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Entropy | Free Full-Text | Network Decomposition and Complexity Measures: An Information Geometrical Approach

Entropy | Free Full-Text | Network Decomposition and Complexity Measures: An Information Geometrical Approach | To Read \ Interesting | Scoop.it
We consider the graph representation of the stochastic model with n binary variables, and develop an information theoretical framework to measure the degree of statistical association existing between subsystems as well as the ones represented by each edge of the graph representation. Besides, we consider the novel measures of complexity with respect to the system decompositionability, by introducing the geometric product of Kullback–Leibler (KL-) divergence. The novel complexity measures satisfy the boundary condition of vanishing at the limit of completely random and ordered state, and also with the existence of independent subsystem of any size. Such complexity measures based on the geometric means are relevant to the heterogeneity of dependencies between subsystems, and the amount of information propagation shared entirely in the system.
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Histogram vs Kernel Density Estimation — astroML 0.2 documentation

Histogram vs Kernel Density Estimation — astroML 0.2 documentation | To Read \ Interesting | Scoop.it
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[0712.0689] Introduction to AdS-CFT

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An introduction to AdS-CFT correspondence that seems to be accessible and I would really like to read one day (or actually, to have read already). Perhaps someday I'll make it...

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How collective comparisons emerge without individual comparisons of the options

How collective comparisons emerge without individual comparisons of the options | To Read \ Interesting | Scoop.it
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Entropy | Free Full-Text | Using Geometry to Select One Dimensional Exponential Families That Are Monotone Likelihood Ratio in the Sample Space, Are Weakly Unimodal and Can Be Parametrized by a Mea...

Entropy | Free Full-Text | Using Geometry to Select One Dimensional Exponential Families That Are Monotone Likelihood Ratio in the Sample Space, Are Weakly Unimodal and Can Be Parametrized by a Mea... | To Read \ Interesting | Scoop.it
One dimensional exponential families on finite sample spaces are studied using the geometry of the simplex Δn°-1  and that of a transformation Vn-1 of its interior. This transformation is the natural parameter space associated with the family of multinomial distributions. The space Vn-1  is partitioned into cones that are used to find one dimensional families with desirable properties for modeling and inference. These properties include the availability of uniformly most powerful tests and estimators that exhibit optimal properties in terms of variability and unbiasedness.
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Entropy | Free Full-Text | Many Can Work Better than the Best: Diagnosing with Medical Images via Crowdsourcing

Entropy | Free Full-Text | Many Can Work Better than the Best: Diagnosing with Medical Images via Crowdsourcing | To Read \ Interesting | Scoop.it
We study a crowdsourcing-based diagnosis algorithm, which is against the fact that currently we do not lack medical staff, but high level experts. Our approach is to make use of the general practitioners’ efforts: For every patient whose illness cannot be judged definitely, we arrange for them to be diagnosed multiple times by different doctors, and we collect the all diagnosis results to derive the final judgement. Our inference model is based on the statistical consistency of the diagnosis data. To evaluate the proposed model, we conduct experiments on both the synthetic and real data; the results show that it outperforms the benchmarks.
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Entropy | Free Full-Text | Entropy Evolution and Uncertainty Estimation with Dynamical Systems

Entropy | Free Full-Text | Entropy Evolution and Uncertainty Estimation with Dynamical Systems | To Read \ Interesting | Scoop.it
This paper presents a comprehensive introduction and systematic derivation of the evolutionary equations for absolute entropy H and relative entropy D, some of which exist sporadically in the literature in different forms under different subjects, within the framework of dynamical systems. In general, both H and D are dissipated, and the dissipation bears a form reminiscent of the Fisher information; in the absence of stochasticity, dH/dt is connected to the rate of phase space expansion, and D stays invariant, i.e., the separation of two probability density functions is always conserved. These formulas are validated with linear systems, and put to application with the Lorenz system and a large-dimensional stochastic quasi-geostrophic flow problem. In the Lorenz case, H falls at a constant rate with time, implying that H will eventually become negative, a situation beyond the capability of the commonly used computational technique like coarse-graining and bin counting. For the stochastic flow problem, it is first reduced to a computationally tractable low-dimensional system, using a reduced model approach, and then handled through ensemble prediction. Both the Lorenz system and the stochastic flow system are examples of self-organization in the light of uncertainty reduction. The latter particularly shows that, sometimes stochasticity may actually enhance the self-organization process.
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The Fascinating World of Complex Systems

Part 1:             http://www.multimedia.ethz.ch/campus/zurichmeetsny/?doi=10.3930/ETHZ/AV-80b92958-97b0-4ad7-b07f-b15192931efc&autostart=false
 
Part 2:             http://www.multimedia.ethz.ch/campus/zurichmeetsny/?doi=10.3930/ETHZ/AV-1db36e67-b2d7-4229-8973-ef1bb54dde27&autostart=false
  
http://www.complexsys.org/publicprograms.html


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june holley's curator insight, July 9, 2014 8:40 AM

Videos on complex systems.

Tom Cockburn's curator insight, July 17, 2014 4:07 AM

Interesting

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Coding Together at Scale: GitHub as a Collaborative Social Network

GitHub is the most popular repository for open source code. It has more than 3.5 million users, as the company declared in April 2013, and more than 10 million repositories, as of December 2013. It has a publicly accessible API and, since March 2012, it also publishes a stream of all the events occurring on public projects. Interactions among GitHub users are of a complex nature and take place in different forms. Developers create and fork repositories, push code, approve code pushed by others, bookmark their favorite projects and follow other developers to keep track of their activities.
In this paper we present a characterization of GitHub, as both a social network and a collaborative platform. To the best of our knowledge, this is the first quantitative study about the interactions happening on GitHub. We analyze the logs from the service over 18 months (between March 11, 2012 and September 11, 2013), describing 183.54 million events and we obtain information about 2.19 million users and 5.68 million repositories, both growing linearly in time. We show that the distributions of the number of contributors per project, watchers per project and followers per user show a power-law-like shape. We analyze social ties and repository-mediated collaboration patterns, and we observe a remarkably low level of reciprocity of the social connections. We also measure the activity of each user in terms of authored events and we observe that very active users do not necessarily have a large number of followers. Finally, we provide a geographic characterization of the centers of activity and we investigate how distance influences collaboration.

 

Coding Together at Scale: GitHub as a Collaborative Social Network
Antonio Lima, Luca Rossi, Mirco Musolesi

http://arxiv.org/abs/1407.2535


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Early Warning Signs in Social-Ecological Networks

Early Warning Signs in Social-Ecological Networks | To Read \ Interesting | Scoop.it

A number of social-ecological systems exhibit complex behavior associated with nonlinearities, bifurcations, and interaction with stochastic drivers. These systems are often prone to abrupt and unexpected instabilities and state shifts that emerge as a discontinuous response to gradual changes in environmental drivers. Predicting such behaviors is crucial to the prevention of or preparation for unwanted regime shifts. Recent research in ecology has investigated early warning signs that anticipate the divergence of univariate ecosystem dynamics from a stable attractor. To date, leading indicators of instability in systems with multiple interacting components have remained poorly investigated. This is a major limitation in the understanding of the dynamics of complex social-ecological networks. Here, we develop a theoretical framework to demonstrate that rising variance—measured, for example, by the maximum element of the covariance matrix of the network—is an effective leading indicator of network instability. We show that its reliability and robustness depend more on the sign of the interactions within the network than the network structure or noise intensity. Mutualistic, scale free and small world networks are less stable than their antagonistic or random counterparts but their instability is more reliably predicted by this leading indicator. These results provide new advances in multidimensional early warning analysis and offer a framework to evaluate the resilience of social-ecological networks.

 

Early Warning Signs in Social-Ecological Networks.

PLoS ONE 9(7): e101851. doi:10.1371/journal.pone.0101851 (2014)

Suweis Samir, D'Odorico Paolo

 

Code of the analysis available at https://github.com/suweis

 

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0101851


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Tom Cockburn's curator insight, July 31, 2014 3:24 AM

Reliably unreliable systems interacting

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4. Unsupervised Learning: Density Estimation — astroML 0.2 documentation

4. Unsupervised Learning: Density Estimation — astroML 0.2 documentation | To Read \ Interesting | Scoop.it
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Emergence in Stigmergic and Complex Adaptive Systems

Emergence in Stigmergic and Complex Adaptive Systems | To Read \ Interesting | Scoop.it

Complex systems have been studied by researchers from every discipline: biology, chemistry, physics, sociology, mathematics and economics and more. Depending upon the discipline, complex systems theory has accrued many flavors. We are after a formal representation, a model that can predict the outcome of acomplex adaptive system (CAS). In this article, we look at the nature of complexity, then provide a perspective based on discrete event systems (DEVS) theory. We pin down many of the shared features between CAS and artificial systems. We begin with an overview of network science showing how adaptive behavior in these scale-free networks can lead to emergence through stigmergy in CAS. We also address how both self-organization and emergence interplay in a CAS. We then build a case for the view that stigmergic systemsare a special case of CAS. We then discuss DEVS levels of systems specifications and present the dynamic structure extensions of DEVS formalism that lends itself to a study of CAS and in turn, stigmergy. Finally, we address the shortcomings and the limitation of current DEVS extensions and propose the required augmentation to model stigmergy and CAS.


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Entropy | Free Full-Text | Information Geometric Complexity of a Trivariate Gaussian Statistical Model

Entropy | Free Full-Text | Information Geometric Complexity of a Trivariate Gaussian Statistical Model | To Read \ Interesting | Scoop.it
We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult it is to make macroscopic predictions about systems in the presence of limited information. Specifically, we observe that the complexity of such entropic inferences not only depends on the amount of available pieces of information but also on the manner in which such pieces are correlated. Finally, we uncover that, for certain correlational structures, the impossibility of reaching the most favorable configuration from an entropic inference viewpoint seems to lead to an information geometric analog of the well-known frustration effect that occurs in statistical physics.
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Decision Making in a Complex and Uncertain World — University of Groningen — FutureLearn

Decision Making in a Complex and Uncertain World — University of Groningen — FutureLearn | To Read \ Interesting | Scoop.it
This course will teach you the first principles of complexity, uncertainty and how to make decisions in a complex world.
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Entropy | Free Full-Text | A Note of Caution on Maximizing Entropy

Entropy | Free Full-Text | A Note of Caution on Maximizing Entropy | To Read \ Interesting | Scoop.it
The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples.
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Entropy | Free Full-Text | Variational Bayes for Regime-Switching Log-Normal Models

Entropy | Free Full-Text | Variational Bayes for Regime-Switching Log-Normal Models | To Read \ Interesting | Scoop.it
The power of projection using divergence functions is a major theme in information geometry. One version of this is the variational Bayes (VB) method. This paper looks at VB in the context of other projection-based methods in information geometry. It also describes how to apply VB to the regime-switching log-normal model and how it provides a computationally fast solution to quantify the uncertainty in the model specification. The results show that the method can recover exactly the model structure, gives the reasonable point estimates and is very computationally efficient. The potential problems of the method in quantifying the parameter uncertainty are discussed.
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▶ Crystal Ball, Magic Wand, or Invisible Hand?

Crystal Ball, Magic Wand, or Invisible Hand?
How to Master our Future in Times of Digital Revolution.

Dirk Helbing

Opening keynote address delivered at CESUN 2014, Hoboken (New York City), on June 9.

http://www.youtube.com/watch?v=tYjX7qlq-AY


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Complexity at the social science interface

This article introduces a special issue of Complexity dedicated to the increasingly important element of complexity science that engages with social policy. We introduce and frame an emerging research agenda that seeks to enhance social policy by working at the interface between the social sciences and the physical sciences (including mathematics and computer science), and term this research area the “social science interface” by analogy with research at the life sciences interface. We locate and exemplify the contribution of complexity science at this new interface before summarizing the contributions collected in this special issue and identifying some common themes that run through them.

 

Complexity at the social science interface
Nigel Gilbert and Seth Bullock

Complexity
Volume 19, Issue 6, pages 1–4, July/August 2014

http://dx.doi.org/10.1002/cplx.21550

 

Special Issue on Complexity Science and Social Policy

http://onlinelibrary.wiley.com/doi/10.1002/cplx.v19.6/issuetoc


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