is reinforced by noting that the Arabic term for the method, shabakh, has the same meaning as the Italian term for the method, gelosia, namely, the metal grille or grating (lattice) for a window.

It is sometimes erroneously stated that lattice multiplication was described by Muḥammad ibn Mūsā al-Khwārizmī (Baghdad, c. 825) or by Fibonacci in his Liber Abaci (Italy, 1202, 1228).[7] In fact, however, no use of lattice multiplication by either of these two authors has been found. In Chapter 3 of his Liber AbaciFibonacci does describe a related technique of multiplication by what he termed quadrilatero in forma scacherii (“rectangle in the form of a chessboard”). In this technique, the square cells are not subdivided diagonally; only the lowest-order digit is written in each cell, while any higher-order digit must be remembered or recorded elsewhere and then "carried" to be added to the next cell. This is in contrast to lattice multiplication, a distinctive feature of which is that the each cell of the rectangle has its own correct place for the carry digit; this also implies that the cells can be filled in any order desired. Swetz [8] compares and contrasts multiplication by gelosia(lattice), by scacherii (chessboard), and other tableau methods.

The grid method (or box method) is an introductory method for multiple-digit multiplication that is often taught to pupils at primary school or elementary school level. It has been a standard part of the national primary-school mathematics curriculum in England and Wales since the late 1990s.[1]


Both factors are broken up ("partitioned") into their hundreds, tens and units parts, and the products of the parts are then calculated explicitly in a relatively simple multiplication-only stage, before these contributions are then totalled to give the final answer in a separate addition stage.


The calculation 34 × 13, for example, could be computed using the grid:





+ 12



× 30 4

10 300 40

3 90 12

followed by addition to obtain 442, either in a single sum (see right), or through forming the row-by-row totals (300 + 40) + (90 + 12) = 340 + 102 = 442.


This calculation approach (though not necessarily with the explicit grid arrangement) is also known as the partial products algorithm. Its essence is the calculation of the simple multiplications separately, with all addition being left to the final gathering-up stage.


The grid method can in principle be applied to factors of any size, although the number of sub-products becomes cumbersome as the number of digits increases. Nevertheless, it is seen as a usefully explicit method to introduce the idea of multiple-digit multiplications; and, in an age when most multiplication calculations are done using a calculator or a spreadsheet, it may in practice be the only multiplication algorithm that some students will ever need.


The U.S. Army particularly emphasizes the fireteam concept.[8][9][10] Per U.S. Army doctrine a typical fire team consists of four soldiers.


  • Team Leader (TL): Usually either a sergeant or corporal (although occasionally a team is led by a specialist or private first class when the platoon has a shortage of junior NCOs). Provides tactical leadership for the team at all times with a "Do As I Do" attitude; standard equipped with backpack GPS/radio set, and either an M16 rifle or M4 carbine.

  • Rifleman (R): Is 'the baseline standard for all infantrymen'. They are equipped with the M16 rifle or M4 carbine. The rifleman is usually assigned with the grenadier to help balance the firepower capabilities of the automatic rifleman.

  • Grenadier Rifleman (GR): Provides limited high-angle fire over 'Dead zones'. A grenadier is equipped with an M4/M16 with the M203 grenade launcher (or newer M320 grenade launcher) mounted to the weapon.

  • Automatic Rifleman (AR): Provides overwatch and suppressive fire through force multiplication. The most casualty producing person in a fireteam, in terms of firepower and maneuverability when compared to the standard nine-man rifle squad. An automatic rifleman is equipped with a M249 light machine gun. The automatic rifleman is usually assigned with the team leader to maximize directed fields of fire and to help balance the firepower capabilities of the grenadier.

In a Stryker Brigade Combat Team (SBCT)'s infantry rifle companies one man in each rifle squad fireteam is either the squad anti-armor specialist (RMAT), armed with the FGM-148 Javelin, or the squad designated marksman (DM), who carries the M4 carbine and M14 rifle. In both cases, these two positions replace the basic rifleman of the standard rifle squad.[15]

Ranger infantry company rifle squads consist of three four-man teams. The headquarters team is led by the squad leaderand consists of the squad machine gunner (MG), the squad assistant gunner (AG), and the squad radiotelephone operator (RTO). The other two teams are led by a team leader (TL) and in one of the teams a squad rifleman/compassman (R/CM) replaces the basic rifleman.

Fireteams have their origins in the early 20th century. From the Napoleonic Wars until World War I, military tactics involved central control of large numbers of soldiers in mass formation where small units were given little initiative. Groups of four soldiers played a role in the context in guard duty, in the Roman Army referred to as quaternio (Greek τετράδιον).

Skirmishers in the Napoleonic War would often work in teams of two, ranging ahead of the main group and providing covering fire for each other. During World War I trench warfare resulted in a stalemate on the Western Front. In order to combat this stalemate, the Germans developed a doctrinal innovation known as infiltration tactics (based on the Russian tactics used in the Brusilov Offensive), in which a brief intensive artillery preparation would be followed by small, autonomous teams of stormtroopers, who would covertly penetrate defensive lines. The Germans used their stormtroopers organized into squads at the lowest levels to provide a cohesive strike force in breaking through Allied lines. The British and Canadian troops on the Western Front started dividing platoons into sections after the Battle of the Somme in 1916. (This idea was later further developed in World War II.) French Chasseur units in WWI were organized into fireteams, equipped with a light machine gun (Chauchat) team and grenades, to destroy German fire positions by fire (not assault) at up to 200 meters using rifle grenades. The light machine gun team would put suppressive fire on the enemy position, while the grenadier team moved to a position where the enemy embrasure could be attacked with grenades. The Chasseur tactics were proven during the Petain Offensive of 1917. Survivors of these French Chasseur units taught these tactics to American infantry, who used them with effectiveness at St. Mihiel and the Argonne. It was typical of a fireteam in this era to consist of four infantrymen: two assaulters with carbines, one grenadier, and one sapper.


In the inter-war years, United States Marine Corps Captain Evans F. Carlson went to China in 1937 and observed Communist 8th Route Army units of the National Revolutionary Army in action against the Imperial Japanese army. Carlson and Merritt A. Edson are believed to have developed the fireteam concept during the United States occupation of Nicaragua(1912–1933). At that time the US Marine squad consisted of a Corporal and seven Marines all armed with a bolt-action M1903 Springfield rifle and an automatic rifleman armed with a Browning Automatic Rifle. The introduction of the Thompson submachine gun and Winchester Model 1912 shotgun was popular with the Marines as a point-defense weapon for countering ambush by Nicaraguan guerrillas within the thick vegetation that could provide cover for a quick overrun of a patrol. A team of four men armed with these weapons had proven more effective in terms of firepower and maneuverability than the standard nine-man rifle squad.



Aida (Italian: [aˈiːda]) is an opera in four acts by Giuseppe Verdi to an Italian libretto by Antonio Ghislanzoni. Set in Egypt, it was commissioned by and first performed at Cairo's Khedivial Opera House on 24 December 1871; Giovanni Bottesini conducted after Verdi himself withdrew. Today the work holds a central place in the operatic canon, receiving performances every year around the world; at New York's Metropolitan Opera alone, Aida has been sung more than 1,100 times since 1886. Ghislanzoni's scheme follows a scenario often attributed to the French Egyptologist Auguste Mariette, but Verdi biographer Mary Jane Phillips-Matz argues that the source is actually Temistocle Solera.[1]




For Žižek, the dialectic is not a triad of three steps, but a quadruple with four steps: There are “four rather than only three stages of a dialectical process. […] to these three steps another is added: the highest level which paradoxically coincides with the lowest—at this highest level, people do exactly the same as at the previous level, but with a subjective attitude which is the same as the attitude of those at the lowest level” (Žižek 2012, 314-315; see also 294, 501). It “is negativity which can be counted two times, as a direct negation and as a self-relating negation” (Žižek 2012, 501).


Hegel’s formulation at the end of the Science of Logicthat Žižek refers to is that “the term counted as third can also be counted as fourth, and instead of a triplicity, the abstract form may also be taken to be a quadruplicity; in this way the negative or the difference is counted as a duality—The third or the fourth is in general the unity of the first and the second moment, of the immediate and the mediated”




There are plenty of people trying to send Caine on an Abel path. He lives with his grandparents, and they try to steer him right, but they’re not Furious enough to make an impact. Caine and O-Dog scoff at their Christian preachings, with no self-awareness about the fact that they wear crosses around their necks every day, the posers.


In TCM, the four diagnostic methods are: inspection, auscultation and olfaction, inquiring, and palpation

Chrysippus developed a syllogistic or system of deduction in which he made use of five types of basic arguments or argument forms called indemonstrable syllogisms, which played the role of axioms, and four inference rules, called themata by means of which complex syllogisms could be reduced to these axioms.[31] The forms of the five indemonstrables were:[32]


Of the four inference rules, only two survived. One, the so-called first thema, was a rule of antilogism. The other, the third thema, was a cut rule by which chain syllogisms could be reduced to simple syllogisms.[34] The purpose of Stoic syllogistic was not merely to create a formal system. It was also understood as the study of the operations of reason, the divine reason (logos) which governs the universe, of which human beings are a part.[35] The goal was to find valid rules of inference and forms of proof to help people find their way in life.[22]