Information Entropy As a Basic Building Block of Complexity Theory

Gao, Jianbo; Liu, Feiyan; Zhang, Jianfang; Hu, Jing; Cao, Yinhe

doi:10.3390/e15093396

Cited by 52 publications

(30 citation statements)

References 80 publications

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“…Given φ, the Sc ,d pφq can be investigated as a function of arguments (c,d) over a region Ω Ă R 2 , which helps significantly to elucidate Equations (7) and (9).…”

Section: Of 17mentioning

confidence: 99%

“…Given , the , * ( ) can be investigated as a function of arguments (c,d) over a region Ω ⊂ ℝ 2 , which helps significantly to elucidate Equations (7) and (9). We have used Mathematica ® (version 10.1) to perform our numerical experiments with (c,d)-entropy given by Equation (8), as well as to discover a more general relation between (c,d)-entropy and SBGS than given by Equations (9) or (7), respectively.…”

Section: Of 17mentioning

confidence: 99%

“…First, we may refer two seminal works on this field [7,8]. Entropy represents the most known quantitative measure of expected amount of information required to describe the state of a system, and builds a basic framework for the development of complexity theory [9,10]. Entropy is used for measuring the complexity of supply chains [11][12][13][14][15][16][17].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

See 2 more Smart Citations

Operational Complexity of Supplier-Customer Systems Measured by Entropy—Case Studies

Lukáš

Hofman

2016

Entropy

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This paper discusses a unified entropy-based approach for the quantitative measurement of operational complexity of company supplier-customer relations. Classical Shannon entropy is utilized. Beside this quantification tool, we also explore the relations between Shannon entropy and (c,d)-entropy in more details. An analytic description of so called iso-quant curves is given, too. We present five case studies, albeit in an anonymous setting, describing various details of general procedures for measuring the operational complexity of supplier-customer systems. In general, we assume a problem-oriented database exists, which contains detailed records of all product forecasts, orders and deliveries both in quantity and time, scheduled and realized, too. Data processing detects important flow variations both in volumes and times, e.g., order-forecast, delivery-order, and actual production-scheduled one. The unifying quantity used for entropy computation is the time gap between actual delivery time and order issue time, which is nothing else but a lead time in inventory control models. After data consistency checks, histograms and empirical distribution functions are constructed. Finally, the entropy, information-theoretic measure of supplier-customer operational complexity, is calculated. Basic steps of the algorithm are mentioned briefly, too. Results of supplier-customer system analysis from selected Czech small and medium-sized enterprises (SMEs) are presented in various computational and managerial decision making details. An enterprise is ranked as SME one, if it has at most 250 employees and its turnover does not exceed 50 million USD per year, or its balance sheet total does not exceed 43 million USD per year, alternatively.

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“…Given φ, the Sc ,d pφq can be investigated as a function of arguments (c,d) over a region Ω Ă R 2 , which helps significantly to elucidate Equations (7) and (9).…”

Section: Of 17mentioning

confidence: 99%

Section: Of 17mentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

Operational Complexity of Supplier-Customer Systems Measured by Entropy—Case Studies

Lukáš

Hofman

2016

Entropy

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“…We need to introduce instead some bias to the probability weights to account for extreme behavior of the variable. The standard method for calculating means assumes that the random variable during periods when it exhibits extremes has an equal probability of occurrence [9]. In reality, as the value of the random variable increases, the probability of occurrence decreases.…”

Section: Introductionmentioning

confidence: 99%

Ambulance Service Resource Planning for Extreme Temperatures: Analysis of Ambulance 999 Calls during Episodes of Extreme Temperature in London, UK

2018

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Abstract:The association between episodes of extreme temperature and ambulance 999 calls has not yet been properly quantified. In this study we propose a statistical physics-based method to estimate the true mean number of ambulance 999 calls during episodes of extreme temperatures. Simple arithmetic mean overestimates the true number of calls during such episodes. Specifically, we apply the physics-based framework of nonextensive statistical mechanics (NESM) for estimating the probability distribution of extreme events to model the positive daily variation of ambulance calls. In addition, we combine NESM with the partitioned multiobjective method (PMRM) to determine the true mean of the positive daily difference of calls during periods of extreme temperature. We show that the use of the standard mean overestimates the true mean number of ambulance calls during episodes of extreme temperature. It is important to correctly estimate the mean value of ambulance 999 calls during such episodes in order for the ambulance service to efficiently manage their resources.

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“…The degree of chaos of a system can be measured by a generalization of the concept of entropy for state space dynamics [2,3]. It is a highly desired property to ensure security in a chaos encryption scheme that the larger the entropy, the larger the unpredictability of the system [4].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

Zhou

Xiong

Cai

2013

Entropy

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In this paper, we investigate adaptive switched generalized function projective synchronization between two new different hyperchaotic systems with unknown parameters, which is an extension of the switched modified function projective synchronization scheme. Based on the Lyapunov stability theory, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve adaptive switched generalized function projective synchronization between two different hyperchaotic systems. A numerical simulation is conducted to illustrate the validity and feasibility of the proposed synchronization scheme.

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Information Entropy As a Basic Building Block of Complexity Theory

Cited by 52 publications

References 80 publications

Operational Complexity of Supplier-Customer Systems Measured by Entropy—Case Studies

Operational Complexity of Supplier-Customer Systems Measured by Entropy—Case Studies

Ambulance Service Resource Planning for Extreme Temperatures: Analysis of Ambulance 999 Calls during Episodes of Extreme Temperature in London, UK

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

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