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The set of n-tuples gn (1), gn (2), , gn (2nR ), denoted by X n (1), , 1 1 n (2nR ), constitutes the codebook, and fn (1), , fn (2nR ) are the X associated assignment regions Many terms are used to describe the replacement of X n by its quantized version X n (w) It is common to refer to X n as the vector quantization, reproduction, reconstruction, representation, source code, or estimate of X n De nition A rate distortion pair (R, D) is said to be achievable if there exists a sequence of (2nR , n)-rate distortion codes (fn , gn ) with limn Ed(X n , gn (fn (X n ))) D De nition The rate distortion region for a source is the closure of the set of achievable rate distortion pairs (R, D).

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De nition The rate distortion function R(D) is the in mum of rates R such that (R, D) is in the rate distortion region of the source for a given distortion D De nition The distortion rate function D(R) is the in mum of all distortions D such that (R, D) is in the rate distortion region of the source for a given rate R The distortion rate function de nes another way of looking at the boundary of the rate distortion region We will in general use the rate distortion function rather than the distortion rate function to describe this boundary, although the two approaches are equivalent We now de ne a mathematical function of the source, which we call the information rate distortion function.

Collagen tested after stretching from 0 up to 50%. Collagen cross-linked and tested after stretching from 0 up to 50%. 3 Collagen rat tail: properties determined by light scattering 4 Dragline silk from Nephila claviceps spider 5 Silkworm silk from Bombyx mori silkworm cocoon 6 L-PLA molecular weights from 50,000 to 300,000, properties for D,L-PLA were in similar ranges

which proves the result. The rst inequality follows from the entropy maximizing property of the Gaussian under the covariance constraint. De nition We say that a random vector X n is causally related to Z n if

The main result of this chapter is the proof that the information rate distortion function is equal to the rate distortion function de ned above (ie, it is the in mum of rates that achieve a particular distortion)..

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Emergency Medical Associates (continued) future, 208 technology implementation, 203 204 vendor selection, 199, 203 Emergency Medicine Analysis and Reporting System (eMARS), 197 198 dashboards, reimplementation, 208 services, 199 Employee costs, 132 Employee satisfaction surveys/feedbacks, 132 End users, 92 experience, 147, 149 151 involvement, 91 learning curve/training, 10 presentation, effectiveness/interaction, 149 Enterprise dashboards business case, 3 elements, 7 9 enhancement, 8 misperceptions, 10 12 Enterprise data warehouse (EDW), 20 information collection, 178 Enterprise performance dashboards, 97 101 Enterprise Performance Management (EPM), 3, 5, 26, 165 application, 13 console, 65 Enterprise Resource Planning (ERP), 7, 166. See also Vendor-specific ERP system, 29 Enterprise-based licensing cost, 168 169 Enterprise-wide deployment. See Dashboards execution, time, 89 Enterprise-wide reporting system, existence, 37 38 EPM. See Enterprise Performance Management ERP. See Enterprise Resource Planning Essbase (Hyperion), 156 ETL. See Extraction transformation and loading Evaluation matrix, 166. See also Dashboards; Organization-specific evaluation matrix usage, 148 EWS. See Early warning system

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