**1. Microarray**(Found in this bioinformatics article)

*An antigen microarray chip was developed and used bioinformatic analysis to study a model of type 1 diabetes...*

**2. Block**

If the words

*wi*appearing in an encoding scheme are all of the same length, the code is said to be a ﬁxed-length or block code, and the common length of the

*wi*is said to be the length of the code. Otherwise, the code is said to be a variable-length code.

**3. Relative**

We have a memoryless channel with input alphabet A = {

*a1,...,an*}, output alphabet B = {

*b1,...,bk*}, and transition probabilities

*qij.*For i ∈ {

*1,...,n*}, let pi denote the relative frequency of transmission, or input frequency, of the input character

*ai*.

**4. Audio**

Imagine a signal, that is, a function

*h*of time

*t*. It it’s helpful, you can think of

*h*as an audio signal, i.e., a voltage level, ﬂuctuating with time

**5. Stream**

Nevertheless, we shall hold to the simplifying assumption that

*pi*, the proportion of

*ai*’s in the input text, is also the probability that the next letter is

*ai*, at any point in the input stream.

**6. Knowledge**

There is a body of knowledge related to the Implicit Function Theorem in the calculus of functions of several variables that provides an answer of sorts.

**7. Missing**

The smoothing procedure sometimes makes good guesses about the missing data, but it cannot recover the original information.

**8. Recover**

To see why we do this, observe that if the decoder is supplied the source word length N and a number in A, then the decoder can recover the sequence

*i1,...,iN*, and thus the source word

*si1···siN*.

**9. Alignment**

The code string is shifted by the same amount in order to maintain alignment.

**10. Transformation**

The transformation x → 2x −1/2 doubles the directed distance from x to 1/2; call it the “doubling expansion around 1/2” if you like.

**11.Approximate**

Using approximate probabilities can permit replacement of multiplications by simple shift operations.

**12. Uniform**

It has been generally assumed that the relative source frequencies are equal, and the dazzling algebraic methods used to produce great coding and decoding under these assumptions automatically produce a sort of uniformity that makes p0 and p1 equal or trivially close to 1/2.

**13. Optimal**

Furthermore, if

*p1*,..., pn are optimal input frequencies satisfying these equations, for some value of C, then C is the channel capacity.

**14. Simultaneously**

Thoughtful quantizing can help suppress both non-meaningful and weak mathematical frequencies simultaneously.

**15. Fixed**

If our attention is fixed to only the part of the graphs over the integers 0, 1, . . . , 7, then we might be led to believe that x is as smooth, if not smoother, than y.

**16. Rate**

The code words would have to be quite long, so that the rate of processing of source text would be quite slow...

**17. Arbitrary**

If, for some reason, we require the M in the WNC algorithm to be small, we

may allow rough and arbitrary approximation of the relative source frequencies.

**18. Mapping**

Given E and F , we can think of the mapping (i, j ) → I (E i , F j ) as a random variable on the system E ∧ F .

**19. Hamming weight**

The Hamming weight of a word

*w ∈ {0, 1}*is

*wt(w)*= number of ones appearing in

*w*.

**20. Noisy**

Shannon’s Noisy Channel theorem applies to a more general sort of source, one which emits source letters, but not necessarily randomly and independently

**21. Ambiguous**

The code determined by φ is said to be unambiguous if and only if φ is one-to-one (injective). Otherwise, the code is ambiguous.

**22. Code**

The code determined by φ is uniquely decodable if and only if it is unam-biguous and there exists a VDR for it.

AND FROM THE PREVIOUS GAME:

**23. Bitwise**

In addition, a number of the steps in the scheme can be managed as simple bitwise operations.

**24. Finite**

Therefore, we will allow ourselves the convenience of sometimes attributing the SPP to finite sets of binary words

**.**

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