Connectivity and strength has a major role in the field of network connecting with real world life. complexity function is one of these parameter which has manifold number of applications in molecular chemistry and th...
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Connectivity and strength has a major role in the field of network connecting with real world life. complexity function is one of these parameter which has manifold number of applications in molecular chemistry and the theory of network. Firstly, this paper introduces the thought of complexity function of fuzzy graph with its properties. Second, based on the highest and lowest load on a network system, the boundaries of complexity function of different types of fuzzy graphs are established. Third, the behavior of complexity function in fuzzy cycle, fuzzy tree and complete fuzzy graph are discussed with their properties. Fourth, applications of these thoughts are bestowed to identify the most effected COVID-19 cycles between some communicated countries using the concept of complexity function of fuzzy graph. Also the selection of the busiest network stations and connected internet paths can be done using the same concept in a graphical wireless network system.
We construct two point-wise periodic flows which are equivalent, such that all the complexity functions of one flow are bounded while the other flow has an unbounded complexity function. Crown Copyright (C) 2011 Publi...
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We construct two point-wise periodic flows which are equivalent, such that all the complexity functions of one flow are bounded while the other flow has an unbounded complexity function. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.
We examine the connections between complexity of a pseudogroup, its equicontinuity, the mixing property and entropy. We prove that the entropy of a pseudogroup can be (under some additional assumptions) computed using...
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We examine the connections between complexity of a pseudogroup, its equicontinuity, the mixing property and entropy. We prove that the entropy of a pseudogroup can be (under some additional assumptions) computed using a continuous and dynamically generating pseudometric. (C) 2016 Elsevier Inc. All rights reserved.
We studied numerically complexity functions for interval exchange transformations. We have shown that they grow linearly in time as well as the c-complexity function. Moreover, we found out that they depend also linea...
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We studied numerically complexity functions for interval exchange transformations. We have shown that they grow linearly in time as well as the c-complexity function. Moreover, we found out that they depend also linearly on E where E is the Lebesgue measure of a set of initial points. This allows us to hypothesize that the dimension of the measure related to the E-complexity function could be determined by studying the dependence of local complexity functions on C. (c) 2008 Elsevier B.V. All rights reserved.
Let c(n)(V) be the sequence of codimension growth for a variety V of associative algebras. We study the complexity function C(V.z) = Sigma (infinity)(n=0) c(n)(V)z(n)/n!, which is the exponential generating function f...
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Let c(n)(V) be the sequence of codimension growth for a variety V of associative algebras. We study the complexity function C(V.z) = Sigma (infinity)(n=0) c(n)(V)z(n)/n!, which is the exponential generating function for the sequence of codimensions. Earlier, the complexity functions were used to study varieties of Lie algebras. The objective of the note is to start the systematic investigation of complexity functions in the associative case. These functions turn out to be a useful tool to study the growth of varieties over a field of arbitrary characteristic. In the present note, the Schreier formula. for the complexity functions of one-sided ideals of a free associative algebra is found. This formula is applied to the study of products of T-ideals. An exact formula is obtained for the complexity function of the variety U-c of associative algebras generated by the algebra of upper triangular matrices, and it is proved that the function c(n)(U-c) is a quasi-polynomial. The complexity functions for proper identities are investigated. The results for the complexity functions are applied to study the asymptotics of codimension growth. Analogies between the complexity functions of varieties and the Hilbert-Poincare series of finitely generated algebras are traced.
The complexity of an algorithm is usually expressed using complexity functions and complexity classes. In this paper we present a method to reduce the work with multi-variable complexity functions to the work with one...
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ISBN:
(纸本)9783901509704
The complexity of an algorithm is usually expressed using complexity functions and complexity classes. In this paper we present a method to reduce the work with multi-variable complexity functions to the work with one-variable complexity functions. We define five complexity classes for multi-variable complexity functions and then we prove some properties for these classes.
A generalization of numeration systems in which NI is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. We show that if P is an element of Q[x] is a p...
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A generalization of numeration systems in which NI is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. We show that if P is an element of Q[x] is a polynomial such that P(N) subset of N then there exists a numeration system in which the set of representations of P(N) is regular. The main issue is to construct a regular language with a complexity function equals to P(n + 1) - P(n) for n large enough. (C) 2002 Elsevier Science B.V. All rights reserved.
The horizontal visibility graph algorithm is a powerful tool to study time series. In this paper, we use this algorithm maps Sturmian sequences to complex networks and find that the degree sequences partly inherit the...
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The horizontal visibility graph algorithm is a powerful tool to study time series. In this paper, we use this algorithm maps Sturmian sequences to complex networks and find that the degree sequences partly inherit the Sturmian character. Firstly, we prove that Sturmian sequences and their horizontal visibility graph (HVG) degree sequences can be generated separately by coding sequences. Then, using coding factors, we divide the Sturmian sequences of type 1 into six types and calculate the complexity functions of their HVG-degree sequences. Moreover, we show that the HVG-degree sequences of Sturmian sequences of type 0 are the same Sturmian sequence. Finally, we use the complexity functions of HVG-degree sequences to uniquely characterize the Sturmian sequences.
We give a definition of topological entropy for tree shifts, prove that the limit in the definition exists, and show that it dominates the topological entropy of the associated one-dimensional shift of finite type whe...
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We give a definition of topological entropy for tree shifts, prove that the limit in the definition exists, and show that it dominates the topological entropy of the associated one-dimensional shift of finite type when the labeling of the tree shares the same restrictions. (C) 2018 Elsevier B.V. All rights reserved.
We consider languages expressed by word equations in two variables and give a complete characterization for their complexity functions, that is, the functions that give the number of words of the same length. Specific...
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We consider languages expressed by word equations in two variables and give a complete characterization for their complexity functions, that is, the functions that give the number of words of the same length. Specifically, we prove that there are only five types of complexities: constant, linear, exponential, and two in between constant and linear. For the latter two, we give precise characterizations in terms of the number of solutions of Diophantine equations of certain types. In particular, we show that the linear upper bound on the nonexponential complexities by Karhumaki et al. in [9], is tight. There are several consequences of our study. First, we derive that both of the sets of all finite Sturmian words and of all finite Standard words are expressible by word equations. Second, we characterize the languages of non-exponential complexity which are expressible by two-variable word equations as finite unions of several simple parametric formulae and solutions of a two-variable word equation with a finite graph. Third, we find optimal upper bounds on the solutions of (solvable) two-variable word equations, namely, linear bound for one variable and quadratric for the other. From this, we obtain an (n(6)) algorithm for testing the solvability of two-variable word equations, improving thus very much Charatonik and Pacholski's (n(100)) algorithm from [3].
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