Thus, in 1003, the emperor installed him as the Count of Aosta, a mountainous region then a part of Burgundy but today within Italy, and granted him the northern Viennois as a reward.

Thus, reinforcement learning is particularly well suited to problems which include a long-term versus short-term reward trade-off.

" Thus indeed do We reward those who do right.

Thus it is not possible to determine if the ACC's implied campaign promise of " free plastic bags for shoppers " as a reward for voting down the referendum was valid.

Thus, groups will generally reward members who treat others equitably and generally punish ( increase the cost for ) members who treat others inequitably.

Legalism assumed that people were naturally evil and always acted to avoid punishment while simultaneously trying to achieve gains ; Thus, the law must severely punish any unwanted action, while at the same time reward those who follow it.

Thus the covenant of works has also been called the covenant of creation, indicating that it is not added but constitutive of the human race ; the covenant of nature in recognition of its consonance with the natural law in the human heart ; and the covenant of life in regard to the promised reward.

Thus if the person is dividing up the work to be performed or the amount of reward he expects to receive, he will work less hard in groups.

Thus according to them the firm emerges because extra output is provided by team production, but that the success of this depends on being able to manage the team so that metering problems ( it is costly to measure the marginal outputs of the co-operating inputs for reward purposes ) and attendant shirking ( the moral hazard problem ) can be overcome, by estimating marginal productivity by observing or specifying input behaviour.

Thus valor and skill had their reward.

Thus, the Jewish Encyclopedia suggests that Elisha was a Sadducee, since belief that reward and punishment must occur on Earth and disbelief in an afterlife are part of Sadducee philosophy.

Thus, it is suggested that human beings have developed the unconscious ability to endure pain or sometimes, even relieve pain if it can be more important for survival to gain a larger reward.

Thus, Logue was able to condition participants to accept a large time delay in order to receive a big reward, rather than to choose not to wait in order to receive a small but immediate reward.

) Thus, in this view, profit income is a reward for those who value future income highly and are thus willing to sacrifice current enjoyment.

Thus the prospect of immediate high reward clearly outweighed the negative long term consequences for SDI.

Thus, dermatillomania could result from a dysfunction in the dopamine reward functions.

Thus, while some markets may highly reward first movers, others may not.

Thus, the avant-garde choreographers have extended the scope of materials available for dance composition.

Thus, many a creativity-oriented aspirant for a career in architecture, drama, or journalism, resigns himself to a real estate business ; ;

Thus a new pattern of days began to develop, for Granny Albright did not die.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus, you avoid headaches when an employee wants off for his fourth cousin's funeral.

Thus it was that Barco, apprehended for mere larceny, now began to suspect that one or another of his murders had been uncovered.

Thus, the dotted line shown in figure 4 was taken as typical for the temperature distribution for all blowing rates.

Thus, for aqueous media, we can think of the idealized organic active as an oleophilic or hydrophobic surface-active agent, and of an idealized builder as a oleophobic or hydrophilic surface-active agent.

Thus, an enemy would probably use this weapon for attack on static population centers such as large cities.

Thus, the alignment of the `` dots '' and `` tips '', respectively, indicate individual variability of the 21 growth centers of each child with respect to the mean values for these boys and girls.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus the multiplicity of Af for a given T must be an even number.

Thus, although the agenda of external assistance in the economic sphere are cumulative, and many of the policies suggested for nations in the earlier stages remain relevant, the basic purpose of American economic policy during the later stages of development should be to assure that movement into a stage of self-sustaining growth is not prevented by lack of foreign exchange.

Thus the lack of effective recognition of the responsibilities involved in caring for two babies showed signs of becoming a disabling problem.

Thus, the writer decided to hold one experimental section of the functional preparation for marriage course in the spring semester of 1960 exclusively for persons already married -- that is, prerequisite: `` marriage ''.

Thus the films seen as they came in ( coordinated for the regular sections ), were often out of context.

Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.

Thus in his friends are stranger than his sisters' strong stresses are normal for his and sisters', but in his friends are stranger than his sisters strong stresses are normal for friends and sisters.

Thus in Mary wrote an account of the trip first strong stress on Mary marks Mary as the first in a series of people who wrote accounts of the trip, strong stress on wrote marks the writing as the first of a series of actions of Mary's concerned with an account of her trip ( about which she may later have made speeches, for example ), and strong stress on trip makes the trip the first of a series of subjects about which Mary wrote accounts.

Thus his persistence values for some stem frequencies per meaning are: stem identical in 8 languages, 100% ; ;

Thus while his theory or technique may not be oversubscribed, it is commonplace for bullish and bearish positions to become temporarily over-subscribed.

Thus, ayahuasqueros and most others working with the brew maintain that the B. caapi vine is the defining ingredient, and that this beverage is not ayahuasca unless B. caapi is in the brew.

Thus, egoism will prescribe actions that may be beneficial, detrimental, or neutral to the welfare of others.

Thus, as an ethnic religion, Judaism holds that others may have their own, different, paths to God ( or holiness, or " salvation "), as long as they are consistent with the Seven Laws of Noah.

Thus three major themes in 19th century mathematics were combined by Lie in creating his new theory: the idea of symmetry, as exemplified by Galois through the algebraic notion of a group ; geometric theory and the explicit solutions of differential equations of mechanics, worked out by Poisson and Jacobi ; and the new understanding of geometry that emerged in the works of Plücker, Möbius, Grassmann and others, and culminated in Riemann's revolutionary vision of the subject.

Thus, each Sumerian city became a city-state, independent of the others and protective of its independence.

Thus, certain color contrasts may look fuzzier than others, depending on the allocation of the primary colors ( green has twice as many elements as red or blue in the Bayer arrangement ).

" Thus, consideration of others ' interests has long been a necessary part of the human experience.

Thus, a worker is not promoted to managing others if they do not already display management abilities.

Thus, it follows that all power laws with a particular scaling exponent are equivalent up to constant factors, since each is simply a scaled version of the others.

Thus it is important to be able to see the topic from different angles in order to anticipate the reaction others have to a proposal.

Thus, early text projects such as Roberto Busa's Index Thomisticus, the Brown Corpus, and others had to resort to conventions such as keying an asterisk preceding letters actually intended to be upper-case.

Thus, people pray for many reasons such as personal benefit or for the sake of others.

Thus it provides an upper bound on what can be achieved with rational ( self-interested ) coordination or knowledge of others ' preferences.

Thus, the so-called blub paradox ( after a hypothetical programming language of average complexity called ' Blub ') says that anyone preferentially using some particular programming language will ' know ' that it is more powerful than some, but not that it is less powerful than others.

Thus the picture theory allows us to be shown that some things can be said while others are shown.

Thus, John Dryden, among many others, compares the " irregular " Shakespeare with the " regular " Ben Jonson in his Essay of Dramatick Poesie ( 1668 ), and makes use of the unity of time in this passage criticizing Shakespeare's history plays:

Thus, the answer naturally arises whether the Gaius of 3 John is the same man mention in any of the others contexts.

Thus, although Buddhas possess no limitation from their side on their ability to help others, sentient beings continue to experience suffering as a result of the limitations of their own former negative actions.

Thus several psychologists such as Howe have argued against the existence of innate talent, while in neuroscience there have been debates that the brain functions with Mass action, rather than by a series of interacting mechanisms – for instance by Karl Lashley and others.

Thus, strategy becomes important as players attempt to predict each others ' moves, similar to rock-paper-scissors.

Thus cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero – sum game if all participants value each unit of cake equally ( see marginal utility ).

Thus, a more isolated society with the same level of technology and culture as other societies is more likely to survive than one in closer proximity to others that may encroach on their resources.

Thus US Army SIS was able to break the cipher used for the six letters before it was able to break the one used for the 20 others.

Thus, some cultures prohibit certain types of substances, which they call " taboo ", while they make use of others in various types of ceremonies.

Thus, market capitalization is one measure of " float " i. e., share value times an equity aggregate, with free and public being others.