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If we de ne P = cov([ , ), then based on the above analysis a b] P= which checks with eqn. (4.24). Analysis similar to that of Example 4.9 will have utility in Part II for the initialization of navigation systems. Related to this example, the case where a is a vector and the case where y is a nonlinear function of a are considered in Exercise 4.11.

Notice that cost[s] = cs 420 There is a network of roads G = (V, E) connecting a set of cities V Each road in E has an associated length le There is a proposal to add one new road to this network, and there is a list E of pairs of cities between which the new road can be built Each such potential road e E has an associated length As a designer for the public works department you are asked to determine the road e E whose addition to the existing network G would result in the maximum decrease in the driving distance between two xed cities s and t in the network Give an ef cient algorithm for solving this problem 421 Shortest path algorithms can be applied in currency trading Let c1 , c2 , .

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amplitude and may add the effects of an enhanced physiologic or essential tremor; with advance of the disease, increasing rigidity of the limbs obscures or reduces it Parkinsonian tremor interferes surprisingly little with voluntary movement; for example, it is possible for a tremulous patient to raise a full glass of water to his lips and drain its contents without spilling a drop; ironically, this is not always the case with advanced benign essential tremor, as already emphasized Resting tremor is most often a manifestation of the Parkinson syndrome, whether the idiopathic variety described by James Parkinson (paralysis agitans) or the drug-induced type In the former, the tremor is sometimes relatively gentle and more or less limited to the distal muscles; almost always it is asymmetrical; at the outset, it may be unilateral The tremor of postencephalitic parkinsonism (which is now extinct) often had greater amplitude and involved proximal muscles.

, cn be various currencies; for instance, c1 might be dollars, c2 pounds, and c3 lire For any two currencies ci and cj , there is an exchange rate ri,j ; this means that you can purchase ri,j units of currency cj in exchange for one unit of ci These exchange rates satisfy the condition that ri,j rj,i < 1, so that if you start with a unit of currency ci , change it into currency cj and then convert back to currency ci , you end up with less than one unit of currency ci (the difference is the cost of the transaction) (a) Give an ef cient algorithm for the following problem: Given a set of exchange rates r i,j , and two currencies s and t, nd the most advantageous sequence of currency exchanges for converting currency s into currency t.

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In neither disease is there a close correspondence between the degree of tremor and the degree of rigidity or akinesia A parkinsonian type of tremor may also be seen in elderly persons without akinesia, rigidity, or mask-like facies In some of these patients, the tremor is followed years later by the other manifestations of Parkinson disease, but in many others it is not, the tremor remaining unchanged for many years or progressing very slowly, unaffected by anti-Parkinson drugs This probably equates with the earlier mentioned alternate-beat type of essential tremor Patients with the familial (wilsonian) or acquired form of hepatocerebral degeneration may also show a tremor of parkinsonian type, usually mixed with ataxic tremor and other extrapyramidal motor abnormalities.

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