On a variance associated with the distribution of general sequences in arithmetic progressions. I

1998 ◽  
Vol 356 (1738) ◽  
pp. 781-791 ◽  
Author(s):  
R.C. Vaughan
Keyword(s):  
Arithmetic Progressions ◽  
General Sequences

ALMOST ADDITIVE THERMODYNAMIC FORMALISM: SOME RECENT DEVELOPMENTS

2010 ◽  
Vol 22 (10) ◽  
pp. 1147-1179 ◽  
Author(s):  
LUIS BARREIRA
Keyword(s):  
Variational Principle ◽  
Existence And Uniqueness ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Topological Pressure ◽  
Present Stage ◽  
The Past ◽  
Recent Developments ◽  
General Sequences ◽  
Uniqueness Of Equilibrium

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning, for example, a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures (at least without further restrictive assumptions). On the other hand, in the case of almost additive sequences, it is possible to establish a variational principle and to discuss the existence and uniqueness of equilibrium and Gibbs measures, among several other results. After presenting in a self-contained manner the foundations of the theory, the survey includes the description of three applications of the almost additive thermodynamic formalism: a multifractal analysis of Lyapunov exponents for a class of nonconformal repellers; a conditional variational principle for limits of almost additive sequences; and the study of dimension spectra that consider simultaneously limits into the future and into the past.

scholarly journals Colorings with only rainbow arithmetic progressions

2020 ◽  
Vol 161 (2) ◽  
pp. 507-515
Author(s):  
J. Pach ◽  
I. Tomon
Keyword(s):  
Arithmetic Progressions

Frequent Closed Partial Orders Mining in Sequences

2013 ◽  
Vol 846-847 ◽  
pp. 1304-1307
Author(s):  
Ye Wang ◽  
Yan Jia ◽  
Lu Min Zhang
Keyword(s):  
Sequence Data ◽  
Real Data ◽  
Partial Orders ◽  
Hard Problem ◽  
Important Data ◽  
Data Set ◽  
Pruning Algorithm ◽  
Equal Chance ◽  
Np Hard Problem ◽  
General Sequences

Mining partial orders from sequence data is an important data mining task with broad applications. As partial orders mining is a NP-hard problem, many efficient pruning algorithm have been proposed. In this paper, we improve a classical algorithm of discovering frequent closed partial orders from string. For general sequences, we consider items appearing together having equal chance to calculate the detecting matrix used for pruning. Experimental evaluations from a real data set show that our algorithm can effectively mine FCPO from sequences.

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