On Runs in Independent Sequences
author
Abstract:
Given an i.i.d. sequence of n letters from a finite alphabet, we consider the length of the longest run of any letter. In the equiprobable case, results for this run turn out to be closely related to the well-known results for the longest run of a given letter. For coin-tossing, tail probabilities are compared for both kinds of runs via Poisson approximation.
similar resources
A Further Note on Runs in Independent Sequences
Given a sequence of letters generated independently from a finite alphabet, we consider the case when more than one, but not all, letters are generated with the highest probability. The length of the longest run of any of these letters is shown to be one greater than the length of the longest run in a particular state of an associated Markov chain. Using results of Foulser and Karlin (19...
full textComplexity of VC-classes of sequences with long repetitive runs
The Vapnik-Chervonenkis (VC) dimension (also known as the trace number) and the Sauer-Shelah lemma have found applications in numerous areas including set theory, combinatorial geometry, graph theory and statistical learning theory. Estimation of the complexity of discrete structures associated with the search space of algorithms often amounts to estimating the cardinality of a simpler class wh...
full textAlgorithmically Independent Sequences
Two objects are independent if they do not affect each other. Independence is wellunderstood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper proposes two types of independence for arbitrary infinite binary sequences and studies their properties. Our two proposed notions of independence have some o...
full textNeuroscience Runs on GNU/Linux
1 Center for Cognitive Neuroscience, Dartmouth College, Hanover, NH, USA 2 Department of Psychological and Brain Sciences, Dartmouth College, Hanover, NH, USA 3 Department of Experimental Psychology, University of Magdeburg, Magdeburg, Germany *Correspondence: [email protected]; [email protected] †Michael Hanke and Yaroslav O. Halchenko have contributed equally to this a...
full textWhen Short Runs Beat Long Runs
What will yield the best results: doing one run n generations long or doing m runs n/m generations long each? This paper presents a techniqueindependent analysis which answers this question, and has direct applicability to scheduling and restart theory in evolutionary computation and other stochastic methods. The paper then applies this technique to three problem domains in genetic programming....
full textGenetic instability within monotonous runs of CpG sequences in Escherichia coli.
Genetic information can be altered by base substitutions, frameshift mutations, and addition or deletion of nucleotides. Deletions represent an important class of genetic aberration occurring at DNA sequences where it is often possible to predict the existence of intermediates of mutation. Instability within tracts of repetitive sequence have recently been associated with several genetic disord...
full textMy Resources
Journal title
volume 2 issue None
pages 43- 52
publication date 2003-03
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023