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However, the obtained fuzzy systems frequently are without practical utility because it is impossible to give some semantic meaning to the rules due to fuzzy sets superposition, and rules that are sometimes redundant and sometimes contradictory, frequently with high complexity In [5] a comprehensive collection of papers present several approaches for evolving the fuzzy systems to more interpretability (mainly of ine trained or expert-based ones) In recent years, interpretability has been considered to be the key feature of fuzzy models [6, 7], continuing previous important works [8, 9], and can be pursued by rule base simpli cation and reduction methods There is actually considerable activity concerning this challenging problem Several perspectives are being developed, for example, by fuzzy set merging using entropy measures [10], by genetic optimization [11 13], by multiobjective evolutionary algorithms [14 16], by manipulating the cost index [17, 18], or by Radial Basis Function Networks [19].

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This theorem provides another justi cation for the de nition of entropy rate it is the expected number of bits per symbol required to describe the process. Finally, we ask what happens to the expected description length if the code is designed for the wrong distribution. For example, the wrong distribution may be the best estimate that we can make of the unknown true 1 distribution. We consider the Shannon code assignment l(x) = log q(x) designed for the probability mass function q(x). Suppose that the true probability mass function is p(x). Thus, we will not achieve expected length L H (p) = p(x) log p(x). We now show that the increase in expected description length due to the incorrect distribution is the relative entropy D(p||q). Thus, D(p||q) has a concrete interpretation as the increase in descriptive complexity due to incorrect information. Theorem 5.4.3 (Wrong code) The expected length under p(x) of the 1 code assignment l(x) = log q(x) satis es H (p) + D(p||q) Ep l(X) < H (p) + D(p||q) + 1. Proof: The expected codelength is El(X) =

base region silicon concentration; base region germanium concentration and pro le design; base region carbon concentration and pro le placement. Transistor layout and design of the emitter base region have an in uence on the RF performance and ESD robustness of a homojunction bipolar transistor or a heterojunction bipolar transistor. The transistor design layout features of interest can be as follows: SA or NSA emitter base design; emitter area; emitter aspect ratio (e.g., width to length ratio); emitter base space; wrap-around or nonwrap around emitter base design layout; ordering: EBC, BEC, or ECB; single emitter or multiemitter; higher order design layouts: CBEBC, CEBEBEC, among others. All the aforementioned features from a structural, semiconductor process, and design layout have an in uence on the performance aspects as well as the ESD robustness of homojunctions and heterojunction bipolar transistors. The evaluation of process variations and device design spacings on ESD robustness is evaluated for both positive and negative stress conditions as a function of the salicide location, emitter base spacing, and collector opening. The evaluation of process variations and device design spacings on ESD robustness is evaluated for both positive and negative stress conditions as a function of the salicide location, emitter base spacing, and collector opening.

Figure 3.2 RF CMOS ESD device comparison of a grounded gate n-channel MOSFET with and without drain extension

For a more detailed review and treatment, see [22] or [23] Most of the known methods have been developed for batch processing for an already-existing rule base Kernel-based learning methods, such as Support Vector Machines (SVMs), Relevance Vector Machines (RVMs), or Kernel PCA, have been studied extensively in the machine-learning community, being among the best learning techniques for many benchmark data sets and real-world applications [24] The basic idea of these methods is to preprocess the data by some nonlinear mapping (using the kernel trick) and then apply a linear algorithm in a usually higher-dimensional feature space Such large feature spaces are handled with the simple computational cost of the kernel function This approach indicates an alternative point of view to the parameters learning of a fuzzy system, with the membership functions being those examples that are critical to solving the given task.

There isn t a great deal of difference between the files, and you generally won t notice any speed differences. VBA code is always compiled before it is executed. This is true whether it s in an XLS file or an XLA file. However, XLA files contain the actual VBA code, not compiled code.

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