However, the analytical expressions for the logarithmic expectations have been rarely systematically provided in literature, resulting in inconvenience for related performance analysis. To overcome this issue, in this work, the analytical expressions for the logarithmic expectations of the sums of independent exponential RVs are summarized. Especially, for the case where the sum is composed of both independent non-identically distributed i. To demonstrate the effectiveness of the derived logarithmic expectations, case studies are performed by applying the derived logarithmic expectations to the analysis and derivations of the ergodic capacity of several multiple antenna systems.
The bottom axis shows the values in the original scale. This labeling follows the advice of William Cleveland with the top and bottom axes interchanged. The data values are spread out better with the logarithmic scale. This is what I mean by responding to skewness of large values. The revenue for Boeing is about 2 6 billion dollars while the revenue for Ford Motor is about 2 7.
In Figure 1, the linear scale, the revenue for Ford is the revenue for Boeing plus the difference between these two revenues. We call this additive. In Figure 2 the difference is multiplicative. This is what I mean by saying that we use logarithmic scales to show multiplicative factors. The previous example showed both responding to large values and multiplicative factors. The next example just describes rates of change.
Suppose we had one widget in and doubled the number each year. The following charts show the number of widgets on a linear and logarithmic scale:.
The linear scale shows the absolute number of widgets over time while the logarithmic scale shows the rate of change of the number of widgets over time. The bottom chart of Figure 4 makes it much clearer that the rate of change or growth rate is constant. A chart with a linear scale similar to the top chart of Figure 4 showing a quantity such as our national debt causes panic even if the rate of change is constant.
Logarithmic scales are extremely useful but are not understood by all. As in all presentations, designers must know their audiences. This is a BETA experience. You may opt-out by clicking here. More From Forbes.
In addition to system log, OTRS provides specialized logging back end for any communication related logging. The system comes with dedicated tables and front ends to track and display communication logs for easier debugging and operational overview.
To take advantage of the new system, first create a non-singleton instance of communication log object:. When you have a communication log object instance, you can start an object log for logging individual messages. There are two object logs currently implemented: Connection and Message. Connection object log should be used for logging any connection related messages for example: authenticating on server or retrieving incoming messages.
If you encounter an unrecoverable error, you can choose to close the object log and mark it as failed:. Message object log should be used for any log entries regarding specific messages and their processing.
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