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1980 to less than a cent per megabyte in 2000. The slide in component prices, though phenomenal, accounts for only about 15 percent of the cost of a desktop computer. Thus, the Congressional Budget Of ce attributes the drop in computer system prices, illustrated in Figure 4.5, only partially to technological improvements. The majority of the precipitous drop in computer system prices is attributed to the Asian currency crisis during the late 1990s, along with the increased competition among computer manu facturers and suppliers. According to the Bureau of Economic Analysis, desktop computer sys tem prices in 1987 were nearly three times greater than prices in 1996. The downward trend in computer prices accelerated through the end of the 1990s and into the 2000s, with prices in 2002 approximately one-quarter of those in 1996. What s more, the virtual doubling of capacity of the com puter processing chips every 18 months the so-called Moore s Law has made personal digital assistants (PDAs) nearly as powerful as the rst room-sized mainframe computers were. Because of the massive amounts of data involved and the computa tional overhead in biotech research and development, not all work in biotech computing is relegated to desktop computer systems, even if

if;+(p,>.,r,t) = PT'I/;_(p,>.,r,t).

(3.171)

To view the Pro t and Loss Statement, go to Report Company & Financial Pro t & Loss Standard. A sample Pro t and Loss Statement is shown in Figure 28-12.

What are these operators for our Schrodinger-like equation (3.167) for the photon Under time inversion, t - t -t, P - t -p, and 0- - t -0-. Let t' = -t and 'l/J'(t') = T'l/J(t); then the transformed (3.167) reads

TiT-Iii ~, 'l/J'(t')

10 1985 1990 1995 2000

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The amount of money that you have to run your business is called working capital. To calculate working capital, subtract the total of the company s current liabilities from its current assets. (You obtain this information from your company s Balance Sheet as shown in Figure 28-13.) In other words, Working Capital = Current Assets Current Liabilities. If this number is a negative, the company is likely to have a problem meeting its current obligations.

-TH(t)T-1'l/J'(t').

(3.172)

Figure 28-12: A Pro t and Loss Statement is shown here. You may remember from 4 that current assets either are cash equivalents or are assets expected to be reduced to cash equivalents within one year. Current liabilities must be paid within one year.

For (3.167) to be invariant under time inversion [i.e., for (3.172) to have the same form as (3.167)] we must take TiT- 1 = -i if we take TH(t)T-l = H'(t'). As the helicity operator does not change under time inversion, H' (t') = H (t). So T is just the ordinary complex conjugation and, as (X*)* = X, T-l is also. Under space inversion (parity operation), r - t -r, p - t -p, and 0- - t 0-. Let r' = - rand 'l/J' (r') = P'l/J (r). The transformed SchrOdinger-like equation (3.167) is given by (3.173) Then if we take PH(r)p- 1 = H'(r'), we have to take PiP- 1 = i to keep (3.167) invariant. Moreover, as the helicity changes sign under parity, H'(r') = -H(r). Then we can take P to be the 4 x 4 matrix that swaps the pairs of upper and lower rows,

FIGURE 4.5 Desktop computer system price declines, 1987 2002.

P=[~ ~],

(3.174)

Let s gauge the working capital of Larry s Landscaping. Its current assets are shown at $164,387.90. The total amount of the company s other current liabilities is $18,222.07. Subtracting current assets from current liabilities discloses working capital in the amount of $37,273.75. This is the amount of money that Larry s Landscaping has available to run its business and initiate new ventures after paying its current bills.

where 0 is the 2 x 2 null matrix and 1 is the 2 x 2 unit matrix. Now that we have P and T, we can find the wavefunction of an antiphoton. Using (3.171), we get +(p,A,r,t) = PT'l/J_(p,A,r,t)

- v'2

they are increasingly affordable. For example, in 2001, IBM committed $100 million over ve years to computational biology, predominantly in the form of a commitment to build Blue Gene, the next generation su percomputer for genomic and proteomic research. Similarly, in 2001, Celera Genomics Corporation, Sandia National Laboratories, and Com paq entered a partnership to develop algorithms and software for life sciences research on supercomputers. For some problems, the computa tional requirements are so great that even the most powerful desktop systems aren t practical. Tasks such as protein modeling need the power of a supercomputer or grid computing to provide results in hours or days instead of the weeks or months that would be required on a desk top computer.

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