Random tape

In cryptology, probabilistic algorithms are usually represented as deterministic Turing machines with an additional input tape, the so-called random tape. The random tape contains a (potentially infinite) sequence of random bits. Each bit on this tape is read exactly once. The content (or each finite subsequence) is supposed to be uniformly distributed. If A is a probabilistic algorithm, A(i) denotes the probability space on the outputs if A is run on input i (i.e., with i on the input tape — i does not include the content of the random tape). To cover non-terminating computations, the output space is augmented by an element t. The probabilistic function computed by A is not distinguished from A in the notation. 

The running time of a probabilistic polynomial-time algorithm is deterministically polynomial, i.e., there is a polynomial Q such that the algorithm never needs more than Q k) steps on an input of binary length k. Of course, the random tape does not count as an input. 

Functional notation. The secret value sk temp is exactly the secret information that the signer s entity stores at the end of initialization. However, more secret random bits may be generated later. (Formally, they are read from a random tape.) It is sometimes useful to have a notation for all the secret information that a signer s entity ever uses. Hence let be a sufficiently long string of random bits, and let... 

It may be infinite, like the content of the random tape. In most existing schemes, an upper bound is known (as a function of par). The existence of such a bound is guaranteed if entities are polynomial-time in their initial states (see Section 4.4.3, Complexity ). In the following, however, the other model is used The complexity of sign is allowed to depend on the message length, too. 

These free energies determine the critical concentrations for observing each peptide structure. In very dilute conditions, this class of peptides exist as random coil monomers in conformational flux. Above a critical concentration, C( pg, the concentration of monomer remains constant and formation of tapes occurs ... 

The standard deviation of each scanner reading has been estimated to be 0. 7 when using a scale of 0-255 units, and the positional accuracy of the instrument is claimed to be 2pm. Data from the microdensitometer are stored in binary format on magnetic tape as an array, typical dimensions being 600 x 600. Prior to analysis the data are reconverted to integer format and copied into a random-access disc file. 

The use of self-assembling peptides is also explored beyond the medical, pharmaceutical, or cosmetics industry. Areas of interest are among others functional foods, electronics, functional coatings, and catalysis (but different from enzyme research). As an example, peptides can be designed to switch from a random coil-like primary structure organization into an a-helix or [3-sheet secondary structure with unique properties. Short peptides align to form [3-sheet tapes with different functionalities, for example, hydrophilic and hydrophobic on either side of the tape to form monolayer coatings (Boden et al., 1996). 

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