### Table 2.1: Notations in the de nition of time warping distance As for Euclidean distance, searching techniques are proposed to support the retrieval of similar time series based on the increasingly important time warping distance. In [47], a time series database supporting time warping is proposed whose strategy is shown in Figure 2.2. It follows the architecture of the general strategy shown in Figure 1.1, by further specifying the transformation used in index creation/pre-processing and the ltering functions in post-processing. To elaborate, two steps are involved. First, K-L transform is applied to map the original time sequences to lower dimension feature vectors, then a multi-dimensional index is built (Fastmap in- dex). If we are looking for set of sequences ~ y within time warping distance

1999

### Table 1 shows that the above distance is a special case of our framework, by setting (a) the `basic apos; transformation language T0 to consist of only the stutter transforma- tion, with cost = 0 and (b) the D0() distance function to be the L1 metric, that is, the city-block distance. Figure 3 shows two time sequences, before and after the time-warping. The se- quences are mixtures of similar harmonics: x(t) = 10 sin(0:5t) + 5sin(:25t) and y(t) = 11 sin(:55t) + 4:5 sin(:26t) respectively.

1997

"... In PAGE 14: ... D(s; t) = min8 gt; lt; gt; : cost(Del(t[1])) + D(s; Rest(t)) cost(Del(s[1])) + D(Rest(s); t) cost(Sub(s[1]; t[1])) + D(Rest(s); Rest(t)) (14) where Del(t[1]) (Del(s[1])) stands for deleting the rst character of t (s), and (Sub(s[1]; t[1])) for substituting the rst character of s by the rst character of t, cost is the cost of the deletion/substitution, and Rest(t) (Rest(s)) is the string t (s) without its rst character. As shown in Table1 , our framework includes the string editing distance, by choos- ing: T0 to have only one transformation, the drop lt; p gt; transformation, with cost=1... In PAGE 15: ...Euclidean string-edit time-warping drop lt; p gt; 1 1 1 stutter lt; p gt; 1 1 0 D0 Euclidean Hamming city-block Table1 : Cost of operators of our framework, for popular distance functions The distance can be computed in time O(NxNy), where Nx, Ny are the number of samples in each string [14], [18]. Distance functions with time-warping: Such functions are used for example in digitized voice signals, where there are uctuations in the rate of speech.... ..."

Cited by 24

### Table 1 shows that the above distance is a special case of our framework, by setting (a) the `basic apos; transformation language T0 to consist of only the stutter transformation, with cost = 0 and (b) the D0() distance function to be the L1 metric, that is, the city-block distance. Figure 3 shows two time sequences, before and after the time-warping. The sequences are mixtures of similar harmonics: x(t) = 10 sin(0:5t) + 5sin(:25t) and y(t) = 11 sin(:55t) + 4:5 sin(:26t) respectively.

1997

"... In PAGE 11: ... D(s; t) = min8 lt; : cost(Del(t[1])) + D(s; Rest(t)) cost(Del(s[1])) + D(Rest(s); t) cost(Sub(s[1]; t[1])) + D(Rest(s); Rest(t)) (14) where Del(t[1]) (Del(s[1])) stands for deleting the rst character of t (s), and (Sub(s[1]; t[1])) for substituting the rst character of s by the rst character of t, cost is the cost of the deletion/substitution, and Rest(t) (Rest(s)) is the string t (s) without its rst character. As shown in Table1 , our framework includes the string editing distance, by choosing: T0 to have only one transformation, the drop lt; p gt; transformation, with cost=1 and by setting D0() to be the Hamming distance. The distance can be computed in time O(NxNy), where Nx, Ny are the number of samples in each string [13], [16].... In PAGE 12: ...Euclidean string-edit time-warping drop lt; p gt; 1 1 1 stutter lt; p gt; 1 1 0 D0 Euclidean Hamming city-block Table1 : Cost of operators of our framework, for popular distance functions Table 1 shows that the above distance is a special case of our framework, by setting (a) the `basic apos; transformation language T0 to consist of only the stutter transformation, with cost = 0 and (b) the D0() distance function to be the L1 metric, that is, the city-block distance. Figure 3 shows two time sequences, before and after the time-warping.... ..."

Cited by 24

### Table 2: Timings for noninteractive warping

"... In PAGE 53: ...Table 2: Timings for noninteractive warping The image calculated for Table2 contains only translational warps. Scal- ing warps are somewhat slower because their mapping function includes a square root, and rotation warps are the slowest because their mapping function requires the calculation of a sine/cosine pair.... ..."

### Table 1. Time Warp: Sensors and Indicators

"... In PAGE 61: ... It is possible to omit certain characteristics if they are irrelevant for the particular system under test or if they do not provide any information useful in the performance evaluation study. Table1 summarizes the characterization of the three layers. Descriptions Layer Functional Sequential Parallel Quantitative application structural multiplicity Application set of algorithms behavior parallelism of algorithms, graph graph volume of data algorithm structural multiplicity Algorithm set of routines behavior parallelism of routines, graph graph volume of data routine structural multiplicity Routine set of statements behavior parallelism of statements, graph graph volume of data Table 1.... In PAGE 61: ... Table 1 summarizes the characterization of the three layers. Descriptions Layer Functional Sequential Parallel Quantitative application structural multiplicity Application set of algorithms behavior parallelism of algorithms, graph graph volume of data algorithm structural multiplicity Algorithm set of routines behavior parallelism of routines, graph graph volume of data routine structural multiplicity Routine set of statements behavior parallelism of statements, graph graph volume of data Table1 . Characterization at the three hierarchical layers Functional Description The identi cation of the basic components for each... In PAGE 69: ...Action Netscape start, quit Windows open, close Conversations http, ftp Methods GET Table1 : Types of Actions at eachLevel web browsers (level 2). The time between starting a browser and quitting it is referred to as the life-time of the browser and is represented at the second level byathick line.... In PAGE 70: ... Thus, we are only considering the 4 inner levels in the hierarchy. Table1 summarizes these four levels and the actions that could occur at each of them. Applying the proposed approachofPACFG for workload modeling in performance evaluation studies has already been demonstrated in previous papers [Ragh 93, SV R 94, Ragh 95, SV R 96].... In PAGE 86: ...246 seconds. The MIME types of the downloaded file were grouped together, forming the five groups stated in Table1 . Each session then was represented by its mixture of downloaded filetypes in percent, yielding 196 5-dimensional vectors.... In PAGE 86: ... CC BD CC BE CC BF CC BG CC BH appl. audio/video image text unknown Table1 . MIME type groups.... In PAGE 98: ... In this work we study the distributed execution of Time Warp logical processes (LPs) under the performance super- vision of the PPMM environment (Figure 3). State and performance characteristics of a Time Warp LP are sampled at runtime via the sensors listed in Table1 . Time Warp is knownrequire a sufficient amount ofmemory to be operable.... In PAGE 99: ... The structure of the simulation model guarantees balanced load among the four LPs, and the communication structure among LPs adheres to a ring topology. The eight sensors outlined in Table1 have been inserted into the Time Warp code. The point sample sensor (PS) as well as each of the cumulative sensors (CS) are transformed into a corresponding indicators (see Table 1).... ..."

### Table 1: List of Top Gene Profile Similarities (Lowest posterior expected warping distance).

2007

"... In PAGE 17: ... The interactions with YER001W and BYL032W have not been reported in the literature. In Table1 we report the top 15 relationships with lowest expected posterior warping distance. For all known genes the inferred relationships have biological support as they share similar cellular functions and/or have been reported in the literature to interact with each other.... ..."

### Table 2. u-plot Kolmogorov Distance

1996

Cited by 6

### Table 3: Example of common functions of devices: Same functions are mapped to the same gesture; similar functions may be mapped to the same gesture if this is intuitive and no other function is overloaded.

1997

"... In PAGE 13: ... Depending on the gesture commands are sent to the devices and feedback is applied. The correlation of gestures and commands is shown in Table3 . If the dialogue nishes by time out or by the pointing gesture or a certain termination gesture the control ow enters the direction determination (Figure 12).... In PAGE 30: ...evice at a time. First a device is selected by the unique pointer click. Depending on the selected device, the gesture will execute a certain command. Table3 shows a possible mapping. The stars indicate that the device in that column supports the function of the row.... ..."

Cited by 4

### Table 1: Warp synchronisation actions Operation Function

"... In PAGE 4: ...DESIGN ISSUES 3 Table1 summarises the primary synchronisations of the Warp protocol. Table 1: Warp synchronisation actions Operation Function... ..."