Polynomial Entropy of the Logistic Map

2021 ◽  
Vol 58 (2) ◽  
pp. 206-215
Author(s):  
Milan Perić
Keyword(s):  
Topological Entropy ◽  
Logistic Map ◽  
Low Complexity ◽  
Almost All

We study the polynomial entropy of the logistic map depending on a parameter, and we calculate it for almost all values of the parameter. We show that polynomial entropy distinguishes systems with a low complexity (i.e. for which the topological entropy vanishes).

scholarly journals The hourglass effect in hierarchical dependency networks

2017 ◽  
Vol 5 (4) ◽  
pp. 490-528 ◽  
Author(s):  
KAESER M. SABRIN ◽  
CONSTANTINE DOVROLIS
Keyword(s):  
Low Complexity ◽  
Core Size ◽  
Original Network ◽  
Hierarchical Network ◽  
Modular Systems ◽  
The Core ◽  
Dependency Networks ◽  
Dependency Network ◽  
Hierarchical Dependency ◽  
Almost All

AbstractMany hierarchically modular systems are structured in a way that resembles an hourglass. This “hourglass effect” means that the system generates many outputs from many inputs through a relatively small number of intermediate modules that are critical for the operation of the entire system, referred to as the waist of the hourglass. We investigate the hourglass effect in general, not necessarily layered, hierarchical dependency networks. Our analysis focuses on the number of source-to-target dependency paths that traverse each vertex, and it identifies the core of a dependency network as the smallest set of vertices that collectively cover almost all dependency paths. We then examine if a given network exhibits the hourglass property or not, comparing its core size with a “flat” (i.e., non-hierarchical) network that preserves the source dependencies of each target in the original network. As a possible explanation for the hourglass effect, we propose the Reuse Preference model that captures the bias of new modules to reuse intermediate modules of similar complexity instead of connecting directly to sources or low complexity modules. We have applied the proposed framework in a diverse set of dependency networks from technological, natural, and information systems, showing that all these networks exhibit the general hourglass property but to a varying degree and with different waist characteristics.

scholarly journals The Dynamics of a Four-Step Feedback Procedure to Control Chaos

2021 ◽  
Author(s):  
Jose S. Cánovas
Keyword(s):  
Topological Entropy ◽  
Dynamical Behavior ◽  
Logistic Map ◽  
Simple Complex ◽  
Step Procedure ◽  
Parrondo’S Paradox

Abstract In this paper we make a description of the dynamics of a four-step procedure to control the dynamics of the logistic map. Some massive calculations are made for computing the topological entropy with prescribed accuracy. This provides us the parameter regions where the model has a complicated dynamical behavior. Our computations also show the dynamic Parrondo's paradox ``simple+simple=complex'', which should be taking into account to avoid undesirable dynamics.

scholarly journals Computational Genomics of RELA gene of Pig and its protein prescription

2020 ◽  
Vol 45 (1) ◽  
pp. 9-17
Author(s):  
O. O. Oluwole
Keyword(s):  
Protein Structure ◽  
Guinea Pig ◽  
Mammalian Species ◽  
Domain Architecture ◽  
Low Complexity ◽  
Rna Recognition Motif ◽  
Rna Recognition ◽  
Starting Point ◽  
Almost All ◽  
Relationship Of

RELA gene is a pleiotropic transcription that is present in almost all living cells where several signal transduction events end points were initiated by many arrays of stimuli that were related to many biological processes such as inflammation, immunity, differentiation, cell growth, tumorigenesis and apoptosis in the cells. The nucleotide and amino acid sequence (AAS) of RELA gene of pig and other mammalian species were downloaded from the National Center for Biotechnology information (NCBI) data base, United State of America and Universal protein resources (Uniprot) database, United Kingdom. Data generated were analyzed by bioinformatics tools. The results showed a high variation of AAS among the mammals where only four mammals have the same AAS length (551) with pig while others were not. The RELA gene of pig shared very high percent identity with all mammals ranging from 95.5% (warthog) to 83.5% (guinea pig) and similarity percentage ranged from 85.1 to 99.5% where the warthog had the highest percentage value while the least mammal was Guinea pig. The tree showed RELA gene with two clades; the first for mammals and the second for non-mammals. The RELA gene of pig was in the same cluster with the other Suidae family, warthog and babirusa. For the protein structure obtained, only 43% can be meaningfully predicted from the 61% residues modelled at more than 90%. The domain architecture of RELA protein structure contained mainly RNA Recognition motif and region of low complexity. The domainstarting position of all the organisms ranged from 191 to 210 while the termination of all the mammals ranged from 102 to 306 amino acids.The region of low complexity starting point ranged from position 173 to 462while termination positions ranged from 184 to 474. The evolution relationship of RELA gene of pig and other mammalian species were highly related and conserved among the mammalian species; they have high comparability and they evolved from common ancestors.  

scholarly journals Low complexity algorithms in knot theory

2019 ◽  
Vol 29 (02) ◽  
pp. 245-262
Author(s):  
Olga Kharlampovich ◽  
Alina Vdovina
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Linear Time ◽  
Circuit Complexity ◽  
Equivalence Problem ◽  
Low Complexity ◽  
Combinatorial Structure ◽  
Complexity Classes ◽  
Np Complete ◽  
Almost All

Agol, Haas and Thurston showed that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. This shows that (unless P[Formula: see text]NP) the genus problem has high computational complexity even for knots in a 3-manifold. We initiate the study of classes of knots where the genus problem and even the equivalence problem have very low computational complexity. We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace[Formula: see text]. Alternating knots with some additional combinatorial structure will be referred to as standard. As expected, almost all alternating knots of a given genus are standard. We show that the genus problem for these knots belongs to [Formula: see text] circuit complexity class. We also show, that the equivalence problem for such knots with [Formula: see text] crossings has time complexity [Formula: see text] and is in Logspace[Formula: see text] and [Formula: see text] complexity classes.

Advanced Space-Time Block Codes and Low Complexity Near Optimal Detection for Future Wireless Networks

2009 ◽  
pp. 107-129
Author(s):  
W. H. Chin ◽  
C. Yuen
Keyword(s):  
Maximum Likelihood ◽  
Low Complexity ◽  
Block Codes ◽  
Space Time ◽  
Time Block ◽  
Block Coding ◽  
Detection Algorithms ◽  
Space Time Block Codes ◽  
Space Time Block Coding ◽  
Almost All

Space-time block coding is a way of introducing multiplexing and diversity gain in wireless systems equipped with multiple antennas. There are several classes of codes tailored for different channel conditions. However, in almost all the cases, maximum likelihood detection is required to fully realize the diversity introduced. In this chapter, we present the fundamentals of space-time block coding, as well as introduce new codes with better performance. Additionally, we introduce the basic detection algorithms which can be used for detecting space-time block codes. Several low complexity pseudo-maximum likelihood algorithms will also be introduced and discussed.

scholarly journals Superconvergence of topological entropy in the symbolic dynamics of substitution sequences

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Leon Zaporski ◽  
Felix Flicker
Keyword(s):  
Topological Entropy ◽  
Symbolic Dynamics ◽  
Convergence Rates ◽  
Nonlinear Dynamical Systems ◽  
Logistic Map ◽  
Universality Class ◽  
Accumulation Point ◽  
Nonlinear Dynamical ◽  
Double Exponential ◽  
Symbolic Sequences

We consider infinite sequences of superstable orbits (cascades) generated by systematic substitutions of letters in the symbolic dynamics of one-dimensional nonlinear systems in the logistic map universality class. We identify the conditions under which the topological entropy of successive words converges as a double exponential onto the accumulation point, and find the convergence rates analytically for selected cascades. Numerical tests of the convergence of the control parameter reveal a tendency to quantitatively universal double-exponential convergence. Taking a specific physical example, we consider cascades of stable orbits described by symbolic sequences with the symmetries of quasilattices. We show that all quasilattices can be realised as stable trajectories in nonlinear dynamical systems, extending previous results in which two were identified.

scholarly journals Knowledge Graph Representation via Similarity-Based Embedding

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Zhen Tan ◽  
Xiang Zhao ◽  
Yang Fang ◽  
Bin Ge ◽  
Weidong Xiao
Keyword(s):  
Large Scale ◽  
Low Complexity ◽  
Graph Representation ◽  
Knowledge Graph ◽  
Continuous Space ◽  
Memory Space ◽  
Representation Method ◽  
Relation Prediction ◽  
Low Dimensional ◽  
Almost All

Knowledge graph, a typical multi-relational structure, includes large-scale facts of the world, yet it is still far away from completeness. Knowledge graph embedding, as a representation method, constructs a low-dimensional and continuous space to describe the latent semantic information and predict the missing facts. Among various solutions, almost all embedding models have high time and memory-space complexities and, hence, are difficult to apply to large-scale knowledge graphs. Some other embedding models, such as TransE and DistMult, although with lower complexity, ignore inherent features and only use correlations between different entities to represent the features of each entity. To overcome these shortcomings, we present a novel low-complexity embedding model, namely, SimE-ER, to calculate the similarity of entities in independent and associated spaces. In SimE-ER, each entity (relation) is described as two parts. The entity (relation) features in independent space are represented by the features entity (relation) intrinsically owns and, in associated space, the entity (relation) features are expressed by the entity (relation) features they connect. And the similarity between the embeddings of the same entities in different representation spaces is high. In experiments, we evaluate our model with two typical tasks: entity prediction and relation prediction. Compared with the state-of-the-art models, our experimental results demonstrate that SimE-ER outperforms existing competitors and has low time and memory-space complexities.

scholarly journals An Accurate Analytical Model for 802.11e EDCA under Different Traffic Conditions with Contention-Free Bursting

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Nada Chendeb Taher ◽  
Yacine Ghamri-Doudane ◽  
Bachar El Hassan ◽  
Nazim Agoulmine
Keyword(s):  
Analytical Model ◽  
Low Complexity ◽  
Analytical Models ◽  
Ieee 802.11E ◽  
Time Interval ◽  
Control Procedure ◽  
Traffic Conditions ◽  
Proposed Model ◽  
Transmission Opportunity ◽  
Almost All

Extensive research addressing IEEE 802.11e enhanced distributed channel access (EDCA) performance analysis, by means of analytical models, exist in the literature. Unfortunately, the currently proposed models, even though numerous, do not reach this accuracy due to the great number of simplifications that have been done. Particularly, none of these models considers the 802.11e contention free burst (CFB) mode which allows a given station to transmit a burst of frames without contention during a given transmission opportunity limit (TXOPLimit) time interval. Despite its influence on the global performance, TXOPLimit is ignored in almost all existing models. To fill in this gap, we develop in this paper a new and complete analytical model that (i) reflects the correct functioning of EDCA, (ii) includes all the 802.11e EDCA differentiation parameters, (iii) takes into account all the features of the protocol, and (iv) can be applied to all network conditions, going from nonsaturation to saturation conditions. Additionally, this model is developed in order to be used in admission control procedure, so it was designed to have a low complexity and an acceptable response time. The proposed model is validated by means of both calculations and extensive simulations.

A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

2017 ◽  
Vol 27 (07) ◽  
pp. 1750103 ◽  
Author(s):  
Lingfeng Liu ◽  
Jun Lin ◽  
Suoxia Miao ◽  
Bocheng Liu
Keyword(s):  
Perturbation Method ◽  
Image Encryption ◽  
Chaotic Map ◽  
Logistic Map ◽  
Simple Algorithm ◽  
Low Complexity ◽  
State Variables ◽  
Dynamical Degradation ◽  
Precision Device ◽  
Baker Map

The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.

scholarly journals MINIMAL GEODESIC FOLIATION ON T2 IN CASE OF VANISHING TOPOLOGICAL ENTROPY

2011 ◽  
Vol 03 (04) ◽  
pp. 511-520 ◽  
Author(s):  
EVA GLASMACHERS ◽  
GERHARD KNIEPER
Keyword(s):  
Topological Entropy ◽  
Rotation Number ◽  
Geodesic Flow ◽  
Universal Cover ◽  
Low Complexity ◽  
Asymptotic Direction ◽  
Geodesic Foliation ◽  
Minimal Geodesic

On a Riemannian 2-torus (T2, g) we study the geodesic flow in the case of low complexity described by zero topological entropy. We show that this assumption implies a nearly integrable behavior. In our previous paper [12] we already obtained that the asymptotic direction and therefore also the rotation number exists for all geodesics. In this paper we show that for all r ∈ ℝ ∪ {∞} the universal cover ℝ2 is foliated by minimal geodesics of rotation number r. For irrational r ∈ ℝ all geodesics are minimal, for rational r ∈ ℝ ∪ {∞} all geodesics stay in strips between neighboring minimal axes. In such a strip the minimal geodesics are asymptotic to the neighboring minimal axes and generate two foliations.

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