Given the following passage "Since approximately 2000, many parts of downtown New Haven have been revitalized, with new restaurants, nightlife, and small retail stores. In particular, the area surrounding the New Haven Green has experienced an influx of apartments and condominiums. In recent years, downtown retail options have increased with the opening of new stores such as Urban Oufitters, J Crew, Origins, American Apparel, Gant Clothing, and an Apple Store, joining older stores such as Barnes & Noble, Cutlers Records, and Raggs Clothing. In addition, downtown's growing residential population will be served by two new supermarkets, a Stop & Shop just outside downtown and Elm City Market located one block from the Green. The recent turnaround of downtown New Haven has received positive press from various periodicals.", answer the following question. Note that the answer is present within the text. Question: What area of New Haven has been imbued with new life and vitality?
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Answer: downtown

Q: Given the following passage "The islands are located about halfway between Hawaii and Australia, north of Nauru and Kiribati, east of the Federated States of Micronesia, and south of the U.S. territory of Wake Island, to which it lays claim. The atolls and islands form two groups: the Ratak (sunrise) and the Ralik (sunset). The two island chains lie approximately parallel to one another, running northwest to southeast, comprising about 750,000 square miles (1,900,000 km2) of ocean but only about 70 square miles (180 km2) of land mass. Each includes 15 to 18 islands and atolls. The country consists of a total of 29 atolls and five isolated islands.", answer the following question. Note that the answer is present within the text. Question: Which is farther south, Ralik or Nauru?
A: Nauru

Question: Given the following passage "Differences in the settlement patterns of eastern and western North Carolina, or the Low Country and uplands, affected the political, economic, and social life of the state from the 18th until the 20th century. The Tidewater in eastern North Carolina was settled chiefly by immigrants from rural England and the Scottish Highlands. The upcountry of western North Carolina was settled chiefly by Scots-Irish, English, and German Protestants, the so-called "cohee". Arriving during the mid- to late 18th century, the Scots-Irish from what is today Northern Ireland were the largest non-English immigrant group before the Revolution; English indentured servants were overwhelmingly the largest immigrant group before the Revolution. During the American Revolutionary War, the English and Highland Scots of eastern North Carolina tended to remain loyal to the British Crown, because of longstanding business and personal connections with Great Britain. The English, Welsh, Scots-Irish, and German settlers of western North Carolina tended to favor American independence from Britain.", answer the following question. Note that the answer is present within the text. Question: Which western N.C. settler was second mentioned?
Answer: Welsh

[Q]: Given the following passage "Stage lifts and orchestra lifts are specialized elevators, typically powered by hydraulics, that are used to raise and lower entire sections of a theater stage. For example, Radio City Music Hall has four such elevators: an orchestra lift that covers a large area of the stage, and three smaller lifts near the rear of the stage. In this case, the orchestra lift is powerful enough to raise an entire orchestra, or an entire cast of performers (including live elephants) up to stage level from below. There's a barrel on the background of the image of the left which can be used as a scale to represent the size of the mechanism", answer the following question. Note that the answer is present within the text. Question: What mechanical helper is found is a lot of theaters?
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[A]: hydraulics

input: Please answer the following: Given the following passage ""Hellenistic" is a modern word and a 19th-century concept; the idea of a Hellenistic period did not exist in Ancient Greece. Although words related in form or meaning, e.g. Hellenist (Ancient Greek: , Hellenistes), have been attested since ancient times, it was J. G. Droysen in the mid-19th century, who in his classic work Geschichte des Hellenismus, i.e. History of Hellenism, coined the term Hellenistic to refer to and define the period when Greek culture spread in the non-Greek world after Alexander's conquest. Following Droysen, Hellenistic and related terms, e.g. Hellenism, have been widely used in various contexts; a notable such use is in Culture and Anarchy by Matthew Arnold, where Hellenism is used in contrast with Hebraism.", answer the following question. Note that the answer is present within the text. Question: Which of the following was born earlier: Droysen or Alexander?
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output: Alexander

Given the following passage "In quantum mechanics and quantum field theory, the vacuum is defined as the state (that is, the solution to the equations of the theory) with the lowest possible energy (the ground state of the Hilbert space). In quantum electrodynamics this vacuum is referred to as 'QED vacuum' to distinguish it from the vacuum of quantum chromodynamics, denoted as QCD vacuum. QED vacuum is a state with no matter particles (hence the name), and also no photons. As described above, this state is impossible to achieve experimentally. (Even if every matter particle could somehow be removed from a volume, it would be impossible to eliminate all the blackbody photons.) Nonetheless, it provides a good model for realizable vacuum, and agrees with a number of experimental observations as described next.", answer the following question. Note that the answer is present within the text. Question: The lowest energy state of a volume of space is mathematically know as what?
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Answer:
the ground state of the Hilbert space