scholarly journals Classification of Discrete Dynamical Systems Based on Transients

2021 ◽  
pp. 1-26
Author(s):  
Barbora Hudcová ◽  
Tomáš Mikolov
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Complex Dynamics ◽  
Computation Time ◽  
Boolean Networks ◽  
Random Boolean Networks ◽  
Average Computation Time ◽  
Design Systems ◽  
Computational Systems

Abstract In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Channon, 2006; Ofria & Wilke, 2004; Ray, 1991).

scholarly journals A neuro-inspired general framework for the evolution of stochastic dynamical systems: Cellular automata, random Boolean networks and echo state networks towards criticality

2020 ◽  
Vol 14 (5) ◽  
pp. 657-674
Author(s):  
Sidney Pontes-Filho ◽  
Pedro Lind ◽  
Anis Yazidi ◽  
Jianhua Zhang ◽  
Hugo Hammer ◽  
...  
Keyword(s):  
Deep Learning ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
General Framework ◽  
Dynamical Behavior ◽  
Boolean Networks ◽  
Stochastic Dynamical Systems ◽  
Random Boolean Networks ◽  
Echo State Networks ◽  
Computing Paradigm

Abstract Although deep learning has recently increased in popularity, it suffers from various problems including high computational complexity, energy greedy computation, and lack of scalability, to mention a few. In this paper, we investigate an alternative brain-inspired method for data analysis that circumvents the deep learning drawbacks by taking the actual dynamical behavior of biological neural networks into account. For this purpose, we develop a general framework for dynamical systems that can evolve and model a variety of substrates that possess computational capacity. Therefore, dynamical systems can be exploited in the reservoir computing paradigm, i.e., an untrained recurrent nonlinear network with a trained linear readout layer. Moreover, our general framework, called EvoDynamic, is based on an optimized deep neural network library. Hence, generalization and performance can be balanced. The EvoDynamic framework contains three kinds of dynamical systems already implemented, namely cellular automata, random Boolean networks, and echo state networks. The evolution of such systems towards a dynamical behavior, called criticality, is investigated because systems with such behavior may be better suited to do useful computation. The implemented dynamical systems are stochastic and their evolution with genetic algorithm mutates their update rules or network initialization. The obtained results are promising and demonstrate that criticality is achieved. In addition to the presented results, our framework can also be utilized to evolve the dynamical systems connectivity, update and learning rules to improve the quality of the reservoir used for solving computational tasks and physical substrate modeling.

Cellular Automata

2017 ◽  
Vol 29 (1) ◽  
pp. 42-50 ◽  
Author(s):  
Rupali Bhardwaj ◽  
Anil Upadhyay
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Empirical Study ◽  
Time Evolution ◽  
Discrete Dynamical Systems ◽  
The State ◽  
Dimensional Lattice ◽  
Elementary Cellular Automata

Cellular automata (CA) are discrete dynamical systems consist of a regular finite grid of cell; each cell encapsulating an equal portion of the state, and arranged spatially in a regular fashion to form an n-dimensional lattice. A cellular automata is like computers, data represented by initial configurations which is processed by time evolution to produce output. This paper is an empirical study of elementary cellular automata which includes concepts of rule equivalence, evolution of cellular automata and classification of cellular automata. In addition, explanation of behaviour of cellular automata is revealed through example.

ASYNCHRONOUS RANDOM BOOLEAN NETWORK MODEL WITH VARIABLE NUMBER OF PARENTS BASED ON ELEMENTARY CELLULAR AUTOMATA RULE 126

2006 ◽  
Vol 20 (08) ◽  
pp. 897-923 ◽  
Author(s):  
MIHAELA T. MATACHE
Keyword(s):  
Cellular Automata ◽  
Network Model ◽  
Boolean Network ◽  
Random Variable ◽  
Variable Number ◽  
Boolean Networks ◽  
Random Boolean Networks ◽  
Elementary Cellular Automata ◽  
Boolean Network Model ◽  
Point Analysis

A Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which can vary from one node to another, is considered. This is a generalization of previous results obtained for a constant number of parent nodes, by Matache and Heidel in "Asynchronous Random Boolean Network Model Based on Elementary Cellular Automata Rule 126", Phys. Rev. E71, 026 232, 2005. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. The Boolean rule is a generalization of rule 126 of elementary cellular automata, and is assumed to be the same for all the nodes. We provide a model for the probability of finding a node in state 1 at a time t for the class of generalized asynchronous random Boolean networks (GARBN) in which a random number of nodes can be updated at each time point. We generate consecutive states of the network for both the real system and the models under the various schemes, and use simulation algorithms to show that the results match well. We use the model to study the dynamics of the system through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the GARBN's dynamics range from order to chaos, depending on the type of random variable generating the asynchrony and the parameter combinations.

scholarly journals Random Networks with Quantum Boolean Functions

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 792 ◽  
Author(s):  
Mario Franco ◽  
Octavio Zapata ◽  
David A. Rosenblueth ◽  
Carlos Gershenson
Keyword(s):  
Boolean Functions ◽  
Boolean Network ◽  
Complex Dynamics ◽  
Boolean Networks ◽  
Stable Complex ◽  
Complex Dynamic ◽  
Random Boolean Networks ◽  
Quantum Simulator ◽  
Novel Model ◽  
Unstable Dynamics

We propose quantum Boolean networks, which can be classified as deterministic reversible asynchronous Boolean networks. This model is based on the previously developed concept of quantum Boolean functions. A quantum Boolean network is a Boolean network where the functions associated with the nodes are quantum Boolean functions. We study some properties of this novel model and, using a quantum simulator, we study how the dynamics change in function of connectivity of the network and the set of operators we allow. For some configurations, this model resembles the behavior of reversible Boolean networks, while for other configurations a more complex dynamic can emerge. For example, cycles larger than 2N were observed. Additionally, using a scheme akin to one used previously with random Boolean networks, we computed the average entropy and complexity of the networks. As opposed to classic random Boolean networks, where “complex” dynamics are restricted mainly to a connectivity close to a phase transition, quantum Boolean networks can exhibit stable, complex, and unstable dynamics independently of their connectivity.

scholarly journals Effects of Antimodularity and Multiscale Influence in Random Boolean Networks

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Luis A. Escobar ◽  
Hyobin Kim ◽  
Carlos Gershenson
Keyword(s):  
Complex Dynamics ◽  
Boolean Networks ◽  
Downward Causation ◽  
Statistical Properties ◽  
The Other ◽  
Random Boolean Networks ◽  
Dynamical Behaviors ◽  
Modular Networks ◽  
Other Hand ◽  
The One

We investigate the effects of modularity, antimodularity, and multiscale influence on random Boolean networks (RBNs). On the one hand, we produced modular, antimodular, and standard RBNs and compared them to identify how antimodularity affects the dynamical behaviors of RBNs. We found that the antimodular networks showed similar dynamics to the standard networks. Confirming previous results, modular networks had more complex dynamics. On the other hand, we generated multilayer RBNs where there are different RBNs in the nodes of a higher scale RBN. We observed the dynamics of micro- and macronetworks by adjusting parameters at each scale to reveal how the behavior of lower layers affects the behavior of higher layers and vice versa. We found that the statistical properties of macro-RBNs were changed by the parameters of micro-RBNs, but not the other way around. However, the precise patterns of networks were dominated by the macro-RBNs. In other words, for statistical properties only upward causation was relevant, while for the detailed dynamics downward causation was prevalent.

Segmentasi Citra Mri Menggunakan Deteksi Tepi Untuk Identifikasi Kanker Payudara

2017 ◽  
Vol 15 (2) ◽  
pp. 17 ◽  
Author(s):  
Ervina Varijki ◽  
Bambang Krismono Triwijoyo
Keyword(s):  
Breast Cancer ◽  
Edge Detection ◽  
Object Segmentation ◽  
Computation Time ◽  
Input Image ◽  
Boundary Line ◽  
Cancer Breast ◽  
Average Computation Time ◽  
Breast Cancer Mri ◽  
Image Format

One type of cancer that is capable identified using MRI technology is breast cancer. Breast cancer is still the leading cause of death world. therefore early detection of this disease is needed. In identifying breast cancer, a doctor or radiologist analyzing the results of magnetic resonance image that is stored in the format of the Digital Imaging Communication In Medicine (DICOM). It takes skill and experience sufficient for diagnosis is appropriate, andaccurate, so it is necessary to create a digital image processing applications by utilizing the process of object segmentation and edge detection to assist the physician or radiologist in identifying breast cancer. MRI image segmentation using edge detection to identification of breast cancer using a method stages gryascale change the image format, then the binary image thresholding and edge detection process using the latest Robert operator. Of the20 tested the input image to produce images with the appearance of the boundary line of each region or object that is visible and there are no edges are cut off, with the average computation time less than one minute.

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

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