From typical sequences to typical genotypes

From typical sequences to typical genotypes.

We demonstrate an application of a core notion of information theory, typical sequences and their related properties, to analysis of population genetic data. Based on the asymptotic equipartition property (AEP) for nonstationary discrete-time sources producing independent symbols, we introduce the concepts of typical genotypes and population entropy and cross entropy rate. We analyze three pers...

Typical Sequences for Polish Alphabets

The notion of typical sequences plays a key role in the theory of information. Central to the idea of typicality is that a sequence x1, x2, . . . , xn that is PX -typical should, loosely speaking, have an empirical distribution that is in some sense close to the distribution PX . The two most common notions of typicality are that of strong (letter) typicality and weak (entropy) typicality. Whil...

hoW tyPical are ‘tyPical’ tremor characteristics?

Backdoors To Typical Case Complexity

There has been significant recent progress in reasoning and constraint processing methods. In areas such as planning and finite model-checking, current solution techniques can handle combinatorial problems with up to a million variables and five million constraints. The good scaling behavior of these methods appears to defy what one would expect based on a worst-case complexity analysis. In ord...

Typical Worlds

Hugh Everett III presented pure wave mechanics, sometimes referred to as the many-worlds interpretation, as a solution to the quantum measurement problem. While pure wave mechanics is a deterministic physical theory with no probabilities, Everett sought to show how the theory might be understood as making the standard quantum statistical predictions as appearances to observers who were themselv...