Space-time mapping

The properties of real-time signal and data processing applications have to be exploited to arrive at fully efficient application-specific architectures. This requires extensions to the basic linear space-time mapping methods [44] as proposed in chapters 3 and 6. In addition, an alternative affine space-time transformation method based on the existence of independent subsets in the index space is introduced in chapter 5. This method has led to efficient arrays with high hardware utilization [24]. 

After space-time mapping, the conditional execution of several operations on the same processing element (PE) may be needed. Regularization techniques to address this problem are presented in chapter 4. 

We will illustrate the entire method on the example of the APP. The initial dependence graph and the computation domain after space-time mapping have been presented in section 5. Assuming that we want a compression factor c = 3, the vector projection s is chosen in the plane (i, j) such that the input data are projected onto a line which will become one of the boundaries of the array. To... 

This localization technique differs from the approach presented in chapter 6 in that a single choice is made before the space-time mapping (see section 3) is considered. As indicated in chapter 6, the pros and cons of the different approaches depend on the application domain. 

The space-time mapping of the parametric URE derived in the previous step is accomplished by decomposing the index space to independent subsets of variable instances. The number of these subsets depends on the DVs and can be modified by alternative selection of the URE parameters. This results in a variety of array architectures in terms of size, PE utilization, and interconnection patterns. This method is complementary to the approaches introduced in chapters 3, 4, and 6, as indicated there. However, many of the proposed techniques can be combined. 

This design method, however, still does not start from true behavioral specifications for realistic image and video applications. Therefore, pre-transformations are needed before the space-time mapping and localization steps to transform the partly irregular high level description to regular WSACs by means of reindexing [24]. 

After re-indexing, broadcast operations and global operations such as sire still present in the description of figure 4. Localization techniques are needed to localize these operations to arrive at a uniform description with only local and constant dependencies, as required by the space-time mapping. We will... 

Localization transformations result in one application description suited for space-time mapping. However, the optimality of the architecture may heavily depend on how the localization was performed [20]. It is therefore necessary to couple the localization task with the space-time assignment. Due to complexity issues, we have found it impossible to perform the complete space-time assignment simultaneously with the localization task. A divide-and-conquer strategy that performs the two tasks sequentially, while monitoring the interaction be-... 

Using this representation model results in a large reduction of the search space if the best combination of space-time mapping and localization must be found. This is indicated in table 1, where the number of domain definitions, dependence vectors and operation definitions that must be considered when iterating over all localization alternatives is compared to what is needed when using the novel representation model. Furthermore, the model can also be used in synthesis environments which do not address array architectures [20]. 

Techniques that are tuned to throughput-based real-time processing have been presented elsewhere [19, 18]. The following extended method is used for the space-time mapping of the indices of the algorithmic index space D ... 

Since only two placement vectors are used, the vector p, and thus also the architecture resulting from space-time mapping, will be two-dimensional. The other indices of the bijective mapping are attributed to a multidimensional time, which has to be sequentialized in order to be executable. 

The ultimate goal of the overall space-time mapping step is to find a transformation matrix f and a set of skewing parameters 7a that result in an optimized... 

Thus the mere presence of metaphorical language does not by itself tell us whether the space-time metaphor is a psychologically real conceptual mapping. For example, the temporal and spatial meanings could be represented as alternate meaning senses or even as separate homophonic lexical entries. The apparent systematicity would then be illusory, the result of post hoc regularization. 

Gentner, D., and Imai, M. (1992). Is the future always ahead Evidence for system-mappings in understanding space-time metaphors. Proceedings of the Fourteenth Annual Meeting of the Cognitive Science Society (pp. 510-515). 

The persistent correlation that recurs between number patterns and physical structures indicates a similarity between the structure of space-time and number. Like numbers and chiral growth, matter has a symmetry-related conjugate counterpart. The mystery about this antimatter is its whereabouts in the universe. By analogy with numbers, the two chiral forms of fermionic matter may be located on opposite sides of an achiral bosonic interface. In the case of numbers this interface is the complex plane, in the physical world it is the vacuum. An equivalent mapping has classical worlds located in the two surfaces and the quantum world, which requires complex formulation, in the interface. 

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