scholarly journals Negative bases and automata

2011 ◽  
Vol Vol. 13 no. 1 (Automata, Logic and Semantics) ◽  
Author(s):  
Christiane Frougny ◽  
Anna Chiara Lai
Keyword(s):  
Finite Type ◽  
Pisot Number ◽  
Sofic System ◽  
Finite Transducer ◽  
International Audience ◽  
On Line ◽  
Negative Base

Automata, Logic and Semantics International audience We study expansions in non-integer negative base -beta introduced by Ito and Sadahiro. Using countable automata associated with (-beta)-expansions, we characterize the case where the (-beta)-shift is a system of finite type. We prove that, if beta is a Pisot number, then the (-beta)-shift is a sofic system. In that case, addition (and more generally normalization on any alphabet) is realizable by a finite transducer. We then give an on-line algorithm for the conversion from positive base beta to negative base -beta. When beta is a Pisot number, the conversion can be realized by a finite on-line transducer.

scholarly journals Local Dimensions of Measures of Finite Type II: Measures Without Full Support and With Non-regular Probabilities

2018 ◽  
Vol 70 (4) ◽  
pp. 824-867 ◽  
Author(s):  
Kathryn E. Hare ◽  
Kevin G. Hare ◽  
Michael Ka Shing Ng
Keyword(s):  
Finite Type ◽  
Hausdorff Measure ◽  
Finite Sequence ◽  
Pisot Number ◽  
Local Dimension ◽  
Bernoulli Convolution ◽  
Similar Measure ◽  
Absolutely Continuous ◽  
Contraction Ratio ◽  
Isolated Point

AbstractConsider a finite sequence of linear contractions Sj(x) = px + dj and probabilities pj > 0 with ∑Pj = 1. We are interested in the self-similar measure , of finite type. In this paper we study the multi-fractal analysis of such measures, extending the theory to measures arising from non-regular probabilities and whose support is not necessarily an interval.Under some mild technical assumptions, we prove that there exists a subset of supp μ of full μ and Hausdorff measure, called the truly essential class, for which the set of (upper or lower) local dimensions is a closed interval. Within the truly essential class we show that there exists a point with local dimension exactly equal to the dimension of the support. We give an example where the set of local dimensions is a two element set, with all the elements of the truly essential class giving the same local dimension. We give general criteria for these measures to be absolutely continuous with respect to the associated Hausdorff measure of their support, and we show that the dimension of the support can be computed using only information about the essential class.To conclude, we present a detailed study of three examples. First, we show that the set of local dimensions of the biased Bernoulli convolution with contraction ratio the inverse of a simple Pisot number always admits an isolated point. We give a precise description of the essential class of a generalized Cantor set of finite type, and show that the k-th convolution of the associated Cantor measure has local dimension at x ∊ (0,1) tending to 1 as ft: tends to infinity. Lastly, we show that within a maximal loop class that is not truly essential, the set of upper local dimensions need not be an interval. This is in contrast to the case for finite type measures with regular probabilities and full interval support.

scholarly journals Analysis of an algorithm catching elephants on the Internet

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Yousra Chabchoub ◽  
Christine Fricker ◽  
Frédéric Meunier ◽  
Danielle Tibi
Keyword(s):  
Asymptotic Behavior ◽  
Markov Chain ◽  
Stochastic Model ◽  
Limit Theorems ◽  
Bloom Filter ◽  
Simplified Model ◽  
The Internet ◽  
Huge Amount ◽  
International Audience ◽  
On Line

International audience The paper deals with the problem of catching the elephants in the Internet traffic. The aim is to investigate an algorithm proposed by Azzana based on a multistage Bloom filter, with a refreshment mechanism (called $\textit{shift}$ in the present paper), able to treat on-line a huge amount of flows with high traffic variations. An analysis of a simplified model estimates the number of false positives. Limit theorems for the Markov chain that describes the algorithm for large filters are rigorously obtained. The asymptotic behavior of the stochastic model is here deterministic. The limit has a nice formulation in terms of a $M/G/1/C$ queue, which is analytically tractable and which allows to tune the algorithm optimally.

scholarly journals Projective subdynamics and universal shifts

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Pierre Guillon
Keyword(s):  
Large Class ◽  
Finite Type ◽  
Positive Entropy ◽  
Two Dimensional ◽  
One Dimensional ◽  
International Audience

International audience We study the projective subdynamics of two-dimensional shifts of finite type, which is the set of one-dimensional configurations that appear as columns in them. We prove that a large class of one-dimensional shifts can be obtained as such, namely the effective subshifts which contain positive-entropy sofic subshifts. The proof involves some simple notions of simulation that may be of interest for other constructions. As an example, it allows us to prove the undecidability of all non-trivial properties of projective subdynamics.

scholarly journals On-line Adaptive Chain Covering of Upgrowing Posets

2005 ◽  
Vol DMTCS Proceedings vol. AF,... (Proceedings) ◽  
Author(s):  
Bartłomiej Bosek ◽  
Piotr Micek
Keyword(s):  
The Other ◽  
International Audience ◽  
On Line ◽  
Partitioning Problem ◽  
A Chain ◽  
The Moment ◽  
Person Game

International audience We analyze on-line chain partitioning problem and its variants as a two-person game. One person (Spoiler) builds an on-line poset presenting one point at time. The other one (Algorithm) assigns new point to a chain. Kierstead gave a strategy for Algorithm showing that width w posets can be on-line chain partitioned into $\frac{{5}^{w-1}}{4}$ chains. Felsner proved that if Spoiler presents an upgrowing poset, i.e., each new point is maximal at the moment of its arrival then there is a strategy for Algorithm using at most $\binom{w+1}{2}$ chains and it is best possible. An adaptive variant of this problem allows Algorithm to assign to the new point a set of chains and than to remove some of them (but not all) while covering next points. Felsner stated a hypothesis that in on-line adaptive chain covering of upgrowing posets Algorithm may use smaller number of chains than in non-adaptive version. In this paper we provide an argument suggesting that it is true. We present a class of upgrowing posets in which Spoiler has a strategy forcing Algorithm to use at least $\binom{w+1}{2}$ chains (in non-adaptive version) and Algorithm has a strategy using at most $O(w\sqrt{w})$ chains in adaptive version.

scholarly journals A sofic system which is not spectrally of finite type

1988 ◽  
Vol 8 (3) ◽  
pp. 483-490 ◽  
Author(s):  
Susan Williams
Keyword(s):  
Finite Type ◽  
Subshift Of Finite Type ◽  
The Core ◽  
Sofic System ◽  
Core Matrix

AbstractWe exhibit a transitive sofic system for which the core matrix has negative trace, and hence cannot share the nonzero spectrum of any subshift of finite type cover. We also show that every transitive sofic system has an integral core matrix.

scholarly journals A generalization of the carries process

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Takahiko Fujita ◽  
Fumihiko Nakano ◽  
Taizo Sadahiro
Keyword(s):  
Representation Theory ◽  
Transition Probability ◽  
Eigenvalues And Eigenvectors ◽  
International Audience ◽  
Transition Probability Matrices ◽  
Probability Matrices ◽  
Negative Base

International audience We consider a carries process which is a generalization of that by Holte in the sense that (i) we take various digit sets, and (ii) we also consider negative base. Our results are : (i) eigenvalues and eigenvectors of the transition probability matrices, and their connection to combinatorics and representation theory, (ii) an application to the computation of the distribution of the sum of i.i.d. uniform r.v.'s on [0,1], (iii) a relation to riffle shuffle.

scholarly journals Compatibility fans realizing graphical nested complexes

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Thibault Manneville ◽  
Vincent Pilaud
Keyword(s):  
Finite Type ◽  
Type B ◽  
Cluster Complexes ◽  
Explicit Constructions ◽  
International Audience ◽  
Connected Subgraphs ◽  
Generalized Associahedra

International audience Graph associahedra are polytopes realizing the nested complex N(G) on connected subgraphs of a graph G.While all known explicit constructions produce polytopes with the same normal fan, the great variety of fan realizationsof classical associahedra and the analogy between finite type cluster complexes and nested complexes incitedus to transpose S. Fomin and A. Zelevinsky's construction of compatibility fans for generalized associahedra (2003)to graph associahedra. Using a compatibility degree, we construct one fan realization of N(G) for each of its facets.Specifying G to paths and cycles, we recover a construction by F. Santos for classical associahedra (2011) and extendF. Chapoton, S. Fomin and A. Zelevinsky's construction (2002) for type B and C generalized associahedra.

scholarly journals A lower bound for approximating the Grundy number

2007 ◽  
Vol Vol. 9 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Guy Kortsarz
Keyword(s):  
Lower Bound ◽  
Grundy Number ◽  
International Audience ◽  
On Line

Graphs and Algorithms International audience The grundy numbering of a graph is the maximum number of colors used by on-line first-fit coloring, under the worst order of arrival of vertices. The grundy numbering problem is to find this ordering. We prove that there is a constant c>1 so that approximating the grundy numbering problem within c is not possible, unless NP ⊆ RP

The binding of fork head proteins to DNA is partly determined by cooperation of bases

2006 ◽  
Vol 1 (4) ◽  
pp. 594-608
Author(s):  
Václav Mach
Keyword(s):  
Transcription Factors ◽  
Dna Binding ◽  
Binding Sites ◽  
In Silico ◽  
Dna Recognition ◽  
Simple Algorithm ◽  
Fork Head ◽  
Statistical Algorithm ◽  
On Line ◽  
Negative Base

AbstractOur previous study revealed that DNA recognition by the insect Fork head transcription factors depends on specific combinations of neighboring bases, a phenomenon called the base cooperation effect. This study presents a simple algorithm designed for in silico investigation of the base cooperation effect. The algorithm measures and evaluates observed and expected frequencies of various base combinations within a set of aligned binding sites. Consequently, statistically significant differences between the observed and expected frequencies are interpreted as evidence of either positive or negative base cooperation effect. Our current results suggest that the base cooperation affects DNA binding of the vertebrate members of the Fork head family, similarly to their insect homologies.The statistical algorithm used in this study is available on line (http://blast.entu.cas.cz/bias/index.htm).

Sign in / Sign up

Export Citation Format

Share Document