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Tecumseh

Tecumseh was a Native American Shawnee warrior and chief, who became the primary leader of a large, multi-tribal confederacy in the early 19th century. Born in the Ohio Country, growing up during the American Revolutionary War and the Northwest Indian War, Tecumseh was exposed to warfare and envisioned the establishment of an independent Native American nation east of the Mississippi River under British protection, he worked to recruit additional members to his tribal confederacy from the southern United States. Tecumseh was among the most celebrated Native American leaders in history and was known as a strong and eloquent orator who promoted tribal unity, he was ambitious, willing to take risks, make significant sacrifices to repel the settlers from Native American lands in the Old Northwest Territory. In 1808, with his brother Tenskwatawa, Tecumseh founded the Native American village the European Americans called Prophetstown, north of present-day Lafayette, Indiana. Prophetstown grew into a large, multi-tribal community and a central point in Tecumseh's political and military alliance.

Tecumseh's confederation fought the United States during Tecumseh's War, but he was unsuccessful in getting the U. S. government to rescind the Treaty of other land-cession treaties. In 1811, as he traveled south to recruit more allies, his brother Tenskwatawa defended Prophetstown against William Henry Harrison's army at the Battle of Tippecanoe, but the Native Americans retreated from the field and the European Americans unearthed graves and burned Prophetstown. Although Tecumseh remained the military leader of the pan-Native American confederation, his plan to enlarge the Native American alliance was never fulfilled. Tecumseh and his confederacy continued to fight the United States after forming an alliance with Great Britain in the War of 1812. During the war, Tecumseh's confederacy helped in the capture of Fort Detroit. However, after U. S. naval forces took control of Lake Erie in 1813, the British and their Native American allies retreated into Upper Canada, where the European American forces engaged them at the Battle of the Thames on October 5, 1813, Tecumseh was killed.

His death and the end of the war caused the pan-Native American alliance to collapse. Within a few years, the remaining tribal lands in the Old Northwest were ceded to the U. S. government and subsequently opened for new settlement and most of the Native Americans moved west, across the Mississippi River. Since his death Tecumseh has become an iconic folk hero in American and Canadian history. Tecumseh was born in March 1768; some accounts identify his birthplace as Old Chillicothe. Because the Shawnee did not settle in Old Chillicothe until 1774, biographer John Sugden concludes that Tecumseh was born either in a different village named "Chillicothe" along the Scioto River, near present-day Chillicothe, Ohio, or in a nearby Kispoko village situated along a small tributary of the Scioto. Tecumseh's father, meaning "alights from flying", "something that drops", or "I light from flying", rendered in various records as Puckeshinwa, Pukshinwa, Pekishinoah and other variations) was a minor Shawnee war chief of the Kispoko band and the panther clan.

According to some sources, Puckshinwa's father was Muscogee and his mother was Shawnee. Tecumseh biographer John Sugden concludes that Puckshinwa's ancestry "must remain a mystery", because other testimonies provide alternate details of his heritage, such as stating that said the Kispoko chief had a British father. Tecumseh's mother, was Puckshinwa's second wife, she is believed to have been either Muscogee Creek, Cherokee, or Shawnee through both her parents of the Pekowi band and the turtle clan. Some traditions argue that Methotaske was Creek because she had lived among that tribe prior to marriage, while others claim that she was Cherokee, having died in old age living among that tribe. Others suggest that she was a white captive due to the family stories that claim Puckshinwa had been married to a white captive. Puckshinwa and Methotaske had at least eight children. Shawnee divisional identity was recorded patrilineally, meaning that inheritance and descent are traced through the male line, which made Tecumseh and his siblings members of the Kispoko.

Tecumseh's great-great grandfather on his mother's side, Straight Tail Meaurroway Opessa, was a prominent chief of the Pekowi and the turtle clan. When Tecumseh's parents met and married, the Pekowi were living somewhere near the present-day site of Tuscaloosa, Alabama; the Pekowi had lived in that region alongside the Creek people, since the Iroquois forced them from the Ohio River valley during the Beaver Wars in the seventeenth century. About 1759 the Pekowi band moved north into the Ohio Country. Not wanting to force Methotaske to choose between staying in the south with him or moving with her family, Puckshinwa deci

Williams FW41

The Williams FW41 is a Formula One racing car designed by Paddy Lowe and Dirk de Beer for the Williams team, to compete in the 2018 FIA Formula One World Championship. The car made its competitive début at the 2018 Australian Grand Prix, was driven by Lance Stroll in his second season with the team. After the mediocre results of the previous season, 2018 was a disaster for Williams. Despite having good reliability, the team ended up at the back of the field fighting the Toro Rossos, their first points came in Azerbaijan. The team would not score points again until Italy, when Stroll and Sirotkin finished 9th and 10th respectively. Williams finished 10th and last in the Constructors' Championship, the lowest ranking in the history of the team, it was the last Williams car to have sponsorship from Martini, who were their title sponsor since 2014. In signing Sergey Sirotkin, Williams formed an alliance with Russian racing outfit SMP Racing, which came with financial investment in the team. While discussing the investment, SMP Racing revealed that under the terms of the agreement their investment would be spent on technical development of the FW41 instead of being used to cover the costs of day-to-day operations.

Testing and development work was carried out by Robert Kubica. The role was Kubica's first with a Formula One team since his 2011 rallying accident that resulted in the traumatic amputation of his arm; the car had problems with its development being cooling and the aerodynamics which resulted in its uncompetitiveness. 2018 was the worst year for Williams since 2013. Despite having good reliability, the car was slow; the car scored points on only two occasions. † Driver failed to finish the race, but was classified as they had completed more than 90% of the race distance

Conditional entropy

In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y given that the value of another random variable X is known. Here, information is measured in nats, or hartleys; the entropy of Y conditioned on X is written as H. The conditional entropy of Y given X is defined as where X and Y denote the support sets of X and Y. Note: It is conventioned that the expressions 0 log ⁡ 0 and 0 log ⁡ c / 0 for fixed c > 0 should be treated as being equal to zero. This is because lim θ → 0 + θ log c / θ = 0 and lim θ → 0 + θ log ⁡ θ = 0 Let H be the entropy of the discrete random variable Y conditioned on the discrete random variable X taking a certain value x. Denote the support sets of X and Y by X and Y. Let Y have probability mass function p Y; the unconditional entropy of Y is calculated as H:= E, i.e. H = ∑ y ∈ Y P r I = − ∑ y ∈ Y p Y log 2 ⁡ p Y, where I ⁡ is the information content of the outcome of Y taking the value y i.

The entropy of Y conditioned on X taking the value x is defined analogously by conditional expectation: H = − ∑ y ∈ Y Pr log 2 ⁡ Pr. H is the result of averaging H over all possible values. Given discrete random variables X with image X and Y with image Y, the conditional entropy of Y given X is defined as the weighted sum of H for each possible value of x, using p as the weights: H ≡ ∑ x ∈ X p H = −