"... In PAGE 3: ... Unfortunately, aggregate computation is traditionally expensive, especially in a temporal database where the problem is complicated byhaving to compute the intervals of time for which the aggre- gate value holds. Consider the sample table in Table1 #28a#29, listing the salaries of employees and when these salaries are valid, indicated by closed-open intervals. Finding the #28time-varying#29 number of employees #28Table 1#28b#29#29 involves computing the temporal extent of eachvalue, which requires deter- mining the tuples that overlap each temporal instant.... In PAGE 3: ... Consider the sample table in Table 1#28a#29, listing the salaries of employees and when these salaries are valid, indicated by closed-open intervals. Finding the #28time-varying#29 number of employees #28 Table1 #28b#29#29 involves computing the temporal extent of eachvalue, which requires deter- mining the tuples that overlap each temporal instant. Similarly, #0Cnding the time-varying maximum salary #28Table 1#28c#29#29 involves computing the temporal extent of each resulting value.... In PAGE 3: ... Finding the #28time-varying#29 number of employees #28Table 1#28b#29#29 involves computing the temporal extent of eachvalue, which requires deter- mining the tuples that overlap each temporal instant. Similarly, #0Cnding the time-varying maximum salary #28 Table1 #28c#29#29 involves computing the temporal extent of each resulting value.... In PAGE 4: ... When an aggregation tree is initialized, it begins with a single node containing #3C 0; 1; 0 #3E #28see the initial tree in Figure 1#29. In the example from the previous section, four tuples from the argument relation #28 Table1 #28a#29#29 are inserted into an empty aggregation tree. The start time value, 18, of the #0Crst entry to be inserted splits the initial tree, resulting in the updated aggregation tree shown in Figure 1.... In PAGE 4: ... Because the original node and the new node share the same end date of 1, a count of 1 is assigned to the new leaf node #3C 18; 1; 1 #3E. The aggregation tree after inserting the rest of the records in Table1 #28a#29 is shown at the bottom of Figure 1. To compute the number of tuples for the period #5B8; 12#29 in this example, we simply take the count from the leaf node #5B8; 12#29 #28which is 1#29, and add its parents apos; countvalues.... In PAGE 4: ... Starting from the root, the sum of the parents apos; counts is 0 + 0 + 1 = 1 and adding the leaf count, gives a total of 2. The six leaf nodes of the aggregation tree correspond to the six tuples in the result of the aggregate #28see Table1 #28b#29#29. Though SEQ correctly computes temporal aggregates, it is still a sequential algorithm, bounded by the resources of a single processor machine.... In PAGE 22: ...4.3 Scale-Up Performance: Time Partitioning The experimental parameters for this are shown in Table1 0, with the results given in Figure 17. We can observe analogous results to the same experiment on data set partitioned by SSN #28cf.... In PAGE 23: ...Actual Values Partitioning Time Number of Processors #28p#29 2, 4, 8, 16, 32 Tuple Size in bytes 93 Tuples per Processor 2,620 Total Number of Tuples p #02 2; 620 Reduction 80.76 percent Table1 0: Experimental Parameters #28Scale-Up, Time Partitioning#29 0 0.5 1 1.... In PAGE 24: ...7.29#2F95.32#2F92.08#2F87.24#2F80.76 percent Table1 1: Experimental Parameters #28Speed-Up, Time Partitioning#29 0 0.5 1 1.... In PAGE 30: ...Node Distributed Centralized Reduction Count Results Results HI Small GTDM GTDM+C Large GTDM PM LOW Small GTDM PM Large GTDM GTDM+C Table1 2: Matrix of Recommendations 4.5.... ..."

"... In PAGE 2: ... When an aggregation tree is initialized, it begins with a single node containing lt; 0; 1; 0 gt; (see the initial tree in Figure 1). In the following example [9], there are 4 tuples to be inserted into an empty aggregation tree (see Table1 (a)). The start time value 18 of the rst entry to be inserted splits the initial tree, resulting in the updated aggregation tree shown in Figure 1.... In PAGE 2: ... Because the original node and the new node share the same end date of 1, a count of 1 is assigned to the new leaf node lt; 18; 1; 1 gt;. The aggregation tree after inserting the rest of the records in Table1 (a) is shown in Figure 1. To compute the number of tuples for the period [8; 12) in this example, we simply take the count from the leaf node [8; 12) (which is 1), and add its parents apos; count values.... In PAGE 4: ...are given in Table1 (b). It should be noted that the order of tuple insertion into the aggregation tree a ects its performance, thought not its result.... In PAGE 19: ... Result Placement Methodology Node Config. Size Hi Reduction Dataset Low Reduction Dataset Distributed Small TDM TDM Large TDM TDM Centralized Small PM PM Large PM TDM+C Table1 0: Matrix of Recommendations 1. Use TDM whenever distributed result placement su ces, regardless of any other parameter.... ..."

"... In PAGE 6: ... For queries, we use the traditional SQL-92 SELECT statement, perhaps with explicit reference to the timestamp attributes. Table2 shows how the modification statements may be mapped to SQL-92. The left column gives temporal query language statements for insertion and dele- tion (updates are combinations of deletions and insertions).... In PAGE 6: ... Later sections will study the issues involved in providing such values, resulting in a fully specified definition of the modification statements. When we insert a tuple (the mapping for such an insertion appears as the second row of Table2 ), it is timestamped with the period [now - nobind now) in the valid-time dimension. This states that the fact is valid from the current time... In PAGE 7: ...Table 2: Initial Translation of Temporal Modification Statements period [start value - until changed), denoting that it was present in the database starting at start value and persists to now, that is, until a future transaction, or a future statement in the current transaction deletes or updates the tuple. A deletion of a tuple (the fourth row of Table2 ) is effected by updating the T-Stop attribute to the stop value, indicating that our old belief no longer holds, and inserting a tuple to record our new belief that the tuple was valid in the modeled reality from the old V-Begin time to the current time (now). Note that all explicit attributes are copied.... In PAGE 9: ... Hence, T2 starts after T1 starts and commits before T1 commits. First consider only transaction T1 in Figure 2 and assume that the statements are evaluated using the translations outlined in Table2 and the obvious approach... In PAGE 11: ...5/ at day 14 in another separate transaction will return (Bob, Toy) and (Jim, Toy). To solve the two problems using the start-time of transactions for now,wecan extend the WHERE clauses for the delete in the fourth row of Table2 to include a check of whether the V-End attribute is equal to nobind now. The predicate for the valid-time dimension is thus extended from V-Begin lt; now AND now lt; V-End ... In PAGE 18: ... Name Dept T-Start T-Stop Joe Shoe 1998-01-06 1998-01-16 Joe Sports 1998-01-16 1998-01-27 Joe Outdoor 1998-01-27 until changed Table 5: The Transaction-Time Table, Emp Table 6 shows how temporal statements are mapped to SQL-92 statements by the stratum. This table is a simplification of Table2 , considering only transaction time and utilizing timestamping after commit with revisitation. For simplicity, we assume that all explicit attributes occur in modification statements.... ..."

"... In PAGE 28: ... Combined, the temporal ER models represent a rich body of insights into the temporal aspects of database design. Table1 provides an overview of the models and contains references to further readings; the reader is encouraged to study the... ..."

"... In PAGE 5: ... This approach allows complex reasoning about temporal interval relationships and is consistent with the TSQL2 standard [9] (ii) Use an implementation of the object model in which time is stored as the key external contextualization of the underlying model, and that allows tractable computation over the model with respect to time. Object models are stored with their associated valid temporal intervals in a database of the form shown in Table1 . These temporal periods define the time for which the object description was observed to be true.... ..."

"... In PAGE 92: ... This approach allows complex reasoning about temporal interval relationships and is consistent with the TSQL2 standard [9] (ii) Use an implementation of the object model in which time is stored as the key external contextualization of the underlying model, and that allows tractable computation over the model with respect to time. Object models are stored with their associated valid temporal intervals in a database of the form shown in Table1 . These temporal periods define the time for which the object description was observed to be true.... In PAGE 116: ...Table1 . Summary of parameters used for the experimental work Parameter Value Frequency 2.... ..."

"... In PAGE 6: ...1 Results improve when the two temporal periodicity fea- tures are added to the features set, that is, when one uses the feature set C (with periodicity) instead of B (without period- icity). In Table5 , the best performing optical flow was se- lected for each confidence measure. The table demonstrates that temporal periodicity consistently improves the peak per-... ..."

"... In PAGE 34: ...Table1 ) representing a set of three independent tasks and the other one (see Table 3) representing a set of three tasks, each introducing release jitter. As mentioned before, the second task configuration implements... In PAGE 68: ...Stimulus Period Deadline ControlLoop (CL) timeout 100ms 100ms EnterCruise (EC) cruise - 200ms ResumeCruise (RC) resume - 200ms CruiseReached (CR) speedReached - 200ms BrakePressed (BP) brakePressed - 50ms AccelPressed (AP) accelPressed - 50ms CruiseOff (CO) cruiseOff - 150ms Table1 0: Description of Automobile Cruise Control Transactions the timing service. The CruiseControl actor sends a speedRequest message to the Speedometer actor, which returns the current speed in a speedValue message.... In PAGE 70: ... To perform the timing and scheduling analysis, we will use the worst-case computation times of each transition as presented in Table 11. CruiseControl Speedometer Other Actors ctimeout = 2ms cspeedRequest = 3ms c = 2ms cspeedValue = 10ms c = 5ms Table1 1: Transition Computation Times... In PAGE 72: ... Although the BrakePressed (BP), AccelPressed (AP), and CruiseOff (CO) transactions have higher priority than CL, we do not need to consider their preemp- tion effect, since any of those transactions terminates the CL transaction. There are four transitions in the CL transaction as shown in Figure 18 with the worst-case exe- cution times (specified in Table1 2) of 2ms, 3ms, 10ms and 2ms respectively. Entering and Preparing for Automatic Cruise Control.... In PAGE 73: ...956 17.584 Table1 2: Specifications of Automobile Cruise Control Transactions Since all of the measured worst-case transaction response times fall below the predicted response times, the response time analysis of our automobile cruise control example further validates the canonical scheduling models developed in Section 5. Note that the cruise con- trol transactions are not preempted by higher priority transactions, and they are subjected to the same blocking intervals within a single- and multi-threaded executable.... ..."

"... In PAGE 6: ... With a focus on the types of relations they provide, we now review 23 of these temporal data models. Table1 lists most of the temporal data models that have been proposed to date. If the model is not given a name, we appropriate the name given the associated query language, where available.... ..."

"... In PAGE 6: ... With a focus on the types of relations they provide, we now review 23 of these temporal data models. Table1 lists most of the temporal data models that have been proposed to date. If the model is not given a name, we appropriate the name given the associated query language, where available.... ..."