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The likelihood function can also be written as (1 - p)". 1-P Consider now the detection problem of deciding if the sequence S 1 or the sequence S2 was sent, where each occur with equal probability. The maximum likelihood decision rule says to choose that value of S for which &dH(R3S) (1 - p)" is the largest. Assuming that p < this corresponds to choosing that value of S for which dH (R, is the smallest, that S) is, the vector S nearest to R in Hamming distance. We see that for detection in a Gaussian channel, the Euclidean distance is the appropriate distance for detection. For the BSC, the Hamming distance is the appropriate distance for detection.



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2.2.2 Cyclic Groups and the Order of an Element In a group G with operation * or multiplication operation we use the notation a" to indicate a * a * a * . . . * a , with the operand a appearing n times. Thus a' = a , a2 = a * a , etc. We take ao to be the identity element in the group G. We use a-2 to indicate (a-')(a-'), and to indicate ( u - ' ) ~ . For a group with an additive operator the notation nu is often used, which means a a a . . . a , with the operand appearing n times. Throughout this section we use the an notation; making the switch to the additive operator notation is straightforward. Let G be a group and let a E G. Any subgroup containing a must also contain a 2 ,a3, and so forth. The subgroup must contain e = aa-l, and hence a-2, aP3,and so forth, are also in the subgroup.





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public static String getCookieValue(Cookie[] cookies, String cookieName, String defaultValue) { if (cookies != null) {

When you want to generate HTML or some other markup, you create something called literal result elements, which are elements you add directly to the processing tree. Take a look at the source document in Listing 32-3; then look at Listing 32-4 to view a transformation using literal result elements.

Ei( j)TW,i, 0(n - j) - Fi( j)TW,i, L(n - j) - Hi( j)qW,i, 0(n - j)

AccountBean -accountId -balance +getAccountId() +setAccountId() +getBalance() +setBalance() +ejbActivate() +ejbPassivate() +ejbLoad() +ejbStore()

A Submit button sends the form to the specified action (generally the URL of a server-side program or a mailto address) using the noted method (generally post). A Reset button clears all the fields in the form. Submit and Reset are both reserved HTML terms used to invoke specific actions. A Command button permits the execution of functions defined by the Web designer, as programmed in JavaScript or other languages. To insert a button in Dreamweaver, follow these steps:

1

Wavelength (nm)

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/** * A class to provide a key into a map. */ public class StringPair { /** * <code>hashCode</code> is used to cache the hash code for * this class */ private int hashCode = -1; /** * The right-hand side string. */ private String right; /** * The left-hand side string. */ private String left; /** * A simple constructor taking the right and left side strings. * @param right * @param left * @throws IllegalArgumentException if either <code>right</code> or * <code>left</code> are null. */ public StringPair(String right, String left) { if (null == right || null == left) { throw new IllegalArgumentException( Should not pass null + right = + right

theDOM.setSelection(currSelection[1],currSelection[1])

Re ectance techniques may be used for samples that are dif cult to analyse by the conventional transmittance methods. Re ectance methods can be divided into two categories. Internal re ectance measurements can be made by using an attenuated total re ectance cell in contact with the sample. There is also a variety of external re ectance measurements which involve an infrared beam re ected directly from the sample surface.

//seek to the beginning of the database CEOID oid = 0; DWORD dwIndex = 0; int iRecIndex = 1; oid = CeSeekDatabase (m_globalHDB, CEDB_SEEK_BEGINNING, iRecIndex, &dwIndex);

Hint: tanh(z/2) = -. (f) Show that if ck is equally likely to be 0 or 1, then h ( z ) = 0. Explain why this is reasonable. (g) Explain why h(z) FZ - ( - l ) z l k ~ n ( c ) l , where Ihmin(C)I = mini Ihi(C)I.

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Table 16.2 Estimates from the model of Equation (16.3). Effects Fixed Parameter Intercept: b00 Slope: b10 Sex: b01 Age sex: b11 Level 2 Intercept: 2 u0 Slope: 2 u1 Covariance: u0u1 Intercept: 2 e Estimate 11 1.0 0.11 0.033 1.8 0.028 0.22 0.58 SE 0.016 0.0025 0.022 0.0035 0.023 0.00058 0.003 0.0077

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the likelihood ratio algorithm is used in the density evolution analysis presented in Section 15.8. However, it is only applicable to binary codes, so the general formulation above has value for nonbinary codes. (The reader is advised to review the log likelihood rule in Appendix A before reading this section.)

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