Marcus Ulpius Traianus was born on 18 September 53AD in the Roman province of Hispania Baetica (in what is now Andalusia in modern Spain), in the city of Italica (now in the municipal area of Santiponce, in the outskirts of Seville). Although frequently designated the first provincial emperor, and dismissed by later writers such as Cassius Dio (himself of provincial origin) as "an Iberian, and neither an Italian nor even an Italiot", Trajan appears to have hailed on his father's side from the area of Tuder (modern Todi) in Umbria, at the border with Etruria, and on his mother's side from the Gens Marcia, of an Italic family of Sabine origin. Trajan's birthplace of Italica was founded as a Roman military colony of "Italian" settlers in 206BC, though it is unknown when the Ulpii arrived there. It is possible, but cannot be substantiated, that Trajan's ancestors married local women and lost their citizenship at some point, but they certainly recovered their status when the city became a municipium with Latin citizenship in the mid-1st century BC.
The imperial period of Rome lasted approximately 1,500 years compared to the 500 years of the Republican era. The first two centuries of the empire's existence were a period of unprecedented political stability and prosperity known as the Pax Romana, or ``Roman Peace ''. Following Octavian's victory, the size of the empire was dramatically increased. After the assassination of Caligula in AD 41, the Senate briefly considered restoring the republic, but the Praetorian Guard proclaimed Claudius emperor instead. Under Claudius, the empire invaded Britannia, its first major expansion since Augustus. After Claudius' successor, Nero, committed suicide in AD 68, the empire suffered a series of brief civil wars, as well as a concurrent major rebellion in Judea, during which four different legionary generals were proclaimed emperor. Vespasian emerged triumphant in AD 69, establishing the Flavian dynasty, before being succeeded by his son Titus, who opened the Colosseum shortly after the eruption of Mount Vesuvius. His short reign was followed by the long reign of his brother Domitian, who was eventually assassinated. The Senate then appointed the first of the Five Good Emperors. The empire reached its greatest extent under Trajan, the second in this line.
John has been assessed as the greatest of the Komnenian emperors. In the course of his twenty-five year reign, John made alliances with the Holy Roman Empire in the west, decisively defeated the Pechenegs, Hungarians and Serbs in the Balkans, and personally led numerous campaigns against the Turks in Asia Minor. John's campaigns fundamentally changed the balance of power in the east, forcing the Turks onto the defensive and restoring to the Byzantines many towns, fortresses and cities right across the Anatolian peninsula. In the southeast, John extended Byzantine control from the Maeander in the west all the way to Cilicia and Tarsus in the east. In an effort to demonstrate the Byzantine ideal of the emperor's role as the leader of the Christian world, John marched into Muslim Syria at the head of the combined forces of Byzantium and the Crusader states; yet despite the great vigour with which he pressed the campaign, John's hopes were disappointed by the evasiveness of his Crusader allies and their reluctance to fight alongside his forces.

Question: Who is the mother of the person under whom the empire where Irene Doukaina was a citizen reached its greatest extent?
Answer: Marcia