A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IX: QUASI-ERGODICITY

2008 ◽  
Vol 18 (09) ◽  
pp. 2487-2642 ◽  
Author(s):  
LEON O. CHUA ◽  
GIOVANNI EGIDIO PAZIENZA ◽  
LASZLO ORZO ◽  
VALERY I. SBITNEV ◽  
JINWOOK SHIN
Keyword(s):  
Bernoulli Shift ◽  
Modular Arithmetic ◽  
Characteristic Functions ◽  
Scale Free ◽  
Return Maps ◽  
Definition Of ◽  
Empirical Property ◽  
Science Part

Our scientific odyssey through the theory of 1-D cellular automata is enriched by the definition of quasi-ergodicity, a new empirical property discovered by analyzing the time-1 return maps of local rules. Quasi-ergodicity plays a key role in the classification of rules into six groups: in fact, it is an exclusive characteristic of complex and hyper Bernoulli-shift rules. Besides introducing quasi-ergodicity, this paper answers several questions posed in the previous chapters of our quest. To start with, we offer a rigorous explanation of the fractal behavior of the time-1 characteristic functions, finding the equations that describe this phenomenon. Then, we propose a classification of rules according to the presence of Isles of Eden, and prove that only 28 local rules out of 256 do not have any of them; this result sheds light on the importance of Isles of Eden. A section of this paper is devoted to the characterization of Bernoulli basin-tree diagrams through modular arithmetic; the formulas obtained allow us to shorten drastically the number of cases to take into consideration during numerical simulations. Last but not least, we present some theorems about additive rules, including an analytical explanation of their scale-free property.

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IV: FROM BERNOULLI SHIFT TO 1/f SPECTRUM

2005 ◽  
Vol 15 (04) ◽  
pp. 1045-1183 ◽  
Author(s):  
LEON O. CHUA ◽  
VALERY I. SBITNEV ◽  
SOOK YOON
Keyword(s):  
Bernoulli Shift ◽  
Dynamical Evolution ◽  
Complete Characterization ◽  
Characteristic Functions ◽  
One Dimensional ◽  
New Concepts ◽  
The Right ◽  
Science Part

By exploiting the new concepts of CA characteristic functions and their associated attractor time-τ maps, a complete characterization of the long-term time-asymptotic behaviors of all 256 one-dimensional CA rules are achieved via a single "probing" random input signal. In particular, the graphs of the time-1 maps of the 256 CA rules represent, in some sense, the generalized Green's functions for Cellular Automata. The asymptotic dynamical evolution on any CA attractor, or invariant orbit, of 206 (out of 256) CA rules can be predicted precisely, by inspection. In particular, a total of 112 CA rules are shown to obey a generalized Bernoulli στ-shift rule, which involves the shifting of any binary string on an attractor, or invariant orbit, either to the left, or to the right, by up to 3 pixels, and followed possibly by a complementation of the resulting bit string. The most intriguing result reported in this paper is the discovery that the four Turing-universal rules [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], and only these rules, exhibit a 1/f power spectrum.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

scholarly journals Experimental characterization of fragile topology in an acoustic metamaterial

Science ◽  
2020 ◽  
Vol 367 (6479) ◽  
pp. 797-800 ◽  
Author(s):  
Valerio Peri ◽  
Zhi-Da Song ◽  
Marc Serra-Garcia ◽  
Pascal Engeler ◽  
Raquel Queiroz ◽  
...  
Keyword(s):  
Spectral Signature ◽  
Experimental Characterization ◽  
Basic Definition ◽  
Acoustic Metamaterial ◽  
Symmetry Properties ◽  
Definition Of ◽  
Topological Phases Of Matter ◽  
Twisted Boundary Conditions

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: Although answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions.

Models of Functional Dependencies of Elements in Sequences for Solving Problems of Control and Management

2019 ◽  
Vol 20 (10) ◽  
pp. 579-588
Author(s):  
V. A. Tverdokhlebov
Keyword(s):  
Linear Order ◽  
Complete Characterization ◽  
Process Models ◽  
Functional Dependencies ◽  
Control Rules ◽  
Sequence Elements ◽  
Definition Of ◽  
Control And Management

In paper developed version of the basic concepts, models and methods for the formulation and solution of problems of control and diagnosing of processes in systems, tasks of constructing models of processes in which the causal relationships of events are transformed into functional dependencies between elements in sequences, problems of formalizing of process control rules, etc. For this extended classical recurrent definition of the sequences, which presents the functional elements depending on the immediately preceding to them m elements to offered Z-recurrent definition, which defines the functional relationship between sets of elements in the sequence. The orders of Z-recurrent forms have the form of a set of numbers and are convenient for accurate and complete characterization of the connections of events in processes. The tasks of control, diagnosing, constructing new models of processes, assessing the complexity of processes and rules for managing processes can be formulated and solved using numerical indicators of Z-recurrent definitions. A classification of Z-recurrent definitions of sequences and a classification of processes are constructed, an algorithm for checking the feasibility of determining a Z-recurrent form for given sequences of form is developed. The Z-recurrent definition of sequence is complemented by the Z-recurrent sequence pattern method, which includes: introducing a linear order on the base set of sequence elements, constructing an image for the sequence in the form of a sequence of executing or non-executing relationships between the elements represented by a linear order, and applying Z-recurrent definitions to the constructed image of the sequence. The problem on which the solution of the considered problems is based is the recognition of two sequences by properties, which are determined by the indicators of Z-recurrent definitions of sequences, which have the form of orders of Z-recurrent forms. Sets of orders in executing or non-executing Z-recurrent forms characterize the sequences and the analyzed sets of sequences, which allows you to set and solve problems related to system management: problems of control and diagnosing of processes in the system, problems of constructing process models, problems of formalizing and complexity estimation of control rules of processes.

scholarly journals Image analysis and definition of nuclear phenotypes

1997 ◽  
Vol 20 (4) ◽  
pp. 749-754 ◽  
Author(s):  
Benedicto de Campos Vidal
Keyword(s):  
Image Analysis ◽  
Cell Nucleus ◽  
Geometric Information ◽  
Definition Of

Some basic topics concerned with the extraction of textural and geometric information from cell nucleus images as well as description and characterization of chromatin supraorganization and consequent classification of nuclear phenotypes are presented.

Development and Evaluation of Fuzzy Criteria for the Diagnosis of Rheumatoid Arthritis

1996 ◽  
Vol 35 (04/05) ◽  
pp. 334-342 ◽  
Author(s):  
K.-P. Adlassnig ◽  
G. Kolarz ◽  
H. Leitich
Keyword(s):  
Rheumatoid Arthritis ◽  
Reference Model ◽  
American Rheumatism Association ◽  
Uniform Definition ◽  
Sensitivity Rate ◽  
Fuzzy Techniques ◽  
Definition Of ◽  
Different Levels ◽  
Specificity Rate

Abstract:In 1987, the American Rheumatism Association issued a set of criteria for the classification of rheumatoid arthritis (RA) to provide a uniform definition of RA patients. Fuzzy set theory and fuzzy logic were used to transform this set of criteria into a diagnostic tool that offers diagnoses at different levels of confidence: a definite level, which was consistent with the original criteria definition, as well as several possible and superdefinite levels. Two fuzzy models and a reference model which provided results at a definite level only were applied to 292 clinical cases from a hospital for rheumatic diseases. At the definite level, all models yielded a sensitivity rate of 72.6% and a specificity rate of 87.0%. Sensitivity and specificity rates at the possible levels ranged from 73.3% to 85.6% and from 83.6% to 87.0%. At the superdefinite levels, sensitivity rates ranged from 39.0% to 63.7% and specificity rates from 90.4% to 95.2%. Fuzzy techniques were helpful to add flexibility to preexisting diagnostic criteria in order to obtain diagnoses at the desired level of confidence.

ABOUT THE PROBLEM OF CLASSIFICATION OF THE CONCEPTS OF INFORMATICS STUDIED AT SECONDARY SCHOOL

2018 ◽  
pp. 4-7
Author(s):  
S. I. Zenko
Keyword(s):  
Secondary School ◽  
Foreign Language ◽  
Computer Science ◽  
Parts Of Speech ◽  
The Third ◽  
The Cross ◽  
Definition Of

The article raises the problem of classification of the concepts of computer science and informatics studied at secondary school. The efficiency of creation of techniques of training of pupils in these concepts depends on its solution. The author proposes to consider classifications of the concepts of school informatics from four positions: on the cross-subject basis, the content lines of the educational subject "Informatics", the logical and structural interrelations and interactions of the studied concepts, the etymology of foreign-language and translated words in the definition of the concepts of informatics. As a result of the first classification general and special concepts are allocated; the second classification — inter-content and intra-content concepts; the third classification — stable (steady), expanding, key and auxiliary concepts; the fourth classification — concepts-nouns, conceptsverbs, concepts-adjectives and concepts — combinations of parts of speech.

Determining the discount rate when evaluating trade organizations: Some features

2020 ◽  
Vol 13 (1) ◽  
pp. 71-84
Author(s):  
E.A. Grigor'eva ◽  
A.S. Buzhikeeva
Keyword(s):  
Discount Rate ◽  
Economic Activity ◽  
Systems Approach ◽  
Market Value ◽  
Additional Risk ◽  
Evaluation Procedures ◽  
Analytical Research ◽  
Definition Of ◽  
Traditional Approaches

Subject. This article deals with the issues of determining the market value of the trading business, taking into account a number of characteristics. Objectives. The article aims to develop certain provisions of the methodology and practice of evaluating the business of trading organizations, namely, taking into account the additional risk of inventory feasibility when calculating the discount rate. Methods. For the study, we used a systems approach, and the cognition, and economic and analytical research methods. Results. The article presents a three-tiered classification of stocks and a definition of risk based on the criteria for dividing stocks by purpose, degree of implementation, and shelf life in accordance with the scale. Based on the classification, the article offers certain recommendations for determining the discount rate when evaluating trading organizations, aimed at taking into account additional risk. Conclusions. Various evaluation procedures within the framework of traditional approaches and methods in relation to trading organizations do not take into account risk specific to this type of economic activity. The proposed methodology for calculating the discount rate for trade organizations takes into account the features of their functioning.

State Failure and the Political Violence Phenomenon: A Comparative Analysis of Iraq and Syria Cases

2016 ◽  
Vol 4 (2) ◽  
pp. 170 ◽  
Author(s):  
K. Eylem Özkaya Lassalle
Keyword(s):  
Cold War ◽  
Political Violence ◽  
State Failure ◽  
The Political ◽  
Collective Violence ◽  
Short Run ◽  
Definition Of ◽  
The Cold War

The concept of failed state came to the fore with the end of the Cold War, the collapse of the USSR and the disintegration of Yugoslavia. Political violence is central in these discussions on the definition of the concept or the determination of its dimensions (indicators). Specifically, the level of political violence, the type of political violence and intensity of political violence has been broached in the literature. An effective classification of political violence can lead us to a better understanding of state failure phenomenon. By using Tilly’s classification of collective violence which is based on extent of coordination among violent actors and salience of short-run damage, the role played by political violence in state failure can be understood clearly. In order to do this, two recent cases, Iraq and Syria will be examined.

ECOLOGICAL SIGNIFICANCE OF PHEROMONES

2020 ◽  
Vol 6 (2) ◽  
pp. 64-68
Author(s):  
Nondira Khondhodjayeva ◽  
◽  
Nurmamat Rajabov ◽  
Keyword(s):  
Biological Significance ◽  
Ecological Significance ◽  
Definition Of

This article reveals the essence of the concept of "pheromones" and their biological significance. In the article variants of their application in agriculture for struggle against insects-pests are presented. The definition of term and classification of pheromones and their types are given: feromons of insects, feromons of fish, feromons of vertebrates, feromons of humans, fermons of plants, sexual feromons, anxiety feromons, trace feromons, epidemic feromons and their functions and significance for the representative's organism and the environment as a whole

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