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Problem V.9 (Learning curves) Consider the general setting of Thm. 25.2, which deals with data-normalized adaptive filters. The purpose of this problem is to use the variance relation (25.14) to characterize not only the time evolution of E ((Gi', as was done in the statement of theorem, but I) also the time evolution of E [ea(i)12,which relates to the learning curve of the filter. Recall that the learning curve of an adaptive filter is defined by E le(i)j2, which in view of (22.16) is given by E le(i)l' = E lea(i)12 +u:, so that the learning curve can be equivalently characterized by studying the evolution of E lea(i)i2. Under the conditions on the data stated in Thm. 25.2, we know from (23.55) that E lea(i)I2 = E lJ2zli-111iu. This means that the learning curve can be determined by studying the evolution of the above weighted norm of Gi-1. This evolution can be deduced from the variance relation (25.14), namely,

det(R)

~---------- - ------ - - - -- - -- - - - --- -

(a) Consider the state-space model of part (a) of that problem, which relates to projecting onto pM,i. Verify that the corresponding Kalman recursion for the state estimator is given by:

Looking Technically at Keyboards . . . . . . . . . . . . . . . . . . . 487 Alphabetic keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 Toggle keys and locks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 Repeating keystrokes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 Cursor keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 The number pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 Function keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

Target Address: Enter the IP address of the node you are trying to reach. Source Address (Optional): Specify the IP address of where you want the trace route to begin. This is an optional section. Max Hops (Optional): Specify the maximum number of hops that you would like to pass through. This is optional. Wait Timeout (Optional): Specify the timeout value for non-responsiveness. It is also an optional field.

Futures margin has historically been calculated individually for various futures positions (and options on futures). Futures exchanges allow brokers to collect lower margin for positions with less risk than an outright long or short position. As the variety of futures products has risen, exchanges have adopted a more comprehensive way to allow for the combined riskiness of a futures portfolio. The margin method is called standardized portfolio analysis of risk (SPAN). SPAN margin equals the largest likely loss on the entire position for a one-day horizon. For hedge strategies, this can be substantially less than the margin calculated in the traditional way. Brokers may require more margin that the minimum SPAN margin. See the futures exchanges for more information about how their SPAN margin is calculated.

h(.)

J( t)

= 0.1227

Another strategic implication of cloud computing is the speed of competition. In addition to enabling a new pack of asymmetric competitors, cloud enables a new pace of competition from current competitors as well. Cloud offers a new model to get to market with new solutions, services, and capabilities that can literally pop onto your radar and take market share before you can blink an eye. This is a unique feature of cloud-based business models and even cloudenabled business models. As Stalk and Hout (in their book Competing Against Time1) advocate, cloud-based competitors have a clear advantage simply on the basis of speed, cycles of learning, and accelerating up the learning curve for new business model innovations.

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The local transformer in Fig. 10.26 provides the last voltage stepdown in a power distribu tion system. A common sight on utility poles in residential areas, it is a single-phase transformer th at typically has a 13.8-kY rms line to neutral on its primary coil, and a center tap secondary coil provides both 120 Y rms and 240 Y rrns to service several residences. A typo ical example of this transformer, often referred to as a "pole pig," is shown in Fig. 10.27 .