lunes, 27 de mayo de 2013

Extra points: Card Game

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.

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.

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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