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Entropy, Volume 13, Issue 3 (March 2011), Pages 570-743

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Research

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Open AccessArticle Towards an Evolutionary Model of Animal-Associated Microbiomes
Entropy 2011, 13(3), 570-594; doi:10.3390/e13030570
Received: 16 December 2010 / Revised: 19 February 2011 / Accepted: 22 February 2011 / Published: 25 February 2011
Cited by 19 | PDF Full-text (931 KB) | HTML Full-text | XML Full-text
Abstract
Second-generation sequencing technologies have granted us greater access to the diversity and genetics of microbial communities that naturally reside endo- and ecto-symbiotically with animal hosts. Substantial research has emerged describing the diversity and broader trends that exist within and between host species and
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Second-generation sequencing technologies have granted us greater access to the diversity and genetics of microbial communities that naturally reside endo- and ecto-symbiotically with animal hosts. Substantial research has emerged describing the diversity and broader trends that exist within and between host species and their associated microbial ecosystems, yet the application of these data to our evolutionary understanding of microbiomes appears fragmented. For the most part biological perspectives are based on limited observations of oversimplified communities, while mathematical and/or computational modeling of these concepts often lack biological precedence. In recognition of this disconnect, both fields have attempted to incorporate ecological theories, although their applicability is currently a subject of debate because most ecological theories were developed based on observations of macro-organisms and their ecosystems. For the purposes of this review, we attempt to transcend the biological, ecological and computational realms, drawing on extensive literature, to forge a useful framework that can, at a minimum be built upon, but ideally will shape the hypotheses of each field as they move forward. In evaluating the top-down selection pressures that are exerted on a microbiome we find cause to warrant reconsideration of the much-maligned theory of multi-level selection and reason that complexity must be underscored by modularity. Full article
(This article belongs to the Special Issue Emergence of Information in Evolutionary Processes)
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Open AccessArticle Entropy Measures vs. Kolmogorov Complexity
Entropy 2011, 13(3), 595-611; doi:10.3390/e13030595
Received: 14 January 2011 / Revised: 25 February 2011 / Accepted: 26 February 2011 / Published: 3 March 2011
Cited by 11 | PDF Full-text (172 KB) | HTML Full-text | XML Full-text
Abstract
Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for R´enyi and Tsallis entropies of order
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Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for R´enyi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we show that, for some distributions we have a similar result. We prove that, for universal time-bounded distribution mt(x), Tsallis and Rényi entropies converge if and only if α is greater than 1. We also establish the uniform continuity of these entropies. Full article
(This article belongs to the Special Issue Kolmogorov Complexity)
Open AccessArticle Information Theory and Dynamical System Predictability
Entropy 2011, 13(3), 612-649; doi:10.3390/e13030612
Received: 25 January 2011 / Revised: 14 February 2011 / Accepted: 20 February 2011 / Published: 7 March 2011
Cited by 13 | PDF Full-text (1206 KB) | HTML Full-text | XML Full-text
Abstract
Predicting the future state of a turbulent dynamical system such as the atmosphere has been recognized for several decades to be an essentially statistical undertaking. Uncertainties from a variety of sources are magnified by dynamical mechanisms and given sufficient time, compromise any prediction.
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Predicting the future state of a turbulent dynamical system such as the atmosphere has been recognized for several decades to be an essentially statistical undertaking. Uncertainties from a variety of sources are magnified by dynamical mechanisms and given sufficient time, compromise any prediction. In the last decade or so this process of uncertainty evolution has been studied using a variety of tools from information theory. These provide both a conceptually general view of the problem as well as a way of probing its non-linearity. Here we review these advances from both a theoretical and practical perspective. Connections with other theoretical areas such as statistical mechanics are emphasized. The importance of obtaining practical results for prediction also guides the development presented. Full article
(This article belongs to the Special Issue Advances in Information Theory)
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Open AccessArticle k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions
Entropy 2011, 13(3), 650-667; doi:10.3390/e13030650
Received: 22 December 2010 / Revised: 27 January 2011 / Accepted: 28 February 2011 / Published: 8 March 2011
Cited by 6 | PDF Full-text (302 KB) | HTML Full-text | XML Full-text
Abstract
A consistent entropy estimator for hyperspherical data is proposed based on the k-nearest neighbor (knn) approach. The asymptotic unbiasedness and consistency of the estimator are proved. Moreover, cross entropy and Kullback-Leibler (KL) divergence estimators are also discussed. Simulation studies are conducted to
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A consistent entropy estimator for hyperspherical data is proposed based on the k-nearest neighbor (knn) approach. The asymptotic unbiasedness and consistency of the estimator are proved. Moreover, cross entropy and Kullback-Leibler (KL) divergence estimators are also discussed. Simulation studies are conducted to assess the performance of the estimators for models including uniform and von Mises-Fisher distributions. The proposed knn entropy estimator is compared with the moment based counterpart via simulations. The results show that these two methods are comparable. Full article
Open AccessArticle Did the Federal Agriculture Improvement and Reform Act of 1996 Affect Farmland Values?
Entropy 2011, 13(3), 668-682; doi:10.3390/e13030668
Received: 4 March 2011 / Revised: 13 March 2011 / Accepted: 14 March 2011 / Published: 17 March 2011
PDF Full-text (138 KB) | HTML Full-text | XML Full-text
Abstract
Farmland values are affected by numerous factors, including farm policy, shifts in demand for agricultural output both foreign and domestic, monetary policy and urban pressure. In this study we use an information measure to examine whether the shift toward a more market-oriented policy
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Farmland values are affected by numerous factors, including farm policy, shifts in demand for agricultural output both foreign and domestic, monetary policy and urban pressure. In this study we use an information measure to examine whether the shift toward a more market-oriented policy in 1996 changed the relationship between farmland values and government payments. The results indicated that the shift in agricultural policy resulted in significant shift in this relationship. Full article
(This article belongs to the Special Issue Advances in Statistical Mechanics)
Open AccessArticle Mode Switching and Collective Behavior in Chemical Oil Droplets
Entropy 2011, 13(3), 709-719; doi:10.3390/e13030709
Received: 17 December 2010 / Revised: 31 January 2011 / Accepted: 4 March 2011 / Published: 18 March 2011
Cited by 11 | PDF Full-text (1691 KB) | HTML Full-text | XML Full-text
Abstract
We have characterized several dynamic aspects of a simple chemical system capable of self-movement: An oil droplet in water system. We focused on spontaneous mode switching and collective behavior of droplets as emergent properties of the system. Droplets demonstrated spontaneous mode switching by
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We have characterized several dynamic aspects of a simple chemical system capable of self-movement: An oil droplet in water system. We focused on spontaneous mode switching and collective behavior of droplets as emergent properties of the system. Droplets demonstrated spontaneous mode switching by changing speed, direction and acceleration over time, and collective behaviors of droplets resulted from such autonomous characteristics. In this paper, we quantitatively measured those characteristics to show that droplets did not act completely independently in the same system, but tend to be attracted to one another and interact with each other by adjusting their motion. Full article
(This article belongs to the Special Issue Emergence in Chemical Systems)
Open AccessArticle Analysis of Resource and Emission Impacts: An Emergy-Based Multiple Spatial Scale Framework for Urban Ecological and Economic Evaluation
Entropy 2011, 13(3), 720-743; doi:10.3390/e13030720
Received: 3 December 2010 / Revised: 17 January 2011 / Accepted: 1 March 2011 / Published: 23 March 2011
Cited by 10 | PDF Full-text (261 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
The development of the complex and multi-dimensional urban socio-economic system creates impacts on natural capital and human capital, which range from a local to a global scale. An emergy-based multiple spatial scale analysis framework and a rigorous accounting method that can quantify the
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The development of the complex and multi-dimensional urban socio-economic system creates impacts on natural capital and human capital, which range from a local to a global scale. An emergy-based multiple spatial scale analysis framework and a rigorous accounting method that can quantify the values of human-made and natural capital losses were proposed in this study. With the intent of comparing the trajectory of Beijing over time, the characteristics of the interface between different scales are considered to explain the resource trade and the impacts of emissions. In addition, our improved determination of emergy analysis and acceptable management options that are in agreement with Beijing’s overall sustainability strategy were examined. The results showed that Beijing’s economy was closely correlated with the consumption of nonrenewable resources and exerted rising pressure on the environment. Of the total emergy use by the economic system, the imported nonrenewable resources from other provinces contribute the most, and the multi‑scale environmental impacts of waterborne and airborne pollution continued to increase from 1999 to 2006. Given the inputs structure, Beijing was chiefly making greater profits by shifting resources from other provinces in China and transferring the emissions outside. The results of our study should enable urban policy planners to better understand the multi-scale policy planning and development design of an urban ecological economic system. Full article
(This article belongs to the Special Issue Advances in Information Theory)

Review

Jump to: Research

Open AccessReview On a Connection between Information and Group Lattices
Entropy 2011, 13(3), 683-708; doi:10.3390/e13030683
Received: 19 January 2011 / Revised: 14 March 2011 / Accepted: 14 March 2011 / Published: 18 March 2011
Cited by 4 | PDF Full-text (220 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we review a particular connection between information theory and group theory. We formalize the notions of information elements and information lattices, first proposed by Shannon. Exploiting this formalization, we expose a comprehensive parallelism between information lattices and subgroup lattices. Qualitatively,
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In this paper we review a particular connection between information theory and group theory. We formalize the notions of information elements and information lattices, first proposed by Shannon. Exploiting this formalization, we expose a comprehensive parallelism between information lattices and subgroup lattices. Qualitatively, isomorphisms between information lattices and subgroup lattices are demonstrated. Quantitatively, a decisive approximation relation between the entropy structures of information lattices and the log-index structures of the corresponding subgroup lattices, first discovered by Chan and Yeung, is highlighted. This approximation, addressing both joint and common entropies, extends the work of Chan and Yeung on joint entropy. A consequence of this approximation result is that any continuous law holds in general for the entropies of information elements if and only if the same law holds in general for the log-indices of subgroups. As an application, by constructing subgroup counterexamples, we find surprisingly that common information, unlike joint information, obeys neither the submodularity nor the supermodularity law. We emphasize that the notion of information elements is conceptually significant—formalizing it helps to reveal the deep connection between information theory and group theory. The parallelism established in this paper admits an appealing group-action explanation and provides useful insights into the intrinsic structure among information elements from a group-theoretic perspective. Full article
(This article belongs to the Special Issue Advances in Information Theory)

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