scholarly journals Branching Densities of Cube-Free and Square-Free Words

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 126
Author(s):  
Elena A. Petrova ◽  
Arseny M. Shur
Keyword(s):  
Lower Bound ◽  
Wide Class ◽  
Binary Tree ◽  
Search Algorithm ◽  
Numerical Results ◽  
Maximal Density ◽  
Efficient Search ◽  
Branching Points ◽  
Free Language

Binary cube-free language and ternary square-free language are two “canonical” representatives of a wide class of languages defined by avoidance properties. Each of these two languages can be viewed as an infinite binary tree reflecting the prefix order of its elements. We study how “homogenious” these trees are, analysing the following parameter: the density of branching nodes along infinite paths. We present combinatorial results and an efficient search algorithm, which together allowed us to get the following numerical results for the cube-free language: the minimal density of branching points is between 3509/9120≈0.38476 and 13/29≈0.44828, and the maximal density is between 0.72 and 67/93≈0.72043. We also prove the lower bound 223/868≈0.25691 on the density of branching points in the tree of the ternary square-free language.

scholarly journals General decay rate of a weakly dissipative viscoelastic equation with a general damping

2020 ◽  
Vol 40 (6) ◽  
pp. 647-666
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Wide Class ◽  
Nonlinear Damping ◽  
Numerical Results ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Viscoelastic Equation

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

scholarly journals A Unifying View on Individual Bounds and Heuristic Inaccuracies in Bidirectional Search

2020 ◽  
Vol 34 (03) ◽  
pp. 2327-2334
Author(s):  
Vidal Alcázar ◽  
Pat Riddle ◽  
Mike Barley
Keyword(s):  
Lower Bound ◽  
Heuristic Search ◽  
Search Algorithm ◽  
Substantial Improvement ◽  
Full Potential ◽  
The Past ◽  
Heuristic Search Algorithms ◽  
Bidirectional Search ◽  
Order Of Magnitude ◽  
The Cost

In the past few years, new very successful bidirectional heuristic search algorithms have been proposed. Their key novelty is a lower bound on the cost of a solution that includes information from the g values in both directions. Kaindl and Kainz (1997) proposed measuring how inaccurate a heuristic is while expanding nodes in the opposite direction, and using this information to raise the f value of the evaluated nodes. However, this comes with a set of disadvantages and remains yet to be exploited to its full potential. Additionally, Sadhukhan (2013) presented BAE∗, a bidirectional best-first search algorithm based on the accumulated heuristic inaccuracy along a path. However, no complete comparison in regards to other bidirectional algorithms has yet been done, neither theoretical nor empirical. In this paper we define individual bounds within the lower-bound framework and show how both Kaindl and Kainz's and Sadhukhan's methods can be generalized thus creating new bounds. This overcomes previous shortcomings and allows newer algorithms to benefit from these techniques as well. Experimental results show a substantial improvement, up to an order of magnitude in the number of necessarily-expanded nodes compared to state-of-the-art near-optimal algorithms in common benchmarks.

scholarly journals Design of a Labeling Scheme for 32-QAM Delayed Bit-Interleaved Coded Modulation

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3528
Author(s):  
Zhe Zhang ◽  
Liang Zhou ◽  
Junyi Du ◽  
Yue Zhao
Keyword(s):  
Channel Capacity ◽  
Time Slot ◽  
Search Algorithm ◽  
Search Space ◽  
Coded Modulation ◽  
Numerical Results ◽  
Information Rate ◽  
Labeling Schemes ◽  
Labeling Scheme ◽  
Bit Interleaved Coded Modulation

It is very challenging to design the capacity-approaching labeling schemes for large constellations, such as 32-QAM, in delayed bit-interleaved coded modulation (DBICM). In this paper, we investigate the labeling design for 32-QAM DBICM with various numbers of bits delayed by one time slot. In particular, we aim to obtain the labeling schemes with a high DBICM channel capacity by searching the possible labeling schemes. To reduce the search space of the candidate labeling schemes, we propose the criteria that are necessary for good labeling. Based on the proposed criteria, a three-step search algorithm is proposed to obtain the candidate labeling efficiently. Numerical results demonstrate that the DBICM with our proposed labeling scheme can approach the capacity of 32-QAM within 0.015 dB at an information rate greater than 2.5 bits/symbol.

BIFURCATION STRUCTURE OF SCALAR DIFFERENTIAL DELAYED EQUATIONS

1991 ◽  
Vol 01 (03) ◽  
pp. 657-665 ◽  
Author(s):  
C. P. MALTA ◽  
C. GROTTA RAGAZZO
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Negative Feedback ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Feedback Condition ◽  
Numerical Results ◽  
The Other ◽  
Bifurcation Structure ◽  
Dominant Frequencies

We study periodic solutions of the equation [Formula: see text], with f(X) given by f1(X) = AX(1 − X) or f2(X) = πµ (1 − sin X), grouped in some sets characterized by different dominant frequencies. Numerical results with f(X) = f1(X) are given. One of these sets is shown to exhibit period-doubling cascade in the direction of both parameters A and τ. The other sets are shown to exhibit many other period-doubling cascades as τ is varied establishing a relation between the bifurcation structure within the sets. Furthermore we obtain a lower bound on A and µ for the existence of more complex dynamics. We conjecture that this fact is related to the violation of the so-called "negative-feedback condition."

An Evolution Model for Monte Carlo Estimation of Equilibrium Network Renewal Parameters

1992 ◽  
Vol 6 (4) ◽  
pp. 457-469 ◽  
Author(s):  
T. Elperin ◽  
I. Gertsbakh ◽  
M. Lomonosov
Keyword(s):  
Monte Carlo ◽  
Wide Class ◽  
Numerical Results ◽  
Evolution Model ◽  
Main Difficulty ◽  
Monte Carlo Techniques ◽  
Border States ◽  
Low Probability ◽  
Monte Carlo Estimation ◽  
Operational Criteria

This paper presents Monte Carlo techniques for evaluating equilibrium availability and mean up and down periods of a renewable network for a wide class of network operational criteria. The suggested method is based on a graph evolution model that overcomes the main difficulty–hitting low-probability “border” states of the criterion. Theoretical efficiency of the method is briefly discussed and numerical results are presented.

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