Entropy maximization as a holistic design principle for complex optimal networks

Venkatasubramanian, Venkat; Politis, Dimitris N.; Patkar, Priyan R.

doi:10.1002/aic.10693

Cited by 10 publications

(7 citation statements)

References 18 publications

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“…Nevertheless, our freedom in choosing the constraints is restricted by any prior information, coming through independent tests. On the other hand, there are constraints which are "naturally" imposed either as design principles [28] or as experimental conditions. In what follows we discuss two relevant examples.…”

Section: Constraintsmentioning

confidence: 99%

Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

Vakarin

Badiali

2006

Phys. Rev. E

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Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a nonequilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.

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Section: Constraintsmentioning

confidence: 99%

Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

Vakarin

Badiali

2006

Phys. Rev. E

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“…Because I could not find the framework I was looking for in the literature at that time, I went about developing one in the following years, not realizing that this odyssey would take me 34 years! This led to a series of papers − that culminated in my book in 2017. Progress came only in fits and starts, in a series of six key insights, which I call my “happy thought” moments, with years of quiescence in between.…”

Section: Going From the Parts To The Whole: Backgroundmentioning

confidence: 99%

“…Although many elements of this theory have appeared elsewhere, − the background, organization, presentation, and discussion in this article have new material. Furthermore, as a summary of six papers and a book, I believe this article will be helpful to a new reader who is not familiar with the literature on complexity science, emergence, teleological systems, game theory, information theory, systems engineering, economics, and political philosophy, all of which are drawn upon in my theory.…”

Section: Going From the Parts To The Whole: Backgroundmentioning

confidence: 99%

“…This study led me, in 2004, to investigate the maximum entropy framework in the design of such networks. 2 This resulted in the formulation of my initial theoretic ideas about a new constructionist or emergent framework, in 2007, which I have named statistical teleodynamics. 3 The name comes from telos, a Greek word meaning goal or purpose or end.…”

Section: Going From the Parts To The Whole: Backgroundmentioning

confidence: 99%

“…For a more complete discussion, the reader is referred to my book. 7 In our earlier papers, 2,3 we have discussed the theory's predictions of vertex degree distributions for three classes of complex teleological networks commonly seen in a wide variety of domains such as engineering, biology, sociology, economics, and so on. For networks that have nodes with, on an average, a small number of connections (i.e., low vertex degree), it predicts the exponential distribution of the vertex degree.…”

Section: Statistical Teleodynamics: Macroview and Microviewmentioning

confidence: 99%

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Statistical Teleodynamics: Toward a Theory of Emergence

Venkatasubramanian

2017

Langmuir

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The central scientific challenge of the 21st century is developing a mathematical theory of emergence that can explain and predict phenomena such as consciousness and self-awareness. The most successful research program of the 20th century, reductionism, which goes from the whole to parts, seems unable to address this challenge. This is because addressing this challenge inherently requires an opposite approach, going from parts to the whole. In addition, reductionism, by the very nature of its inquiry, typically does not concern itself with teleology or purposeful behavior. Modeling emergence, in contrast, requires the addressing of teleology. Together, these two requirements present a formidable challenge in developing a successful mathematical theory of emergence. In this article, I describe a new theory of emergence, called statistical teleodynamics, that addresses certain aspects of the general problem. Statistical teleodynamics is a mathematical framework that unifies three seemingly disparate domains-purpose-free entities in statistical mechanics, human engineered teleological systems in systems engineering, and nature-evolved teleological systems in biology and sociology-within the same conceptual formalism. This theory rests on several key conceptual insights, the most important one being the recognition that entropy mathematically models the concept of fairness in economics and philosophy and, equivalently, the concept of robustness in systems engineering. These insights help prove that the fairest inequality of income is a log-normal distribution, which will emerge naturally at equilibrium in an ideal free market society. Similarly, the theory predicts the emergence of the three classes of network organization-exponential, scale-free, and Poisson-seen widely in a variety of domains. Statistical teleodynamics is the natural generalization of statistical thermodynamics, the most successful parts-to-whole systems theory to date, but this generalization is only a modest step toward a more comprehensive mathematical theory of emergence.

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Entropy maximization as a holistic design principle for complex optimal networks

Cited by 10 publications

References 18 publications

Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

Statistical Teleodynamics: Toward a Theory of Emergence

A theory of design of complex teleological systems: Unifying the Darwinian and Boltzmannian perspectives

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