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The approach we chose for specifying the service requirements in this new environment was to create an overall top-level speci cation named 22101 UMTS service principles This gave a brief description of all our requirements, many of which would then be elaborated in more detail in the remaining speci cations of what became the 22 series We also kept much of the old GSM speci cation base Life tends to follow history and inevitably, we found that we needed a deadline for start of service and hence for the speci cations for the rst release to be frozen This was Release 99 and for the rst time, this contained new speci cations for UMTS (221xx series) and also renumbered GSM speci cations which were transferred, often with minimal change, becoming dual purpose GSM and UMTS speci cations (220xy series were equivalent to the GSM 02xy).



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The spanning trees used to construct routing tables have to generate unique paths between all pairs of nodes in the network to ensure loop-free data forwarding operation The choice of these paths is made unique by imposing some optimality criteria, for example, having the smallest number of hops, or edge-weighted hops, thus yielding a shortest path tree (SPT) Several algorithms exist to compute the SPT for a network graph The two most widespread methods are based either on Dijkstra s [1] or the Bellman Ford [2,3] algorithm Both algorithms work by computing some minimal spanning tree at each node that contains a consistent set of shortest paths between any pair of nodes Dijkstra s algorithm requires that the complete graph of the network is known in advance at each node and that the costs of edges between nodes are nonnegative.





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approximation to the data, one cannot hedge with the xed for oating instrument As noted above, the best hedge with the xed for oating instrument would fully hedge against a hypothetical portfolio with a pro t given by the best linear approximation The deviations from a constant pro t of the hedged portfolio are the same as the deviations of the unhedged portfolio from the best linear approximation If those deviations are large, then hedging will not be effective Also note that in the case that the deviations from the best linear approximation are large, Corr(R,B) is close to 0 Recall that the correlation gives a measurement of how well data t to a line and if they do not t well, then the correlation is close to 0 For those familiar with regression, the hedge is explained by the regression formula.

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Dijkstra s algorithm has (computation) time complexity O(m + n log n), where n is the number of nodes in the graph and m is the number of edges In the case of a completely connected graph, m = n(n 1)/2 (for a review cf the work by Zwick [4]), it yields a worst-case performance of O(n2 ) However, Dijkstra s algorithm incurs a signi cant communication overhead (or communication complexity) in order to disseminate the topology information through a ooding procedure that does not scale well with increasing n, whereby all nodes advertise the weights of the links to their neighbors through networkwide broadcasts..

Regressing the retailer portfolio against the baseload ISO index provides the following: R = aB + Z where a is the regression coef cient and Z is the error term Adding a baseload instrument provides the following: R + eB = aB + Z + eB = (a + e)B + Z One cannot hedge against the error, Z, since it is completely uncorrelated with the variable B However, it is possible to hedge against the component of R that is explained by the baseload variable The best hedge eliminates the uncertainty; set e* = a The variance of the hedged portfolio is identically the variance of Z Low variance in Z is equivalent to a correlation between R and B that is close to 1 or negative 1 A further generalization of the geometric interpretation of the optimal hedge is the following.

Financial Modelling in Python leverage = 0.0 target = 0.0 redemption floor = -100 redemption cap = 100 coupon leg = create tarn coupon leg(floor, fixed rate, leverage\ , target, redemption floor, redemption cap) funding leg = create tarn funding leg() env = create environment() tarn = ppf.core.trade((funding leg, coupon leg)) # note the # ordering pricer = create pricer(tarn, env) symbol value pairs to add = [] symbol value pairs to add.append( ("accrued coupon", numpy.zeros(5000))) symbol value pairs to add.append( ("target indicator", numpy.zeros(5000))) actual = pricer(symbol value pairs to add) expected = exotic first flow pv(coupon leg, env)\ + funding first flow pv(funding leg, env) assert seq close([actual/10000000], [expected/10000000], 1.0e-4)

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