title: Janet Mills

text: On June 24, 2021, Mills vetoed seven bills, including one that would have closed the Long Creek Youth Development Center, a juvenile prison. The vetoes received harsh rebuke from progressive Democrats in the Legislature.


title: Janet Mills

text: On April 20, 2022, Mills signed into law the Maine state supplemental budget, which included free community college for students of the class of 2020, 2021, 2022 and 2023.


title: Janet Mills

text: Mills identifies as a moderate Democrat and has often broken the party line with other members of her caucus.


title: Janet Mills

text: Mills has taken steps to expand access to abortion procedures, signing legislation to mandate that both public and private insurance agencies include abortion procedures within the scope of their coverage. After the leak of the 2022 Supreme Court decision in "Dobbs v. Jackson Women's Health Organization", Mills reaffirmed her position that "unlike an apparent majority of the Supreme Court, I do not consider the rights of women to be dispensable."


title: Janet Mills

text: Mills has enacted regulations to curb the use of materials that harm the environment. One such policy, prohibiting the use of plastic bags by Maine retailers, went into effect on April 22, 2020. She also signed into law a ban on the use of styrofoam containers by various industries within the state. This regulation became effective on January 1, 2021.


title: Janet Mills

text: In 2019, the Central Maine Power Company was granted all necessary permissions to begin work on a corridor running from Beattie Township to a power grid in Lewiston, Maine. Despite Mills's initial skepticism of the proposal and pushback from critics, changes to the budget caused Mills to sign the agreement.


title: Janet Mills

text: Mills has also enacted regulatory standards for the quality of water on Indigenous reservations used for sustenance fishing.


title: Janet Mills

text: During her remarks at the UN General Assembly, Mills pledged that Maine would have a carbon-neutral economy by 2045.


title: Janet Mills

text: Mills supports LGBT rights. In May 2019, she signed a bill banning conversion therapy, the pseudoscientific practice aimed at changing one's sexual orientation, from being used on minors. One year earlier, the same bill had passed both chambers of the Maine Legislature, but was vetoed by then-Governor Paul LePage. In June 2021, she officially declared June LGBTQ+ Pride Month.


title: Janet Mills

text: Mills has taken steps to improve relations with Maine's native tribes, despite her prior rocky relationship with them as attorney general. This includes signing a bill to replace the Columbus Day state holiday with Indigenous People's Day and pledging to work to fill seats on a state-tribal commission that had been left empty under her predecessor. She also signed a bill to establish stricter water quality standards for rivers used by Maine's tribes for sustenance fishing, something long sought by the tribes. It also ended a legal dispute between the tribes and the state, for which Mills as attorney general had defended the state's position.


title: Janet Mills

text: As governor-elect, Mills said that the use of Native American imagery and nomenclature associated with Maine School District 54 and its Skowhegan establishment was "a source of pain and anguish" for the state's Indigenous population. After taking office, she signed into law a measure to ban the use of such references in public schools.


title: Janet Mills

text: In 1985, Mills married real estate developer Stanley Kuklinski, with whom she had five stepdaughters and three stepgrandsons and two stepgranddaughters. Kuklinski died due to the effects of a stroke on September 24, 2014. She is the sister of Peter Mills (a former Republican state senator and gubernatorial candidate in 2006 and 2010), Dora Anne Mills, and Paul Mills.


title: Latins (Italic tribe)

text: The Latins (Latin: "Latini"), sometimes known as the Latians, were an Italic tribe which included the early inhabitants of the city of Rome (see Roman people). From about 1000 BC, the Latins inhabited the small region known to the Romans as Old Latium (in Latin "Latium vetus"), that is, the area between the river Tiber and the promontory of Mount Circeo southeast of Rome. Following the Roman expansion, the Latins spread into the Latium adiectum, inhabited by Osco-Umbrian peoples.


title: Latins (Italic tribe)

text: Their language, Latin, belonged to the Italic branch of Indo-European. Speakers of Italic languages are assumed to have migrated into the Italian Peninsula during the late Bronze Age (1200–900 BC). The material culture of the Latins, known as the Latial culture, was a distinctive subset of the proto-Villanovan culture that appeared in parts of the Italian peninsula in the first half of the 12th century BC. The Latins maintained close culturo-religious relations until they were definitively united politically under Rome in 338 BC, and for centuries beyond. These included common festivals and religious sanctuaries.


title: Latins (Italic tribe)

text: The rise of Rome as by far the most populous and powerful Latin state from 600 BC led to volatile relations with the other Latin states, which numbered about 14 in 500 BC. In the period of the Tarquin monarchy ( 550–500 BC), Rome apparently acquired political hegemony over the other states. After the fall of the Roman monarchy around 500 BC, there appears to have been a century of military alliance between Rome and the other Latin states to confront the threat posed to all Latium by raiding by the surrounding Italic mountain tribes, especially the Volsci and Aequi. This system progressively broke down after roughly 390 BC, when Rome's aggressive expansionism led to conflict with other Latin states, both individually and collectively. In 341–338 BC, the Latin states jointly fought the Latin War against Rome in a final attempt to preserve their independence. The war resulted in 338 BC in a decisive Roman victory. The other Latin states were either annexed or permanently subjugated to Rome.


title: Latins (Italic tribe)

text: The name "Latium" has been suggested to derive from the Latin word "latus" ("wide, broad"), referring, by extension, to the plains of the region (in contrast to the mainly mountainous Italian peninsula). If this is true, then "Latini" originally meant "men of the plain".


title: Latins (Italic tribe)

text: The Latins belonged to a group of Indo-European-speaking (IE) tribes, conventionally known as the Italic tribes, that populated central and southern Italy during the Italian Iron Age, which began around 900 BC. The most widely accepted theory suggests that Latins and other proto-Italic tribes first entered Italy in the late Bronze Age proto-Villanovan culture, then part of the central European Urnfield culture system. In particular various authors, such as Marija Gimbutas, had noted important similarities between the proto-Villanovan culture, the South-German Urnfield culture of Bavaria-Upper Austria and Middle-Danube Urnfield culture. According to David W. Anthony proto-Latins originated in today's eastern Hungary, kurganized around 3100 BC by the Yamna culture, while Kristian Kristiansen associated the proto-Villanovans with the Velatice-Baierdorf culture of Moravia and Austria. This is further confirmed by the fact that the subsequent Latial culture, Este culture and Villanovan culture, which introduced iron-working to the Italian peninsula, were so closely related to the Central European Urnfield culture (c. 1300–750 BC), and Hallstatt culture (which succeeded the Urnfield culture), that it is not possible to tell them apart in their earlier stages. Furthermore, the contemporary Canegrate culture of Northern Italy represented a typical western example of the western Hallstatt culture, whose diffusion most probably took place in a Celtic-speaking context.


title: Latins (Italic tribe)

text: Similarly, several authors have suggested that the Beaker culture of Central and Western Europe was a candidate for an early Indo-European culture, and more specifically, for an ancestral European branch of Indo-European dialects, termed "North-west Indo-European", ancestral to Celtic, Italic, Germanic and Balto-Slavic branches. All these groups were descended from Proto-Indo-European speakers from Yamna-culture, whose migrations in Central Europe probably split off Pre-Italic, Pre-Celtic and Pre-Germanic from Proto-Indo-European.


title: Latins (Italic tribe)

text: Leaving archaeology aside, the geographical distribution of the ancient languages of the peninsula may plausibly be explained by the immigration of successive waves of peoples with different languages, according to Cornell. On this model, it appears likely that the "West Italic" group (including the Latins) were the first wave, followed, and largely displaced by, the East Italic (Osco-Umbrian) group. This is deduced from the marginal locations of the surviving West Italic niches. Besides Latin, putative members of the West Italic group are Faliscan (now regarded as merely a Latin dialect), and perhaps Sicel, spoken in central Sicily. The West Italic languages were thus spoken in limited and isolated areas, whereas the "East Italic" group comprised the Oscan and Umbrian dialects spoken over much of central and southern Italy. The chronology of Indo-European immigration remains elusive, as does the relative chronology between the Italic IE languages and the non-IE languages of the peninsula, notably the Etruscan, which is considered related to the Raetic spoken in the Alps. Other examples of non-IE languages in Iron Age Italy are the Camunic language, spoken in the Alps, and the unattested ancient Ligurian and Paleo-Sardinian languages. Most scholars consider that Etruscan is a pre-IE survival, a Paleo-European language part of an older European linguistic substratum, spoken long before the arrival of proto Indo-European speakers. Some scholars have earlier speculated that Etruscan language could have been introduced by later migrants. The ancient Greek historian Herodotus preserves the tradition that the "Tyrrhenoi" (Etruscans) originated in Lydia in Anatolia, but Lydians spoke an Indo-European language, completely different from the Etruscan language. Despite, a possible support for an eastern origin for Etruscan may be provided by two inscriptions in a language closely related to Etruscan found on the island of Lemnos in the northern Aegean sea (see Lemnian language), some scholars believe that the Lemnian language might have arrived in the Aegean Sea during the Late Bronze Age, when Mycenaean rulers recruited groups of mercenaries from Sicily, Sardinia and various parts of the Italian peninsula. Other scholars, however, argue that the presence of a language similar to Etruscan in Lemnos was due to Etruscan commercial adventurers arrived from the west shortly before 700 BC. The archaeological evidence available from Iron Age Etruria shows no sign of any invasion, migration, or arrival of small immigrant-elites from the Eastern Mediterranean who may have imposed their language. Between the end of the Bronze Age and the beginning of the Iron Age, Etruria shows above all contacts with Central Europe and the Urnfield culture, as there is great consensus that the subsequent orientalizing period was an artistic-cultural phenomenon not exclusively Etruscan, also spread to other areas of Italy and the Greek world, and that can be better explained by trade and exchange rather than by migrations. Genetic studies on samples of Etruscan individuals, both on mitochondrial and autosomal DNA, are also against an eastern origin of the Etruscans and have supported a deep, local origin. A 2019 Stanford genetic study, which has analyzed the autosomal DNA of Iron Age samples from the areas around Rome, has concluded that Etruscans were similar to the Latins from Latium vetus. According to British archeologist Phil Perkins, "there are indications that the evidence of DNA can support the theory that Etruscan people are autochthonous in central Italy".


title: Latins (Italic tribe)

text: The tribe spoke the Latin language (specifically Old Latin), a member of the western branch of the Italic languages, in turn a branch of the Indo-European (IE) family of languages in Europe


title: Latins (Italic tribe)

text: The oldest extant inscription in the Latin language is believed to be engraved on the "Lapis Niger" ("Black Stone") discovered in 1899 in the Roman Forum, dating from around 600 BC: in the mid-Roman kingdom, according to the traditional Roman chronology, but more likely close to its inception. Written in a primitive form of Archaic Latin, it indicates that the Romans remained Latin-speakers in the period when some historians have suggested that Rome had become "Etruscanised" in both language and culture. It also lends support to the existence of the Kings of Rome in this era, whom some historians regarded as mythical: the inscription contains the word "recei", the word for "king" in the dative singular in archaic Latin - "regi" in classical Latin, or to the "rex sacrorum", rather than the political king of Rome.


title: Latins (Italic tribe)

text: There is no archaeological evidence at present that Old Latium hosted permanent settlements during the Bronze Age. Some very small amounts of Apennine culture pottery shards have been found in Latium, most likely belonging to transient pastoralists engaged in transhumance. It thus appears that the Latins occupied Latium Vetus not earlier than around 1000 BC. Initially, the Latin immigrants into Latium were probably concentrated in the low hills that extend from the central Apennine range into the coastal plain (much of which was then marshy and malarial, and thus uninhabitable). A notable area of early settlement were the Alban Hills, a plateau about 20 km (13 mi) SE of Rome containing a number of extinct volcanoes and 5 lakes, of which the largest are "lacus Nemorensis" (Lake Nemi) and "lacus Tusculensis" (Lake Albano). These hills provided a defensible, well-watered base. Also the hills on the site of Rome, certainly the Palatine and possibly the Capitoline and the Quirinal, hosted permanent settlements at a very early stage.


title: Latins (Italic tribe)

text: The Latins appear to have become culturally differentiated from the surrounding Osco-Umbrian Italic tribes from c. 1000 BC onwards. From this time, the Latins exhibit the features of the Iron Age Latial culture found in Etruria and the Po valley. In contrast, the Osco-Umbrian tribes do not exhibit the same features of the Latins, who thus shared the broadly same material culture as the Etruscans. The variant of Villanovan found in Latium is dubbed the Latial culture. The most distinctive feature of Latial culture were cinerary urns in the shape of miniature "tuguria" ("huts"). In Phase I of the Latium culture (c. 1000–900 BC) these hut-urns only appear in some burials, but they become standard in Phase II cremation burials (900–770 BC). They represent the typical single-roomed hovels of contemporary peasants, which were made from simple, readily available materials: wattle-and-daub walls and straw roofs supported by wooden posts. The huts remained the main form of Latin housing until about 650 BC. The most famous exemplar was the "Casa Romuli" ("Hut of Romulus") on the southern slope of the Palatine Hill, supposedly built by the legendary founder of Rome with his own hands and which reportedly survived until the time of emperor Augustus (ruled 30 BC - AD 14).


title: Latins (Italic tribe)

text: Around 650 BC began a period of urbanisation, with the establishment of political city-states in Latium. The most notable example is Rome itself, which was originally a group of separate settlements on the various hills. It appears that they coalesced into a single entity around 625 BC, when the first buildings were established on the site of the later Roman Forum.


title: Latins (Italic tribe)

text: According to the mainstream Kurgan hypothesis, the earliest Indo-Europeans were a nomadic steppe people, originating in the Eurasian steppes (southern Russia, northern Caucasus and central Asia). Their livelihood was based on horses and herding. In the historical era, the same socio-cultural lifestyle was maintained, in the same regions, by peoples descended from the Proto-Indo-Europeans (PIEs) known to the Greco-Romans as Scythians, Sarmatians and Alans, whose languages belonged to the Iranian branch of IE. On the basis of common steppe-nomadic features in the cultures of the various Indo-European peoples in the historical era, scholars have reconstructed elements of proto-Indo-European culture. Relics of such elements have been discerned in Roman and Latin customs. Examples include:


title: Latins (Italic tribe)

text: Despite their frequent internecine wars, the Latin city-states maintained close culturo-religious relations throughout their history. Their most important common tribal event was the four-day "Latiar" or "Feriae Latinae" ("Latin Festival"), held each winter on the sacred "mons Albanus" (Monte Cavo, Alban Hills, SE of Rome), an extinct volcano. The climax of the festival was a number of sacrifices to Jupiter Latiaris ("Jupiter of Latium"); the sacrificed meat was shared by the representatives of the Latin communities. These elaborate rituals, as did all Roman religious ceremonies, had to be performed with absolute precision and, if any procedural mistakes were made, had to be repeated from the start. The Latin Festival continued to be held long after all "Latium Vetus" was integrated into the Roman Republic after 338 BC (from then on, the Roman consuls presided over them) and into the Roman imperial era. The historian Livy, writing around AD 20, ascribed Rome's disastrous defeat by the Carthaginian general Hannibal at the Battle of Lake Trasimene in 217 BC to the impiety of the consul Gaius Flaminius, who, in his eagerness to join his army at its assembly-point of Arretium, omitted to attend the Latin Festival.


title: Latins (Italic tribe)

text: Latin cultural-religious events were also held at other common cult-centres e.g. the major common shrine to Diana at Aricia. This may be the sacred grove to Diana which a fragment of Cato's "Origines" recorded dedicated, probably c. 500 BC, by various Latin communities under the leadership of the dictator of Tusculum, Egerius Baebius. Cornell argues that the temple of Diana reportedly founded by the Roman king Servius Tullius on the Aventine hill at Rome was also a common Latin shrine, as it was built outside the "pomerium" or City boundary. There was also an important Latin cult-centre at Lavinium. Lavinium hosted the cult of the Penates, or Latin ancestor-gods. Cornell suggests that the "Sanctuary of the 13 altars" discovered in the 1960s at Lavinium was the site of the Penates cult. Since each of the altars differ in style and date, it has been suggested that each was erected by a separate Latin city-state.


title: Latins (Italic tribe)

text: Under the ever-growing influence of the Italiote Greeks, the Romans acquired their own national origin myth sometime during the early Republican era (500–300 BC). It was centred on the figure of Aeneas, a supposed Trojan survivor of the destruction of Troy by the Achaean Greeks, as related in the poet Homer's epic the "Iliad" (composed c. 800 BC). The legend provided the Romans with a heroic "Homeric" pedigree, as well as a (spurious) ethnic distinctiveness from the other Latins. It also provided a rationale (as poetic revenge for the destruction of Troy) for Rome's hostilities against, and eventual subjugation of, the Greek cities of southern Italy, especially Taras (mod. Taranto) in the period ending 275 BC.


title: Latins (Italic tribe)

text: The figure of Aeneas as portrayed in the "Iliad" lent itself to his adoption as the Roman "Abraham": a mighty warrior of (minor) royal blood who personally slew 28 Achaeans in the war, he was twice saved from certain death by the gods, implying that he had a great destiny to fulfil. A passage in Homer's "Iliad" contains the prophecy that Aeneas and his descendants would one day rule the Trojans. Since the Trojans had been expelled from their own city, it was speculated that Aeneas and other Trojan survivors must have migrated elsewhere.


title: Latins (Italic tribe)

text: The legend is given its most vivid and detailed treatment in the Roman poet Virgil's epic, the "Aeneid" (published around AD 20). According to this, the Latin tribe's first king was Latinus, who gave his name to the tribe and founded the first capital of the Latins, Laurentum, whose exact location is uncertain. The Trojan hero Aeneas and his men fled by sea after the capture and sack of their city, Troy, by the Greeks in 1184 BC, according to one ancient calculation. After many adventures, Aeneas and his Trojan army landed on the coast of Latium near the mouth of the Tiber. Initially, King Latinus attempted to drive them out, but he was defeated in battle. Later, he accepted Aeneas as an ally and eventually allowed him to marry his daughter, Lavinia. Aeneas supposedly founded the city of Lavinium (Pratica di Mare, Pomezia), named after his wife, on the coast not far from Laurentum. It became the Latin capital after Latinus' death. Aeneas' son (by his previous Trojan wife, a daughter of king Priam of Troy), Ascanius, founded a new city, Alba Longa in the Alban Hills, which replaced Lavinium as capital city. Alba Longa supposedly remained the Latin capital for some 400 years under Aeneas' successors, the Latin kings of Alba, until his descendant (supposedly in direct line after 15 generations) Romulus founded Rome in 753 BC. Under a later king Tullus Hostilius (traditional reign-dates 673–642 BC), the Romans razed Alba Longa to the ground and resettled its inhabitants on the "mons Caelius" (Caelian Hill) in Rome.


title: Latins (Italic tribe)

text: There is controversy about how and when Aeneas and his Trojans were adopted as ethnic ancestors by the Romans. One theory is that the Romans appropriated the legend from the Etruscans, who in turn acquired themselves the legend from the Greeks. There is evidence that the Aeneas legend was well known among the Etruscans by 500 BC: excavations at the ancient Etruscan city of Veii discovered a series of statuettes portraying Aeneas fleeing Troy carrying his father on his back, as in the legend. Indeed, the Bulgarian linguist Vladimir Georgiev argued that the original Etruscans were in fact descendants of those Trojan refugees and that the Aeneas legend has a historical basis. Georgiev disputes the mainstream view that Etruscan was not Indo-European: he argues that Etruscan was closely related to the Indo-European Hittite and Lydian languages. Georgiev's thesis hasn't received support from other scholars. Excavations at Troy have yielded a single written document, a letter in Luwian. But as Luwian (which certainly is closely related to Hittite) was used as a kind of diplomatic "lingua franca" in Anatolia, it cannot be argued conclusively that Luwian was the everyday language of Troy. Cornell points out that the Romans may have acquired the legend directly from the Italiote Greeks. The earliest Greek literary reference to Rome as a foundation of Aeneas dates to c. 400 BC. There is also much archaeological evidence of contacts between the cities of archaic Latium and the Greek world e.g. the archaic sanctuary of the Penates at Lavinium, which shows "heavy Greek influence in architectural design and religious ideology", according to Cornell.


title: Latins (Italic tribe)

text: But whatever the origin of the legend, it is clear that the Latins had no historical connection with Aeneas and none of their cities were founded by Trojan refugees. Furthermore, Cornell regards the city of Alba Longa itself as probably mythical. Early Latial-culture remains have been discovered on the shore of the Alban lake, but they indicate a series of small villages, not an urbanised city-state. In any case, traces of the earliest phase of Latial culture also occur at Rome at the same time (c. 1000 BC), so archaeology cannot be used to support the tradition that Rome was founded by people from Alba Longa. If Alba Longa did not exist, then nor did the "Alban kings", whose genealogy was almost certainly fabricated to "prove" Romulus' descent from Aeneas. The genealogy's dubious nature is shown by the fact that it ascribes the 14 Alban kings an average reign of 30 years' duration, an implausibly high figure. The false nature of the Aeneas-Romulus link is also demonstrated by the fact that, in some early versions of the tradition, Romulus is denoted as Aeneas' grandson, despite being chronologically separated from Aeneas by some 450 years.


title: Latins (Italic tribe)

text: Romulus himself was the subject of the famous legend of the suckling she-wolf ("lupa") that kept Romulus and his twin Remus alive in a cave on the Palatine Hill (the "Lupercal") after they had been thrown into the river Tiber on the orders of their wicked uncle, Amulius. The latter had usurped the throne of Alba from the twins' grandfather, king Numitor, and then confined their mother, Rhea Silvia, to the Vestal convent. They were washed ashore by the river, and after a few days with the wolf, were rescued by shepherds.


title: Latins (Italic tribe)

text: Mainstream scholarly opinion regards Romulus as an entirely mythical character, and the legend fictitious. On this view, Romulus was a name fabricated to provide Rome with an eponymous founding hero, a common feature of classical foundation-myths; it is possible that Romulus was named after Rome instead of "vice versa". The name contains the Latin diminutive "-ulus", so it means simply "Roman" or "little Roman". It has been suggested that the name "Roma" was of Etruscan origin, or that it was derived from the Latin word "ruma" ("teat"), presumably because the shape of the Palatine Hill and/or Capitoline Hill resembled a woman's breasts. If Romulus was named "after" the city, it is more likely that he was historical. Nevertheless, Cornell argues that "Romulus probably never existed... His biography is a complex mixture of legend and folk-tale, interspersed with antiquarian speculation and political propaganda".


title: Latins (Italic tribe)

text: In contrast, Andrea Carandini, an archaeologist who has spent most of his career excavating central Rome, advanced the theory that Romulus was a historical figure who indeed founded the city in c. 753 BC, as related by the ancient chroniclers, by ploughing a symbolic sacred furrow to define the city's boundary. But Carandini's views have received scant support among fellow scholars.


title: Latins (Italic tribe)

text: In contrast to the legend of Aeneas, which was clearly imported into the Latin world from an extraneous culture, it appears that the Romulus legend of the suckling she-wolf is a genuine indigenous Latin myth.


title: Latins (Italic tribe)

text: The traditional number of Latin communities for the purposes of the joint religious festivals is given as 30 in the sources. The same number is reported, probably erroneously, as the membership of the Romano-Latin military alliance, labelled the "Latin League" by modern scholars. But it appears that c. 500 BC there were just 15 independent Latin city-states in Latium Vetus, including Rome itself (the other 15 were annexed by the former as they expanded, especially Rome). The size of the city-state territories in c. 500 BC were estimated by Beloch (1926):


title: Latins (Italic tribe)

text: The table above shows the tiny size of Latium Vetus - only about two-thirds the size of the English county of Kent. Rome was by far the largest state, controlling some 35% of the total land area. The next four largest states ranged from just under half the size of Rome down to a fifth of the size; the remaining ten ranged from a tenth of the size down to less than a twentieth.


title: Latins (Italic tribe)

text: From an early stage, the external relations of the Latin city-states were dominated by their largest and most powerful member, Rome. The vast amount of archaeological evidence uncovered since the 1970s has conclusively discredited A. Alföldi's once-fashionable theory that Rome was an insignificant settlement until about 500 BC, and thus that the Republic was not established before about 450, and possibly as late as 400 BC. There is now no doubt that Rome was a unified city (as opposed to a group of separate hilltop settlements) by c. 625 BC and had become the second-largest city in Italy (after Tarentum, 510 hectares) by around 550 BC, when it had an area of about 285 hectares (1.1 sq mile) and an estimated population of 35,000. Rome was thus about half the size of contemporary Athens (585 hectares, including Piraeus) and far larger than any other Latin city.


title: Latins (Italic tribe)

text: The size of Rome at this time lends credence to the Roman tradition, dismissed by Alföldi, that in the late regal period (550–500 BC), traditionally the rule of the Tarquin dynasty, Rome established its political hegemony over the other city-states of Old Latium. According to Livy, king Tarquin the Proud bound the Latin city-states into a military alliance under Roman leadership. Reportedly, Tarquin also annexed Pometia (later Satricum) and Gabii; established control over Tusculum by a marriage alliance with its leader, Octavus Mamilius; and established Roman colonies at Signia and Circeii. He was engaged in besieging Ardea when the revolt against his monarchy broke out. Rome's political control over Latium Vetus is apparently confirmed by the text of the first recorded Romano-Carthaginian treaty, dated by the ancient Greek historian Polybius to 507 BC, a date accepted by Cornell (although some scholars argue a much later date). The treaty describes the Latin cities of Lavinium and Ardea, among others, as "Roman subjects". Although the text acknowledged that not all the Latin cities were subjects of Rome, it clearly placed them under Rome's hegemony, as it provided that if Carthage captured any Latin city, it was obliged to hand it over to Rome's control. Rome's sphere of influence is implied as extending as far as Terracina, 100 km to the south.


title: Latins (Italic tribe)

text: The fall of the Roman monarchy was probably a more lengthy, violent and international process than the swift, bloodless and internal coup related by tradition. The role in the revolution played by the Etruscan Lars Porsenna, king of Clusium, who led an invasion of Roman territory at the time of the revolution, was probably distorted for propaganda reasons by later Roman chroniclers. Livy claims that Porsenna aimed to restore Tarquin to his throne, but failed to take Rome after a siege. Tacitus suggests that Porsenna's army succeeded in occupying the city. The fact that there is no evidence of Tarquin's restoration during this occupation has led some scholars to suggest that it was Porsenna who was the real agent in the expulsion of Tarquin, and that he aimed to replace him as king of Rome. Any danger of an Etruscan takeover of Rome was removed by Porsenna's defeat at Aricia in 504 BC.


title: Latins (Italic tribe)

text: There followed a war between Rome and the other Latin city-states, which probably took advantage of the political turmoil in Rome to attempt to regain/preserve their independence. It appears that Tusculum and Aricia took the lead in organising an anti-Roman alliance. One ancient source names Egerius Baebius, the leader of Tusculum, as the "Latin dictator" (i.e. commander-in-chief of the Latin forces). It appears that Baebius dedicated a sacred grove to Diana at "lucus Ferentinae" (a wood near Aricia) in c. 500 BC in the presence of representatives of Latin states, including Tusculum, Aricia, Lanuvium, Lavinium, Cora, Tibur, Pometia and Ardea. This event was probably contemporaneous with, and connected with, the launch of the Latin alliance. The Latins could apparently count on the support of the Volsci Italic tribe. In addition, they were joined by the deposed Roman king Tarquin the Proud and his remaining followers.


title: Latins (Italic tribe)

text: The Romans apparently prevailed, scoring a notable victory over the Latin forces at Lake Regillus sometime in the period 499-493 BC (the exact year is disputed among scholars).


title: Latins (Italic tribe)

text: Instead of restoring their previous hegemony, the Romans apparently settled for a military alliance on equal terms with the Latins. According to the sources, the "foedus Cassianum" was a bilateral treaty between the Romans on one side and the other Latin city-states combined. It provided for a perpetual peace between the two parties; a defensive alliance by which the parties pledged mutual assistance in case of attack; a promise not to aid or allow passage to each other's enemies; the equal division of spoils of war (half to Rome, half to the other Latins) and provisions to regulate trade between the parties. In addition the treaty probably provided for overall command of the allies' joint forces to alternate between a Roman and a commander from one of the other Latin city-states each year. As the nature of the Tarquinian hegemony over the Latins is unknown, it is impossible to tell how the terms of the Cassian treaty differed from those imposed by the Tarquins. But it is likely that Tarquin rule was more onerous, involving the payment of tribute, while the Republican terms simply involved a military alliance. The impetus to form such an alliance was probably provided by the acute insecurity caused by a phase of migration and invasion of the lowland areas by Italic mountain tribes in the period after 500 BC. The Latins faced repeated incursions by the Hernici, Aequi and Volsci, whose territories surrounded Latium Vetus on its eastern and southern sides.


title: Latins (Italic tribe)

text: The new Romano-Latin military alliance proved strong enough to repel the incursions of the Italic mountain tribes in the period 500–400 BC. During the succeeding century, after Rome had recovered from the catastrophic Gallic invasion of 390 BC, the Romans began a phase of expansionism. In addition to the establishment of a series of Latin colonies on territories annexed from the mountain tribes, Rome annexed a number of neighbouring Latin city-states in steady succession. The increasing threat posed by Roman encroachment led the more powerful Latin states, such as Praeneste, to attempt to defend their independence and territorial integrity by challenging Rome, often in alliance with their erstwhile enemies, mountain-tribes such as the Volsci. Finally, in 341 BC, all the Latin city-states combined in what proved to be a final effort to regain/preserve their independence. The so-called Latin War ended in 338 with a decisive Roman victory, following which Rome annexed most of "Latium Vetus". A few of the larger Latin states, such as Praeneste and Tibur, were allowed to retain a degree of political autonomy, but only in a subordinate status as Roman "socii" ("allies"), tied to Rome by treaties of military alliance.


title: Latins (Italic tribe)

text: A genetic study published in "Science" in November 2019 examined the remains of six Latin males buried near Rome between 900 BC and 200 BC. They carried the paternal haplogroups R-M269, T-L208, R-311, R-PF7589 and R-P312 (two samples), and the maternal haplogroups H1aj1a, T2c1f, H2a, U4a1a, H11a and H10. These examined individuals were distinguished from preceding populations of Italy by the presence of 30% steppe ancestry. Two out of six individuals from Latin burials were found have a mixture of local Iron Age ancestry and ancestry from an Eastern mediterranean population. Among modern populations, four out of six were closest to Northern and Central Italians, and then Spaniards, while the other two were closest to Southern Italians. Overall, the genetic differentiation between the Latins, Etruscans and the preceding proto-Villanovan population of Italy was found to be insignificant.


title: Latins (Italic tribe)

text: Examined individuals from the city of Rome during the time of the Roman Empire (27 BCE – 300 CE) bore almost no genetic resemblance to Rome's founding populations, and were instead shifted towards the Eastern Mediterranean and Middle East. The Imperial population of Rome was found to have been extremely diverse, with barely any of the examined individuals being of primarily European ancestry. It was suggested that the observed genetic replacement of the city's founding populations was a result of heavy migration of merchants and slaves from the populous urban centres of the Middle East and Greece. During late antiquity, after the Imperial era, Rome's population was drastically reduced as a result of political instability, epidemics and economic changes. In this period, more European ancestry is evident in Rome; its inhabitants started to again approximate present-day Italians, and can be modeled as a genetic mixture of Imperial-era inhabitants of the city of Rome and populations from central or northern Italy. In the following Early Medieval period, invasions of barbarians brought further European ancestry into Rome, resulting in the further loss of genetic link to the Eastern Mediterranean and Middle East. By the Middle Ages, the people of Rome again genetically resembled European populations.


title: Latins (Italic tribe)

text: As regards to the data on the pigmentation of eyes, hair and skin, the following results were obtained from the study on ancient DNA of the 11 individuals of the Iron Age/Republican period, coming from Latium and Abruzzo, and the 27 individuals of Medieval/Early Modern period, coming from Latium.


title: Latins (Italic tribe)

text: For Iron Age/Republic period, the eye color is blue in 27% of the examined and dark in the remaining 73%. Hair color is 9% blond or dark blond and 91% dark brown or black. The skin color is intermediate for 82%, intermediate or dark for 9% and dark or very dark for the remaining 9%.


title: Latins (Italic tribe)

text: By contrast, the following results were obtained for Medieval/Early Modern period: the eye color is blue in 26% of the examined and dark in the remaining 74%. Hair color is 22% blond or dark blond, 11% red and 67% dark brown or black. The skin color is pale for 15%, intermediate for 68%, intermediate or dark for 10% and dark or very dark for the remaining 7%.


title: Exponential family

text: In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family. The terms "distribution" and "family" are often used loosely: specifically, "an" exponential family is a "set" of distributions, where the specific distribution varies with the parameter; however, a parametric "family" of distributions is often referred to as ""a" distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families is sometimes loosely referred to as "the" exponential family. They are distinct because they possess a variety of desirable properties, most importantly the existence of a sufficient statistic.


title: Exponential family

text: The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935–1936. Exponential families of distributions provides a general framework for selecting a possible alternative parameterisation of a parametric family of distributions, in terms of natural parameters, and for defining useful sample statistics, called the natural sufficient statistics of the family.


title: Exponential family

text: Most of the commonly used distributions form an exponential family or subset of an exponential family, listed in the subsection below. The subsections following it are a sequence of increasingly more general mathematical definitions of an exponential family. A casual reader may wish to restrict attention to the first and simplest definition, which corresponds to a single-parameter family of discrete or continuous probability distributions.


title: Exponential family

text: Exponential families include many of the most common distributions. Among many others, exponential families includes the following:


title: Exponential family

text: A number of common distributions are exponential families, but only when certain parameters are fixed and known. For example:


title: Exponential family

text: Notice that in each case, the parameters which must be fixed determine a limit on the size of observation values.


title: Exponential family

text: Examples of common distributions that are "not" exponential families are Student's "t", most mixture distributions, and even the family of uniform distributions when the bounds are not fixed. See the section below on examples for more discussion.


title: Exponential family

text: A single-parameter exponential family is a set of probability distributions whose probability density function (or probability mass function, for the case of a discrete distribution) can be expressed in the form


title: Exponential family

text: In addition, the support of formula_4 (i.e. the set of all formula_5 for which formula_4 is greater than 0) does not depend on formula_7. This can be used to exclude a parametric family distribution from being an exponential family. For example, the Pareto distribution has a pdf which is defined for formula_8 (formula_9 being the scale parameter) and its support, therefore, has a lower limit of formula_10. Since the support of formula_11 is dependent on the value of the parameter, the family of Pareto distributions does not form an exponential family of distributions (at least when formula_10 is unknown).


title: Exponential family

text: Often "x" is a vector of measurements, in which case "T"("x") may be a function from the space of possible values of "x" to the real numbers. More generally, "η"("θ") and "T"("x") can each be vector-valued such that formula_13 is real-valued. However, see the discussion below on vector parameters, regarding the exponential family.


title: Exponential family

text: If "η"("θ") = "θ", then the exponential family is said to be in "canonical form". By defining a transformed parameter "η" = "η"("θ"), it is always possible to convert an exponential family to canonical form. The canonical form is non-unique, since "η"("θ") can be multiplied by any nonzero constant, provided that "T"("x") is multiplied by that constant's reciprocal, or a constant "c" can be added to "η"("θ") and "h"("x") multiplied by formula_14 to offset it. In the special case that "η"("θ") = "θ" and "T"("x") = "x" then the family is called a natural exponential family.


title: Exponential family

text: Even when "x" is a scalar, and there is only a single parameter, the functions "η"("θ") and "T"("x") can still be vectors, as described below.


title: Exponential family

text: The function "A"("θ"), or equivalently "g"("θ"), is automatically determined once the other functions have been chosen, since it must assume a form that causes the distribution to be normalized (sum or integrate to one over the entire domain). Furthermore, both of these functions can always be written as functions of "η", even when "η"("θ") is not a one-to-one function, i.e. two or more different values of "θ" map to the same value of "η"("θ"), and hence "η"("θ") cannot be inverted. In such a case, all values of "θ" mapping to the same "η"("θ") will also have the same value for "A"("θ") and "g"("θ").


title: Exponential family

text: What is important to note, and what characterizes all exponential family variants, is that the parameter(s) and the observation variable(s) must factorize (can be separated into products each of which involves only one type of variable), either directly or within either part (the base or exponent) of an exponentiation operation. Generally, this means that all of the factors constituting the density or mass function must be of one of the following forms:


title: Exponential family

text: where "f" and "h" are arbitrary functions of "x"; "g" and "j" are arbitrary functions of "θ"; and "c" is an arbitrary "constant" expression (i.e. an expression not involving "x" or "θ").


title: Exponential family

text: are the same, i.e. a product of two "allowed" factors. However, when rewritten into the factorized form,


title: Exponential family

text: it can be seen that it cannot be expressed in the required form. (However, a form of this sort is a member of a "curved exponential family", which allows multiple factorized terms in the exponent.)


title: Exponential family

text: A factor consisting of a sum where both types of variables are involved (e.g. a factor of the form formula_21) cannot be factorized in this fashion (except in some cases where occurring directly in an exponent); this is why, for example, the Cauchy distribution and Student's "t" distribution are not exponential families.


title: Exponential family

text: The definition in terms of one "real-number" parameter can be extended to one "real-vector" parameter


title: Exponential family

text: A family of distributions is said to belong to a vector exponential family if the probability density function (or probability mass function, for discrete distributions) can be written as


title: Exponential family

text: That is, if the "dimension", , of the parameter vector is less than the "number of functions", , of the parameter vector in the above representation of the probability density function. Most common distributions in the exponential family are "not" curved, and many algorithms designed to work with any exponential family implicitly or explicitly assume that the distribution is not curved.


title: Exponential family

text: As in the above case of a scalar-valued parameter, the function formula_31 or equivalently formula_32 is automatically determined once the other functions have been chosen, so that the entire distribution is normalized. In addition, as above, both of these functions can always be written as functions of formula_33, regardless of the form of the transformation that generates formula_33 from formula_35. Hence an exponential family in its "natural form" (parametrized by its natural parameter) looks like


title: Exponential family

text: The above forms may sometimes be seen with formula_38 in place of formula_39. These are exactly equivalent formulations, merely using different notation for the dot product.


title: Exponential family

text: The vector-parameter form over a single scalar-valued random variable can be trivially expanded to cover a joint distribution over a vector of random variables. The resulting distribution is simply the same as the above distribution for a scalar-valued random variable with each occurrence of the scalar replaced by the vector


title: Exponential family

text: The dimensions of the random variable need not match the dimension of the parameter vector, nor (in the case of a curved exponential function) the dimension of the natural parameter formula_33 and sufficient statistic  .


title: Exponential family

text: We use cumulative distribution functions (CDF) in order to encompass both discrete and continuous distributions.


title: Exponential family

text: Suppose is a non-decreasing function of a real variable. Then Lebesgue–Stieltjes integrals with respect to formula_45 are integrals with respect to the "reference measure" of the exponential family generated by  .


title: Exponential family

text: In this case, is also absolutely continuous and can be written formula_50 so the formulas reduce to that of the previous paragraphs. If is discrete, then is a step function (with steps on the support of ).


title: Exponential family

text: In the definitions above, the functions , , and were apparently arbitrarily defined. However, these functions play a significant role in the resulting probability distribution.


title: Exponential family

text: The function is important in its own right, because the mean, variance and other moments of the sufficient statistic can be derived simply by differentiating . For example, because is one of the components of the sufficient statistic of the gamma distribution, formula_60 can be easily determined for this distribution using . Technically, this is true because


title: Exponential family

text: Exponential families have a large number of properties that make them extremely useful for statistical analysis. In many cases, it can be shown that "only" exponential families have these properties. Examples:


title: Exponential family

text: Given an exponential family defined by formula_62, where formula_63 is the parameter space, such that formula_64. Then


title: Exponential family

text: It is critical, when considering the examples in this section, to remember the discussion above about what it means to say that a "distribution" is an exponential family, and in particular to keep in mind that the set of parameters that are allowed to vary is critical in determining whether a "distribution" is or is not an exponential family.


title: Exponential family

text: The normal, exponential, log-normal, gamma, chi-squared, beta, Dirichlet, Bernoulli, categorical, Poisson, geometric, inverse Gaussian, von Mises and von Mises-Fisher distributions are all exponential families.


title: Exponential family

text: Some distributions are exponential families only if some of their parameters are held fixed. The family of Pareto distributions with a fixed minimum bound "x" form an exponential family. The families of binomial and multinomial distributions with fixed number of trials "n" but unknown probability parameter(s) are exponential families. The family of negative binomial distributions with fixed number of failures (a.k.a. stopping-time parameter) "r" is an exponential family. However, when any of the above-mentioned fixed parameters are allowed to vary, the resulting family is not an exponential family.


title: Exponential family

text: As mentioned above, as a general rule, the support of an exponential family must remain the same across all parameter settings in the family. This is why the above cases (e.g. binomial with varying number of trials, Pareto with varying minimum bound) are not exponential families — in all of the cases, the parameter in question affects the support (particularly, changing the minimum or maximum possible value). For similar reasons, neither the discrete uniform distribution nor continuous uniform distribution are exponential families as one or both bounds vary.


title: Exponential family

text: The Weibull distribution with fixed shape parameter "k" is an exponential family. Unlike in the previous examples, the shape parameter does not affect the support; the fact that allowing it to vary makes the Weibull non-exponential is due rather to the particular form of the Weibull's probability density function ("k" appears in the exponent of an exponent).


title: Exponential family

text: In general, distributions that result from a finite or infinite mixture of other distributions, e.g. mixture model densities and compound probability distributions, are "not" exponential families. Examples are typical Gaussian mixture models as well as many heavy-tailed distributions that result from compounding (i.e. infinitely mixing) a distribution with a prior distribution over one of its parameters, e.g. the Student's "t"-distribution (compounding a normal distribution over a gamma-distributed precision prior), and the beta-binomial and Dirichlet-multinomial distributions. Other examples of distributions that are not exponential families are the F-distribution, Cauchy distribution, hypergeometric distribution and logistic distribution.


title: Exponential family

text: Following are some detailed examples of the representation of some useful distribution as exponential families.


title: Exponential family

text: As a first example, consider a random variable distributed normally with unknown mean "μ" and "known" variance "σ". The probability density function is then


title: Exponential family

text: Next, consider the case of a normal distribution with unknown mean and unknown variance. The probability density function is then


title: Exponential family

text: As an example of a discrete exponential family, consider the binomial distribution with "known" number of trials "n". The probability mass function for this distribution is


title: Exponential family

text: The following table shows how to rewrite a number of common distributions as exponential-family distributions with natural parameters. Refer to the flashcards for main exponential families.


title: Exponential family

text: The above formulas choose the functional form of the exponential-family with a log-partition function formula_89. The reason for this is so that the moments of the sufficient statistics can be calculated easily, simply by differentiating this function. Alternative forms involve either parameterizing this function in terms of the normal parameter formula_90 instead of the natural parameter, and/or using a factor formula_91 outside of the exponential. The relation between the latter and the former is:


title: Exponential family

text: To convert between the representations involving the two types of parameter, use the formulas below for writing one type of parameter in terms of the other.


title: Exponential family

text: The three variants of the categorical distribution and multinomial distribution are due to the fact that the parameters formula_94 are constrained, such that


title: Exponential family

text: Variants 1 and 2 are not actually standard exponential families at all. Rather they are "curved exponential families", i.e. there are formula_96 independent parameters embedded in a formula_97-dimensional parameter space. Many of the standard results for exponential families do not apply to curved exponential families. An example is the log-partition function formula_106, which has the value of 0 in the curved cases. In standard exponential families, the derivatives of this function correspond to the moments (more technically, the cumulants) of the sufficient statistics, e.g. the mean and variance. However, a value of 0 suggests that the mean and variance of all the sufficient statistics are uniformly 0, whereas in fact the mean of the formula_107th sufficient statistic should be formula_108. (This does emerge correctly when using the form of formula_106 shown in variant 3.)


title: Exponential family

text: We start with the normalization of the probability distribution. In general, any non-negative function "f"("x") that serves as the kernel of a probability distribution (the part encoding all dependence on "x") can be made into a proper distribution by normalizing: i.e.


title: Exponential family

text: The factor "Z" is sometimes termed the "normalizer" or "partition function", based on an analogy to statistical physics.


title: Exponential family

text: An important subclass of exponential families are the natural exponential families, which have a similar form for the moment-generating function for the distribution of "x".


title: Exponential family

text: The first two raw moments and all mixed second moments can be recovered from these two identities. Higher-order moments and cumulants are obtained by higher derivatives. This technique is often useful when "T" is a complicated function of the data, whose moments are difficult to calculate by integration.


title: Exponential family

text: Another way to see this that does not rely on the theory of cumulants is to begin from the fact that the distribution of an exponential family must be normalized, and differentiate. We illustrate using the simple case of a one-dimensional parameter, but an analogous derivation holds more generally.


title: Exponential family

text: Where formula_134 is the digamma function (derivative of log gamma), and we used the reverse substitutions in the last step.


title: Exponential family

text: All of these calculations can be done using integration, making use of various properties of the gamma function, but this requires significantly more work.


title: Exponential family

text: indexed by shape parameter formula_138 (this is called the skew-logistic distribution). The density can be rewritten as


title: Exponential family

text: This example illustrates a case where using this method is very simple, but the direct calculation would be nearly impossible.


title: Exponential family

text: The final example is one where integration would be extremely difficult. This is the case of the Wishart distribution, which is defined over matrices. Even taking derivatives is a bit tricky, as it involves matrix calculus, but the respective identities are listed in that article.


title: Exponential family

text: The log-partition function is written in various forms in the table, to facilitate differentiation and back-substitution. We use the following forms:


title: Exponential family

text: Now, for "η", we first need to expand the part of the log-partition function that involves the multivariate gamma function:


title: Exponential family

text: This latter formula is listed in the Wishart distribution article. Both of these expectations are needed when deriving the variational Bayes update equations in a Bayes network involving a Wishart distribution (which is the conjugate prior of the multivariate normal distribution).


title: Exponential family

text: Computing these formulas using integration would be much more difficult. The first one, for example, would require matrix integration.


title: Exponential family

text: The relative entropy (Kullback–Leibler divergence, KL divergence) of two distributions in an exponential family has a simple expression as the Bregman divergence between the natural parameters with respect to the log-normalizer. The relative entropy is defined in terms of an integral, while the Bregman divergence is defined in terms of a derivative and inner product, and thus is easier to calculate and has a closed-form expression (assuming the derivative has a closed-form expression). Further, the Bregman divergence in terms of the natural parameters and the log-normalizer equals the Bregman divergence of the dual parameters (expectation parameters), in the opposite order, for the convex conjugate function.


title: Exponential family

text: Fixing an exponential family with log-normalizer (with convex conjugate ), writing formula_157 for the distribution in this family corresponding a fixed value of the natural parameter (writing for another value, and with for the corresponding dual expectation/moment parameters), writing for the KL divergence, and for the Bregman divergence, the divergences are related as:


title: Exponential family

text: The KL divergence is conventionally written with respect to the "first" parameter, while the Bregman divergence is conventionally written with respect to the "second" parameter, and thus this can be read as "the relative entropy is equal to the Bregman divergence defined by the log-normalizer on the swapped natural parameters", or equivalently as "equal to the Bregman divergence defined by the dual to the log-normalizer on the expectation parameters".


title: Exponential family

text: Exponential families arise naturally as the answer to the following question: what is the maximum-entropy distribution consistent with given constraints on expected values?


title: Exponential family

text: The information entropy of a probability distribution "dF"("x") can only be computed with respect to some other probability distribution (or, more generally, a positive measure), and both measures must be mutually absolutely continuous. Accordingly, we need to pick a "reference measure" "dH"("x") with the same support as "dF"("x").


title: Exponential family

text: where "dF"/"dH" and "dH"/"dF" are Radon–Nikodym derivatives. The ordinary definition of entropy for a discrete distribution supported on a set "I", namely


title: Exponential family

text: Consider now a collection of observable quantities (random variables) "T". The probability distribution "dF" whose entropy with respect to "dH" is greatest, subject to the conditions that the expected value of "T" be equal to "t", is an exponential family with "dH" as reference measure and ("T", ..., "T") as sufficient statistic.


title: Exponential family

text: The derivation is a simple variational calculation using Lagrange multipliers. Normalization is imposed by letting "T" = 1 be one of the constraints. The natural parameters of the distribution are the Lagrange multipliers, and the normalization factor is the Lagrange multiplier associated to "T".


title: Exponential family

text: According to the Pitman–Koopman–Darmois theorem, among families of probability distributions whose domain does not vary with the parameter being estimated, only in exponential families is there a sufficient statistic whose dimension remains bounded as sample size increases.


title: Exponential family

text: Less tersely, suppose "X", (where "k" = 1, 2, 3, ... "n") are independent, identically distributed random variables. Only if their distribution is one of the "exponential family" of distributions is there a sufficient statistic T("X", ..., "X") whose number of scalar components does not increase as the sample size "n" increases; the statistic T may be a vector or a single scalar number, but whatever it is, its size will neither grow nor shrink when more data are obtained.


title: Exponential family

text: As a counterexample if these conditions are relaxed, the family of uniform distributions (either discrete or continuous, with either or both bounds unknown) has a sufficient statistic, namely the sample maximum, sample minimum, and sample size, but does not form an exponential family, as the domain varies with the parameters.


title: Exponential family

text: Exponential families are also important in Bayesian statistics. In Bayesian statistics a prior distribution is multiplied by a likelihood function and then normalised to produce a posterior distribution. In the case of a likelihood which belongs to an exponential family there exists a conjugate prior, which is often also in an exponential family. A conjugate prior π for the parameter formula_33 of an exponential family


title: Exponential family

text: where "s" is the dimension of formula_33 and formula_167 and formula_168 are hyperparameters (parameters controlling parameters). formula_169 corresponds to the effective number of observations that the prior distribution contributes, and formula_168 corresponds to the total amount that these pseudo-observations contribute to the sufficient statistic over all observations and pseudo-observations. formula_171 is a normalization constant that is automatically determined by the remaining functions and serves to ensure that the given function is a probability density function (i.e. it is normalized). formula_172 and equivalently formula_91 are the same functions as in the definition of the distribution over which π is the conjugate prior.


title: Exponential family

text: A conjugate prior is one which, when combined with the likelihood and normalised, produces a posterior distribution which is of the same type as the prior. For example, if one is estimating the success probability of a binomial distribution, then if one chooses to use a beta distribution as one's prior, the posterior is another beta distribution. This makes the computation of the posterior particularly simple. Similarly, if one is estimating the parameter of a Poisson distribution the use of a gamma prior will lead to another gamma posterior. Conjugate priors are often very flexible and can be very convenient. However, if one's belief about the likely value of the theta parameter of a binomial is represented by (say) a bimodal (two-humped) prior distribution, then this cannot be represented by a beta distribution. It can however be represented by using a mixture density as the prior, here a combination of two beta distributions; this is a form of hyperprior.


title: Exponential family

text: An arbitrary likelihood will not belong to an exponential family, and thus in general no conjugate prior exists. The posterior will then have to be computed by numerical methods.


title: Exponential family

text: First, assume that the probability of a single observation follows an exponential family, parameterized using its natural parameter:


title: Exponential family

text: which is termed the sufficient statistic of the data. That is, the value of the sufficient statistic is sufficient to completely determine the posterior distribution. The actual data points themselves are not needed, and all sets of data points with the same sufficient statistic will have the same distribution. This is important because the dimension of the sufficient statistic does not grow with the data size — it has only as many components as the components of formula_33 (equivalently, the number of parameters of the distribution of a single data point).


title: Exponential family

text: This shows that the update equations can be written simply in terms of the number of data points and the sufficient statistic of the data. This can be seen clearly in the various examples of update equations shown in the conjugate prior page. Because of the way that the sufficient statistic is computed, it necessarily involves sums of components of the data (in some cases disguised as products or other forms — a product can be written in terms of a sum of logarithms). The cases where the update equations for particular distributions don't exactly match the above forms are cases where the conjugate prior has been expressed using a different parameterization than the one that produces a conjugate prior of the above form — often specifically because the above form is defined over the natural parameter formula_33 while conjugate priors are usually defined over the actual parameter formula_184


title: Exponential family

text: A one-parameter exponential family has a monotone non-decreasing likelihood ratio in the sufficient statistic "T"("x"), provided that "η"("θ") is non-decreasing. As a consequence, there exists a uniformly most powerful test for testing the hypothesis "H": "θ" ≥ "θ" "vs". "H": "θ" < "θ".


title: Exponential family

text: Exponential families form the basis for the distribution functions used in generalized linear models (GLM), a class of model that encompasses many of the commonly used regression models in statistics. Examples include logistic regression using the binomial family and Poisson regression.


title: Byzantine art

text: Byzantine art comprises the body of Christian Greek artistic products of the Eastern Roman Empire, as well as the nations and states that inherited culturally from the empire. Though the empire itself emerged from the decline of Rome and lasted until the Fall of Constantinople in 1453, the start date of the Byzantine period is rather clearer in art history than in political history, if still imprecise. Many Eastern Orthodox states in Eastern Europe, as well as to some degree the Islamic states of the eastern Mediterranean, preserved many aspects of the empire's culture and art for centuries afterward.


title: Byzantine art

text: A number of contemporary states with the Byzantine Empire were culturally influenced by it without actually being part of it (the "Byzantine commonwealth"). These included the Rus, as well as some non-Orthodox states like the Republic of Venice, which separated from the Byzantine Empire in the 10th century, and the Kingdom of Sicily, which had close ties to the Byzantine Empire and had also been a Byzantine territory until the 10th century with a large Greek-speaking population persisting into the 12th century. Other states having a Byzantine artistic tradition, had oscillated throughout the Middle Ages between being part of the Byzantine Empire and having periods of independence, such as Serbia and Bulgaria. After the fall of the Byzantine capital of Constantinople in 1453, art produced by Eastern Orthodox Christians living in the Ottoman Empire was often called "post-Byzantine." Certain artistic traditions that originated in the Byzantine Empire, particularly in regard to icon painting and church architecture, are maintained in Greece, Cyprus, Serbia, Bulgaria, Romania, Russia and other Eastern Orthodox countries to the present day.


title: Byzantine art

text: Byzantine art originated and evolved from the Christianized Greek culture of the Eastern Roman Empire; content from both Christianity and classical Greek mythology were artistically expressed through Hellenistic modes of style and iconography. The art of Byzantium never lost sight of its classical heritage; the Byzantine capital, Constantinople, was adorned with a large number of classical sculptures, although they eventually became an object of some puzzlement for its inhabitants (however, Byzantine beholders showed no signs of puzzlement towards other forms of classical media such as wall paintings). The basis of Byzantine art is a fundamental artistic attitude held by the Byzantine Greeks who, like their ancient Greek predecessors, "were never satisfied with a play of forms alone, but stimulated by an innate rationalism, endowed forms with life by associating them with a meaningful content." Although the art produced in the Byzantine Empire was marked by periodic revivals of a classical aesthetic, it was above all marked by the development of a new aesthetic defined by its salient "abstract", or anti-naturalistic character. If classical art was marked by the attempt to create representations that mimicked reality as closely as possible, Byzantine art seems to have abandoned this attempt in favor of a more symbolic approach.


title: Byzantine art

text: The nature and causes of this transformation, which largely took place during late antiquity, have been a subject of scholarly debate for centuries. Giorgio Vasari attributed it to a decline in artistic skills and standards, which had in turn been revived by his contemporaries in the Italian Renaissance. Although this point of view has been occasionally revived, most notably by Bernard Berenson, modern scholars tend to take a more positive view of the Byzantine aesthetic. Alois Riegl and Josef Strzygowski, writing in the early 20th century, were above all responsible for the revaluation of late antique art. Riegl saw it as a natural development of pre-existing tendencies in Roman art, whereas Strzygowski viewed it as a product of "oriental" influences. Notable recent contributions to the debate include those of Ernst Kitzinger, who traced a "dialectic" between "abstract" and "Hellenistic" tendencies in late antiquity, and John Onians, who saw an "increase in visual response" in late antiquity, through which a viewer "could look at something which was in twentieth-century terms purely abstract and find it representational."


title: Byzantine art

text: In any case, the debate is purely modern: it is clear that most Byzantine viewers did not consider their art to be abstract or unnaturalistic. As Cyril Mango has observed, "our own appreciation of Byzantine art stems largely from the fact that this art is not naturalistic; yet the Byzantines themselves, judging by their extant statements, regarded it as being highly naturalistic and as being directly in the tradition of Phidias, Apelles, and Zeuxis."


title: Byzantine art

text: The subject matter of monumental Byzantine art was primarily religious and imperial: the two themes are often combined, as in the portraits of later Byzantine emperors that decorated the interior of the sixth-century church of Hagia Sophia in Constantinople. These preoccupations are partly a result of the pious and autocratic nature of Byzantine society, and partly a result of its economic structure: the wealth of the empire was concentrated in the hands of the church and the imperial office, which had the greatest opportunity to undertake monumental artistic commissions.


title: Byzantine art

text: Religious art was not, however, limited to the monumental decoration of church interiors. One of the most important genres of Byzantine art was the icon, an image of Christ, the Virgin, or a saint, used as an object of veneration in Orthodox churches and private homes alike. Icons were more religious than aesthetic in nature: especially after the end of iconoclasm, they were understood to manifest the unique "presence" of the figure depicted by means of a "likeness" to that figure maintained through carefully maintained canons of representation.


title: Byzantine art

text: The illumination of manuscripts was another major genre of Byzantine art. The most commonly illustrated texts were religious, both scripture itself (particularly the Psalms) and devotional or theological texts (such as the "Ladder of Divine Ascent" of John Climacus or the homilies of Gregory of Nazianzus). Secular texts were also illuminated: important examples include the Alexander Romance and the history of John Skylitzes.


title: Byzantine art

text: The Byzantines inherited the Early Christian distrust of monumental sculpture in religious art, and produced only reliefs, of which very few survivals are anything like life-size, in sharp contrast to the medieval art of the West, where monumental sculpture revived from Carolingian art onwards. Small ivories were also mostly in relief.


title: Byzantine art

text: The so-called "minor arts" were very important in Byzantine art and luxury items, including ivories carved in relief as formal presentation Consular diptychs or caskets such as the Veroli casket, hardstone carvings, enamels, glass, jewelry, metalwork, and figured silks were produced in large quantities throughout the Byzantine era. Many of these were religious in nature, although a large number of objects with secular or non-representational decoration were produced: for example, ivories representing themes from classical mythology. Byzantine ceramics were relatively crude, as pottery was never used at the tables of the rich, who ate off Byzantine silver.


title: Byzantine art

text: Byzantine art and architecture is divided into four periods by convention: the Early period, commencing with the Edict of Milan (when Christian worship was legitimized) and the transfer of the imperial seat to Constantinople, extends to AD 842, with the conclusion of Iconoclasm; the Middle, or high period, begins with the restoration of the icons in 843 and culminates in the Fall of Constantinople to the Crusaders in 1204; the Late period includes the eclectic osmosis between Western European and traditional Byzantine elements in art and architecture, and ends with the Fall of Constantinople to the Ottoman Turks in 1453. The term post-Byzantine is then used for later years, whereas "Neo-Byzantine" is used for art and architecture from the 19th century onwards, when the dissolution of the Ottoman Empire prompted a renewed appreciation of Byzantium by artists and historians alike.


title: Byzantine art

text: Two events were of fundamental importance to the development of a unique, Byzantine art. First, the Edict of Milan, issued by the emperors Constantine I and Licinius in 313, allowed for public Christian worship, and led to the development of a monumental, Christian art. Second, the dedication of Constantinople in 330 created a great new artistic centre for the eastern half of the Empire, and a specifically Christian one. Other artistic traditions flourished in rival cities such as Alexandria, Antioch, and Rome, but it was not until all of these cities had fallen - the first two to the Arabs and Rome to the Goths - that Constantinople established its supremacy.


title: Byzantine art

text: Constantine devoted great effort to the decoration of Constantinople, adorning its public spaces with ancient statuary, and building a forum dominated by a porphyry column that carried a statue of himself. Major Constantinopolitan churches built under Constantine and his son, Constantius II, included the original foundations of Hagia Sophia and the Church of the Holy Apostles.


title: Byzantine art

text: The next major building campaign in Constantinople was sponsored by Theodosius I. The most important surviving monument of this period is the obelisk and base erected by Theodosius in the Hippodrome which, with the large silver dish called the Missorium of Theodosius I, represents the classic examples of what is sometimes called the "Theodosian Renaissance". The earliest surviving church in Constantinople is the Basilica of St. John at the Stoudios Monastery, built in the fifth century.


title: Byzantine art

text: Due to subsequent rebuilding and destruction, relatively few Constantinopolitan monuments of this early period survive. However, the development of monumental early Byzantine art can still be traced through surviving structures in other cities. For example, important early churches are found in Rome (including Santa Sabina and Santa Maria Maggiore), and in Thessaloniki (the Rotunda and the Acheiropoietos Basilica).


title: Byzantine art

text: A number of important illuminated manuscripts, both sacred and secular, survive from this early period. Classical authors, including Virgil (represented by the Vergilius Vaticanus and the Vergilius Romanus) and Homer (represented by the Ambrosian Iliad), were illustrated with narrative paintings. Illuminated biblical manuscripts of this period survive only in fragments: for example, the Quedlinburg Itala fragment is a small portion of what must have been a lavishly illustrated copy of 1 Kings.


title: Byzantine art

text: Early Byzantine art was also marked by the cultivation of ivory carving. Ivory diptychs, often elaborately decorated, were issued as gifts by newly appointed consuls. Silver plates were another important form of luxury art: among the most lavish from this period is the Missorium of Theodosius I. Sarcophagi continued to be produced in great numbers.


title: Byzantine art

text: Significant changes in Byzantine art coincided with the reign of Justinian I (527–565). Justinian devoted much of his reign to reconquering Italy, North Africa and Spain. He also laid the foundations of the imperial absolutism of the Byzantine state, codifying its laws and imposing his religious views on all his subjects by law.


title: Byzantine art

text: A significant component of Justinian's project of imperial renovation was a massive building program, which was described in a book, the "Buildings", written by Justinian's court historian, Procopius. Justinian renovated, rebuilt, or founded anew countless churches within Constantinople, including Hagia Sophia, which had been destroyed during the Nika riots, the Church of the Holy Apostles, and the Church of Saints Sergius and Bacchus. Justinian also built a number of churches and fortifications outside of the imperial capital, including Saint Catherine's Monastery on Mount Sinai in Egypt, Basilica of Saint Sofia in Sofia and the Basilica of St. John in Ephesus.


title: Byzantine art

text: Several major churches of this period were built in the provinces by local bishops in imitation of the new Constantinopolitan foundations. The Basilica of San Vitale in Ravenna, was built by Bishop Maximianus. The decoration of San Vitale includes important mosaics of Justinian and his empress, Theodora, although neither ever visited the church. Also of note is the Euphrasian Basilica in Poreč.


title: Byzantine art

text: Recent archeological discoveries in the 19th and 20th centuries unearthed a large group of Early Byzantine mosaics in the Middle East. The eastern provinces of the Eastern Roman and later the Byzantine Empires inherited a strong artistic tradition from Late Antiquity. Christian mosaic art flourished in this area from the 4th century onwards. The tradition of making mosaics was carried on in the Umayyad era until the end of the 8th century. The most important surviving examples are the Madaba Map, the mosaics of Mount Nebo, Saint Catherine's Monastery and the Church of St Stephen in ancient Kastron Mefaa (now Umm ar-Rasas).


title: Byzantine art

text: The first fully preserved illuminated biblical manuscripts date to the first half of the sixth century, most notably the Vienna Genesis, the Rossano Gospels, and the Sinope Gospels. The Vienna Dioscurides is a lavishly illustrated botanical treatise, presented as a gift to the Byzantine aristocrat Julia Anicia.


title: Byzantine art

text: Important ivory sculptures of this period include the Barberini ivory, which probably depicts Justinian himself, and the Archangel ivory in the British Museum. Silver plate continued to be decorated with scenes drawn from classical mythology; for example, a plate in the Cabinet des Médailles, Paris, depicts Hercules wrestling the Nemean lion.


title: Byzantine art

text: The Age of Justinian was followed by a political decline, since most of Justinian's conquests were lost and the Empire faced acute crisis with the invasions of the Avars, Slavs, Persians and Arabs in the 7th century. Constantinople was also wracked by religious and political conflict.


title: Byzantine art

text: The most significant surviving monumental projects of this period were undertaken outside of the imperial capital. The church of Hagios Demetrios in Thessaloniki was rebuilt after a fire in the mid-seventh century. The new sections include mosaics executed in a remarkably abstract style. The church of the Koimesis in Nicaea (present-day Iznik), destroyed in the early 20th century but documented through photographs, demonstrates the simultaneous survival of a more classical style of church decoration. The churches of Rome, still a Byzantine territory in this period, also include important surviving decorative programs, especially Santa Maria Antiqua, Sant'Agnese fuori le mura, and the Chapel of San Venanzio in San Giovanni in Laterano. Byzantine mosaicists probably also contributed to the decoration of the early Umayyad monuments, including the Dome of the Rock in Jerusalem and the Great Mosque of Damascus.


title: Byzantine art

text: Important works of luxury art from this period include the silver David Plates, produced during the reign of Emperor Heraclius, and depicting scenes from the life of the Hebrew king David. The most notable surviving manuscripts are Syriac gospel books, such as the so-called Syriac Bible of Paris. However, the London Canon Tables bear witness to the continuing production of lavish gospel books in Greek.


title: Byzantine art

text: The period between Justinian and iconoclasm saw major changes in the social and religious roles of images within Byzantium. The veneration of acheiropoieta, or holy images "not made by human hands," became a significant phenomenon, and in some instances these images were credited with saving cities from military assault. By the end of the seventh century, certain images of saints had come to be viewed as "windows" through which one could communicate with the figure depicted. Proskynesis before images is also attested in texts from the late seventh century. These developments mark the beginnings of a theology of icons.


title: Byzantine art

text: At the same time, the debate over the proper role of art in the decoration of churches intensified. Three canons of the Quinisext Council of 692 addressed controversies in this area: prohibition of the representation of the cross on church pavements (Canon 73), prohibition of the representation of Christ as a lamb (Canon 82), and a general injunction against "pictures, whether they are in paintings or in what way so ever, which attract the eye and corrupt the mind, and incite it to the enkindling of base pleasures" (Canon 100).


title: Byzantine art

text: Intense debate over the role of art in worship led eventually to the period of "Byzantine iconoclasm." Sporadic outbreaks of iconoclasm on the part of local bishops are attested in Asia Minor during the 720s. In 726, an underwater earthquake between the islands of Thera and Therasia was interpreted by Emperor Leo III as a sign of God's anger, and may have led Leo to remove a famous icon of Christ from the Chalke Gate outside the imperial palace. However, iconoclasm probably did not become imperial policy until the reign of Leo's son, Constantine V. The Council of Hieria, convened under Constantine in 754, proscribed the manufacture of icons of Christ. This inaugurated the Iconoclastic period, which lasted, with interruptions, until 843.


title: Byzantine art

text: While iconoclasm severely restricted the role of religious art, and led to the removal of some earlier apse mosaics and (possibly) the sporadic destruction of portable icons, it never constituted a total ban on the production of figural art. Ample literary sources indicate that secular art (i.e. hunting scenes and depictions of the games in the hippodrome) continued to be produced, and the few monuments that can be securely dated to the period (most notably the manuscript of Ptolemy's "Handy Tables" today held by the Vatican) demonstrate that metropolitan artists maintained a high quality of production.


title: Byzantine art

text: Major churches dating to this period include Hagia Eirene in Constantinople, which was rebuilt in the 760s following its destruction by the 740 Constantinople earthquake. The interior of Hagia Eirene, which is dominated by a large mosaic cross in the apse, is one of the best-preserved examples of iconoclastic church decoration. The church of Hagia Sophia in Thessaloniki was also rebuilt in the late 8th century.


title: Byzantine art

text: Certain churches built outside of the empire during this period, but decorated in a figural, "Byzantine," style, may also bear witness to the continuing activities of Byzantine artists. Particularly important in this regard are the original mosaics of the Palatine Chapel in Aachen (since either destroyed or heavily restored) and the frescoes in the Church of Maria foris portas in Castelseprio.


title: Byzantine art

text: The rulings of the Council of Hieria were reversed by a new church council in 843, celebrated to this day in the Eastern Orthodox Church as the "Triumph of Orthodoxy." In 867, the installation of a new apse mosaic in Hagia Sophia depicting the Virgin and Child was celebrated by the Patriarch Photios in a famous homily as a victory over the evils of iconoclasm. Later in the same year, the Emperor Basil I, called "the Macedonian," acceded to the throne; as a result the following period of Byzantine art has sometimes been called the "Macedonian Renaissance", although the term is doubly problematic (it was neither "Macedonian", nor, strictly speaking, a "Renaissance").


title: Byzantine art

text: In the 9th and 10th centuries, the Empire's military situation improved, and patronage of art and architecture increased. New churches were commissioned, and the standard architectural form (the "cross-in-square") and decorative scheme of the Middle Byzantine church were standardised. Major surviving examples include Hosios Loukas in Boeotia, the Daphni Monastery near Athens and Nea Moni on Chios.


title: Byzantine art

text: There was a revival of interest in the depiction of subjects from classical Greek mythology (as on the Veroli Casket) and in the use of a "classical" Hellenistic styles to depict religious, and particularly Old Testament, subjects (of which the Paris Psalter and the Joshua Roll are important examples).


title: Byzantine art

text: The Macedonian period also saw a revival of the late antique technique of ivory carving. Many ornate ivory triptychs and diptychs survive, such as the Harbaville Triptych and a triptych at Luton Hoo, dating from the reign of Nicephorus Phocas.


title: Byzantine art

text: The Macedonian emperors were followed by the Komnenian dynasty, beginning with the reign of Alexios I Komnenos in 1081. Byzantium had recently suffered a period of severe dislocation following the Battle of Manzikert in 1071 and the subsequent loss of Asia Minor to the Turks. However, the Komnenoi brought stability to the empire (1081–1185) and during the course of the twelfth century their energetic campaigning did much to restore the fortunes of the empire. The Komnenoi were great patrons of the arts, and with their support Byzantine artists continued to move in the direction of greater humanism and emotion, of which the Theotokos of Vladimir, the cycle of mosaics at Daphni, and the murals at Nerezi yield important examples. Ivory sculpture and other expensive mediums of art gradually gave way to frescoes and icons, which for the first time gained widespread popularity across the Empire. Apart from painted icons, there were other varieties - notably the mosaic and ceramic ones.


title: Byzantine art

text: Some of the finest Byzantine work of this period may be found outside the Empire: in the mosaics of Gelati, Kiev, Torcello, Venice, Monreale, Cefalù and Palermo. For instance, Venice's Basilica of St Mark, begun in 1063, was based on the great Church of the Holy Apostles in Constantinople, now destroyed, and is thus an echo of the age of Justinian. The acquisitive habits of the Venetians mean that the basilica is also a great museum of Byzantine artworks of all kinds (e.g., Pala d'Oro).


title: Byzantine art

text: Centuries of continuous Roman political tradition and Hellenistic civilization underwent a crisis in 1204 with the sacking of Constantinople by the Venetian and French knights of the Fourth Crusade, a disaster from which the Empire recovered in 1261 albeit in a severely weakened state. The destruction by sack or subsequent neglect of the city's secular architecture in particular has left us with an imperfect understanding of Byzantine art.


title: Byzantine art

text: Although the Byzantines regained the city in 1261, the Empire was thereafter a small and weak state confined to the Greek peninsula and the islands of the Aegean. During their half-century of exile, however, the last great flowing of Anatolian Hellenism began. As Nicaea emerged as the center of opposition under the Laskaris emperors, it spawned a renaissance, attracting scholars, poets, and artists from across the Byzantine world. A glittering court emerged as the dispossessed intelligentsia found in the Hellenic side of their traditions a pride and identity unsullied by association with the hated "latin" enemy. With the recapture of the capital under the new Palaeologan Dynasty, Byzantine artists developed a new interest in landscapes and pastoral scenes, and the traditional mosaic-work (of which the Chora Church in Constantinople is the finest extant example) gradually gave way to detailed cycles of narrative frescoes (as evidenced in a large group of Mystras churches). The icons, which became a favoured medium for artistic expression, were characterized by a less austere attitude, new appreciation for purely decorative qualities of painting and meticulous attention to details, earning the popular name of the Paleologan Mannerism for the period in general.


title: Byzantine art

text: Venice came to control Byzantine Crete by 1212, and Byzantine artistic traditions continued long after the Ottoman conquest of the last Byzantine successor state in 1461. The Cretan school, as it is today known, gradually introduced Western elements into its style, and exported large numbers of icons to the West. The tradition's most famous artist was El Greco.


title: Byzantine art

text: The splendour of Byzantine art was always in the mind of early medieval Western artists and patrons, and many of the most important movements in the period were conscious attempts to produce art fit to stand next to both classical Roman and contemporary Byzantine art. This was especially the case for the imperial Carolingian art and Ottonian art. Luxury products from the Empire were highly valued, and reached for example the royal Anglo-Saxon Sutton Hoo burial in Suffolk of the 620s, which contains several pieces of silver. Byzantine silks were especially valued and large quantities were distributed as diplomatic gifts from Constantinople. There are records of Byzantine artists working in the West, especially during the period of iconoclasm, and some works, like the frescos at Castelseprio and miniatures in the Vienna Coronation Gospels, seem to have been produced by such figures.


title: Byzantine art

text: In particular, teams of mosaic artists were dispatched as diplomatic gestures by emperors to Italy, where they often trained locals to continue their work in a style heavily influenced by Byzantium. Venice and Norman Sicily were particular centres of Byzantine influence. The earliest surviving panel paintings in the West were in a style heavily influenced by contemporary Byzantine icons, until a distinctive Western style began to develop in Italy in the Trecento; the traditional and still influential narrative of Vasari and others has the story of Western painting begin as a breakaway by Cimabue and then Giotto from the shackles of the Byzantine tradition. In general, Byzantine artistic influence on Europe was in steep decline by the 14th century if not earlier, despite the continued importance of migrated Byzantine scholars in the Renaissance in other areas.


title: Byzantine art

text: Islamic art began with artists and craftsmen mostly trained in Byzantine styles, and though figurative content was greatly reduced, Byzantine decorative styles remained a great influence on Islamic art, and Byzantine artists continued to be imported for important works for some time, especially for mosaics.


title: Byzantine art

text: The Byzantine era properly defined came to an end with the fall of Constantinople to the Ottoman Turks in 1453, but by this time the Byzantine cultural heritage had been widely diffused, carried by the spread of Orthodox Christianity, to Bulgaria, Serbia, Romania and, most importantly, to Russia, which became the centre of the Orthodox world following the Ottoman conquest of the Balkans. Even under Ottoman rule, Byzantine traditions in icon-painting and other small-scale arts survived, especially in the Venetian-ruled Crete and Rhodes, where a "post-Byzantine" style under increasing Western influence survived for a further two centuries, producing artists including El Greco whose training was in the Cretan School which was the most vigorous post-Byzantine school, exporting great numbers of icons to Europe. The willingness of the Cretan School to accept Western influence was atypical; in most of the post-Byzantine world "as an instrument of ethnic cohesiveness, art became assertively conservative during the "Turcocratia"" (period of Ottoman rule).


title: Byzantine art

text: Russian icon painting began by entirely adopting and imitating Byzantine art, as did the art of other Orthodox nations, and has remained extremely conservative in iconography, although its painting style has developed distinct characteristics, including influences from post-Renaissance Western art. All the Eastern Orthodox churches have remained highly protective of their traditions in terms of the form and content of images and, for example, modern Orthodox depictions of the Nativity of Christ vary little in content from those developed in the 6th century.


The Princess Switch 3: Romancing the Star is a 2021 American Christmas romantic comedy film directed by Mike Rohl and written by Robin Bernheim Burger, based on the characters created by Burger and Megan Metzger. The third film in "The Princess Switch" franchise, stars Vanessa Hudgens, Sam Palladio, Suanne Braun, Nick Sagar and Hazel Beattie. The story follows Margaret Delacourt, Queen of Montenaro, Stacy Juliette DeNovo Wyndham, Princess of Belgravia and Lady Fiona Pembroke, Margaret’s cousin. When a priceless Christmas relic is stolen, the trio come together and track down a mysterious jewel thief.


title: The Princess Switch 3: Romancing the Star

text: The film is produced by Hudgens and Brad Krevoy, and it was released on Netflix on November 18, 2021.


text: Princess Stacy Wyndham of Belgravia and Queen Margaret Delacourt of Montenaro are preparing to host an international Christmas festival in Montenaro, the centerpiece of which is the "Star of Peace", a sacred relic loaned by the Vatican. Shortly after the Star arrives, thieves break into the palace and steal it.


text: Stacy and Margaret decide to approach Lady Fiona Pembroke, who is currently on probation and working as a custodian at an orphanage, for help to track down the Star. Fiona agrees to help in exchange for Margaret putting in a good word for her when her case is reviewed by a disciplinary board after Christmas. She consults her ex-boyfriend, Peter Maxwell, a disgraced former Interpol investigator who now runs his own private security firm. Peter quickly deduces that the mastermind behind the Star's disappearance is Hunter Cunard, a billionaire obsessed with stealing priceless works of art for his personal collection.


text: Fiona charms Hunter into giving her an invitation to the Christmas party at his estate. Peter then recruits Fiona's assistants, Mindy and Reggie, to practice infiltrating Hunter's estate and bypassing his security measures while Fiona distracts Hunter at the party. Reggie injures himself during training and Margaret agrees to impersonate Fiona at the party while Peter and Fiona, stepping in for Reggie, retrieve the Star from the security vault. As they get ready for the mission, Fiona reflects over her unrequited feelings for Peter, whom she knew from her childhood.


text: The plan is set into motion, and at first, everything goes smoothly until Peter accidentally trips a pressure plate alarm while retrieving the Star. Panicked, Reggie and Mindy shut off the fake security footage Peter had installed, alerting Hunter to the theft. Peter gives Fiona a bag with the Star and stays behind to distract Hunter's men while Frank picks up Fiona. Margaret also escapes with the help of the coat check angel man.


text: Meanwhile, Stacy receives word from the head of the orphanage that Fiona's hearing has been rescheduled to the same night as the heist. She decides to dress up like Fiona and appear in front of the committee, accompanied by Prince Edward as a character witness. With Stacy impersonating a remorseful Fiona, the board decides on a commutation of sentence. Everyone regroups at the palace, but Fiona soon discovers that the bag she's carrying contains a decoy. Believing that Peter tricked them, Margaret and Stacy agree to reveal the truth to the Vatican while Fiona, Mindy, and Reggie plan to leave the county despite Margaret inviting them to stay for Christmas.