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Shape normalization is usually an initial step in image analysis tasks or a part of data preprocessing. It is important to provide an ef cient normalization because a signi cant error in this early stage of image analysis would lead to a large cumulative error at the end of processing. Shape normalization starts with the computation of image position. A common approach is that the shape position is determined by its gravity center (i.e., center of mass or, simply, centroid) of a given shape. Formally, for a given planar shape S its gravity center (xc (S), yc (S)) is de ned as a function of the shape area (i.e., the zeroth-order moment of the shape) and the rst-order moments (xc (S), yc (S)) = m1,0 (S) m0,1 (S) , m0,0 (S) m0,0 (S) . (12.8)



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The hand-held device is diversi ed in function, as it can be a two-way radio when necessary to talk to other hand-held devices, or it can turn itself into an AM/FM radio or even a television with the right software downloaded The hand-held device takes a major step beyond the devices available today high powered smart cell phones that access the Web The hand-held device can implement a diversi ed array of functions with the right software to ensure mobility, functionality, and exibility Today s chips process signals the way city traf c ow systems process cars Each signal checks at every intersection to see whether it should turn right or left to get to its destination.





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While the option to check the syntax of rules in the program being edited is fairly complete, there are a few syntax errors TFLOPS will not pick up; these will be picked up by FLOPS when the program is run. The option to relabel rules is very useful when the program is being written and debugged, when (as is usual) all or most rules are automatically labeled by FLOPS itself. Caution: When FLOPS discovers and error in a rule and returns an error message, the number of the offending rule returned is not necessarily the number assigned in a comment statement before the rule in the program. It is instead the rule number that TFLOPS would have assigned by the relabel rules option. Frequent rule relabeling is therefore important. The FLEDIT option is very useful when blackboard les are used to communicate information to a program or between programs. FLEDIT presents a friendly way to construct, review or modify blackboard les.

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In the Oxygen hand-held device, software will logically rearrange the internal circuitry so that each signal knows ahead of time all the turns it must make to allow it to zip through its path without having to slow down Hand-held devices can accept speech and visual input and recon gure themselves For example, when a user uses an anonymous hand-held device, it could customize itself to the user s preferences The hand-held device couples with a wireless network or other nearby hand-held devices Hand-held devices utilize the same hardware components as the embedded devices in the Oxygen system, but differ in connections to the physical world, computational power, and software Like the hand-held device, the Oxygen embedded devices would be built with special purpose chips and be connected via wireless networks.

are generally compounded on an actual/actual (or discrete) basis. To adjust Macaulay s duration to allow for discrete compounding, we solve for: Dmod where Dmod Modified duration Dmac Macaulay s duration Y Bond-equivalent yield This measure of duration is known as modified duration and is generally what is used in the marketplace. Hicks s method to calculate duration is consistent with the properties of modified duration. This text uses modified duration. Table 5.2 calculates duration for a five-year Treasury note using Macaulay s methodology. The modified duration of this 5-year security is 4.0503 years. For Treasury bills and Treasury STRIPS, Macaulay s duration is nothing more than time in years from settlement to maturity dates. For coupon securities, Macaulay s duration is the product of cash flows and time divided by cash flows where cash flows are in present value terms. Using the equations and Treasury securities from above, we calculate Macaulay duration values to be: 1-year Treasury bill, 0.9205 7.75% 10-year Treasury note, 7.032 30-year Treasury STRIPS, 29.925 Modified durations on the same three Treasury securities are: Treasury bill, 0.8927 Treasury note, 6.761 Treasury STRIPS, 28.786 The summation of column (D) gives us the value for the numerator of the duration formula, and the summation of column (C) gives us the value for the denominator of the duration formula. Note that the summation of column (C) is also the dirty price of this Treasury note. Dmac 833.5384/98.9690 8.4222 in half years 8.4222/2 4.2111 in years Dmac 11 Y>22

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