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1. Up to $25,000 of certain passive losses can be used to offset any type of income, including active income. 2. Limited partnerships and other passive activities that have money invested in money market accounts, bonds, or CDs may have a portion of their income categorized as portfolio income instead of passive income. This concept is illustrated in examples later in this chapter. 3. Income from a master limited partnership will generally be categorized as portfolio income instead of passive income, so it can t be offset by your real estate losses. Losses from a master limited partnership generally can t be used to offset income from any investment other than itself, until you sell. 4. For certain professional real estate investors, income or loss from rental activities is not automatically treated as passive. They must work more than 750 hours per year in real estate businesses and meet certain other requirements.

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Figure 9-7 Histological sections of plant tissues with birefringent objects. (a) Radial section of pine wood containing cellulose walls and bordered pits. (b) Cross section of a buttercup root, an herbaceous plant. The cortical cells are filled with starch gains. (Specimen slides are from Carolina Biological Supply Company, Inc.)

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While the TCP- and UDP-based protocols described in earlier sections work well for bulk data transfers such as large data files in the order of gigabytes and terabytes, they are not well suited for another class of Grid applications, namely real-time collaborative and interactive applications, which routinely need to stream comparatively small data objects but at much higher frequencies. For example, to stream high-definition microscopy images from a remote camera, high-definition video, or ultra-high-resolution images from a remote rendering cluster requires the transmission of image frames that are each of the order of a few megabytes but which are updated at 30 frames/second for an hour or more at a time. The total amount of data that can be transmitted in an hour can easily reach a terabyte. These real-time applications often have tight constraints on latency and jitter because new updates need to be sent in response to user interaction. The TCP- and UDP-based protocols described perform very poorly in these applications because their error correction mechanisms introduce large amounts of latency and jitter. In the past, lossy transmission schemes have been acceptable because the applications have revolved around low-resolution video-conferencing. As Grid applications have begun to make greater use of distributed visualization resources, lossy transmission schemes have been found to be unacceptable because errors in transmission visually distort the content being transmitted. When used in scientific or medical applications, image distortions could lead to incorrect conclusions about the presented information.

Note that our assumptions make the owgraph model equivalent to a Markovian M/M/3 queue (cf. Taylor and Karlin, 1984). However, the analysis here gives the actual transient distribution, not the limiting distribution derived from queuing theory. If the data indicated that the waiting times were not exponential, the queuing model would not be tractable, but the owgraph model would still be valid and useful. In this case we would model each branch probability and waiting time distribution separately for the owgraph based on examining histograms of the data to choose parametric models for branch waiting time distributions. Note that this approach models the observable random variables, which are conditional on each branch. It makes no assumption of independence for unconditional (unobservable) branch waiting times, only a much weaker conditional independence assumption. The likelihood function for the M/M/3 queue has a contribution of a probability and a waiting time density from each branch. For example, the 1 2 transition contributes 32,100 data points. The probability of the transition is 6 /(6 + ) and the density is Exp(6 + ), as indicated in Table 9.3. The overall contribution to the likelihood of this transition is 6 6 +

TABLE 3.5 Default Rates at 1- and 5-Year Horizons by Agency (%)

of joule heating resulting in an apparent very large current density dependence and hence high values of n. In general, the correct value of n should lie between 1 and 2 [124]. If the cross-sectional area A is also taken into account [83], then Eq. (5.1.9) is modi ed as Ea n 5:1:10 MTF AJ exp kT It is also interesting to study the speed of the metallic ions and its relationship to MTF. According to Gimpelson [115], the migration velocity vm can be expressed as Ea vm GJ exp 5:1:11 kT

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