scholarly journals Characterization of sets of limit measures of a cellular automaton iterated on a random configuration

2016 ◽  
Vol 38 (2) ◽  
pp. 601-650
Author(s):  
BENJAMIN HELLOUIN DE MENIBUS ◽  
MATHIEU SABLIK
Keyword(s):  
Cellular Automaton ◽  
Additional Hypothesis ◽  
Topological Constraints ◽  
Mean Convergence ◽  
Similar Characterization ◽  
Limit Points ◽  
Limit Probability ◽  
Initial Measure ◽  
Random Configuration

The asymptotic behaviour of a cellular automaton iterated on a random configuration is well described by its limit probability measure(s). In this paper, we characterize measures and sets of measures that can be reached as limit points after iterating a cellular automaton on a simple initial measure. In addition to classical topological constraints, we exhibit necessary computational obstructions. With an additional hypothesis of connectivity, we show these computability conditions are sufficient by constructing a cellular automaton realizing these sets, using auxiliary states in order to perform computations. Adapting this construction, we obtain a similar characterization for the Cesàro mean convergence, a Rice theorem on the sets of limit points, and we are able to perform computation on the set of measures, i.e. the cellular automaton converges towards a set of limit points that depends on the initial measure. Last, under non-surjective hypotheses, it is possible to remove auxiliary states from the construction.

scholarly journals A characterization of the weighted version of McEliece–Rodemich–Rumsey–Schrijver number based on convex quadratic programming

2015 ◽  
Vol 07 (04) ◽  
pp. 1550050
Author(s):  
Carlos J. Luz
Keyword(s):  
Quadratic Programming ◽  
Discrete Math ◽  
Convex Quadratic Programming ◽  
Stability Number ◽  
Weighted Version ◽  
Similar Characterization ◽  
Number Formula ◽  
Weighted Stability ◽  
Theta Number

For any graph [Formula: see text] Luz and Schrijver [A convex quadratic characterization of the Lovász theta number, SIAM J. Discrete Math. 19(2) (2005) 382–387] introduced a characterization of the Lovász number [Formula: see text] based on convex quadratic programming. A similar characterization is now established for the weighted version of the number [Formula: see text] independently introduced by McEliece, Rodemich, and Rumsey [The Lovász bound and some generalizations, J. Combin. Inform. Syst. Sci. 3 (1978) 134–152] and Schrijver [A Comparison of the Delsarte and Lovász bounds, IEEE Trans. Inform. Theory 25(4) (1979) 425–429]. Also, a class of graphs for which the weighted version of [Formula: see text] coincides with the weighted stability number is characterized.

scholarly journals Sequentializing cellular automata

2019 ◽  
Vol 19 (4) ◽  
pp. 759-772 ◽  
Author(s):  
Jarkko Kari ◽  
Ville Salo ◽  
Thomas Worsch
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Intermediate States ◽  
The Right

Abstract We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be written as a single sweep of a bijective rule from left to right over an infinite tape. Such cellular automata are necessarily left-closing, and they move at least as much information to the left as they move information to the right.

scholarly journals Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Pabitra Pal Choudhury ◽  
Sudhakar Sahoo ◽  
Mithun Chakraborty
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Boolean Functions ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
One Dimensional ◽  
State Transition Diagram ◽  
Linear Rule

Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.

scholarly journals A CHARACTERIZATION OF THE SET Ω (f)\ ω (f) FOR CONTINUOUS MAPS OF THE INTERVAL WITH ZERO TOPOLOGICAL ENTROPY

1995 ◽  
Vol 05 (05) ◽  
pp. 1433-1435
Author(s):  
F. BALIBREA ◽  
J. SMÍTAL
Keyword(s):  
Topological Entropy ◽  
Minimal Set ◽  
Continuous Map ◽  
Continuous Maps ◽  
Limit Points ◽  
Infinite Set ◽  
Nonwandering Points

We give a characterization of the set of nonwandering points of a continuous map f of the interval with zero topological entropy, attracted to a single (infinite) minimal set Q. We show that such a map f can have a unique infinite minimal set Q and an infinite set B ⊂ Ω (f)\ ω (f) (of nonwandering points that are not ω-limit points) attracted to Q and such that B has infinite intersections with infinitely many disjoint orbits of f.

Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups

1987 ◽  
Vol 102 (2) ◽  
pp. 251-257 ◽  
Author(s):  
C. MacLachlan ◽  
A. W. Reid
Keyword(s):  
Kleinian Groups ◽  
Fuchsian Groups ◽  
Arithmetic Groups ◽  
Quaternion Algebras ◽  
Isomorphism Classes ◽  
Similar Characterization ◽  
One To One

Arithmetic Fuchsian and Kleinian groups can all be obtained from quaternion algebras (see [2,12]). In a series of papers ([8,9,10,11]), Takeuchi investigated and characterized arithmetic Fuchsian groups among all Fuchsian groups of finite covolume, in terms of the traces of the elements in the group. His methods are readily adaptable to Kleinian groups, and we obtain a similar characterization of arithmetic Kleinian groups in §3. Commensurability classes of Kleinian groups of finite co-volume are discussed in [2] and it is shown there that the arithmetic groups can be characterized as those having dense commensurability subgroup. Here the wide commensurability classes of arithmetic Kleinian groups are shown to be approximately in one-to-one correspondence with the isomorphism classes of the corresponding quaternion algebras (Theorem 2) and it easily follows that there are infinitely many wide commensurability classes of cocompact Kleinian groups, and hence of compact hyperbolic 3-manifolds.

Improved detection of motifs with preferential location in promoters

Genome ◽  
2010 ◽  
Vol 53 (9) ◽  
pp. 739-752 ◽  
Author(s):  
Virginie Bernard ◽  
Alain Lecharny ◽  
Véronique Brunaud
Keyword(s):  
In Silico ◽  
Gene Expression Regulation ◽  
Window Size ◽  
Sliding Window ◽  
In Silico Prediction ◽  
Distribution Profile ◽  
Topological Constraints ◽  
Automatic Adaptation ◽  
Preferential Location

Many transcription factor binding sites (TFBSs) involved in gene expression regulation are preferentially located relative to the transcription start site. This property is exploited in in silico prediction approaches, one of which involves studying the local overrepresentation of motifs using a sliding window to scan promoters with considerable accuracy. Nevertheless, the consequences of the choice of the sliding window size have never before been analysed. We propose an automatic adaptation of this size to each motif distribution profile. This approach allows a better characterization of the topological constraints of the motifs and the lists of genes containing them. Moreover, our approach allowed us to highlight a nonconstant frequency of occurrence of spurious motifs that could be counter-selected close to their functional area. Therefore, to improve the accuracy of in silico prediction of TFBSs and the sensitivity of the promoter cartography, we propose, in addition to automatic adaptation of window size, consideration of the nonconstant frequency of motifs in promoters.

The third and fourth pluricanonical maps of threefolds of general type

2014 ◽  
Vol 157 (2) ◽  
pp. 209-220
Author(s):  
JINSONG XU
Keyword(s):  
General Type ◽  
Complex Numbers ◽  
The Third ◽  
Similar Characterization ◽  
Pluricanonical Maps

AbstractFor a nonsingular projective threefold of general typeXover the field of complex numbers, we show that the fourth pluricanonical map ϕ4is not birational onto its image if and only ifXis birationally fibred by (1,2)-surfaces, provided that vol(X) ≥ 303. We also have similar characterization of birationality of ϕ3.

scholarly journals An Extension of Panjer's Recursion

2002 ◽  
Vol 32 (2) ◽  
pp. 283-297 ◽  
Author(s):  
Klaus Th. Hess ◽  
Anett Liewald ◽  
Klaus D. Schmidt
Keyword(s):  
Size Distribution ◽  
Collective Model ◽  
Risk Theory ◽  
Claim Size ◽  
Similar Characterization ◽  
Claim Number ◽  
Claim Size Distribution ◽  
Aggregate Claims ◽  
Image Position

AbstractSundt and Jewell have shown that a nondegenerate claim number distribution Q = {qn}nϵN0 satisfies the recursionfor all n≥0 if and only if Q is a binomial, Poisson or negativebinomial distribution. This recursion is of interest since it yields a recursion for the aggregate claims distribution in the collective model of risk theory when the claim size distribution is integer-valued as well. A similar characterization of claim number distributions satisfying the above recursion for all n ≥ 1 has been obtained by Willmot. In the present paper we extend these results and the subsequent recursion for the aggregate claims distribution to the case where the recursion holds for all n ≥ k with arbitrary k. Our results are of interest in catastrophe excess-of-loss reinsurance.

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