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Rescooped by Vasileios Basios from Complexity - Complex Systems Theory
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A signature of power law network dynamics

Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two simple graph parameters--the logarithm of the average cluster size and logarithm of the ratio of the edges of the graph to the theoretically maximum number of edges for that graph--that holds for all growing power law graphs. The result establishes a novel property of evolving power-law networks in the asymptotic limit of network size. Numerical simulations as well as fitting to real-world citation co-authorship networks demonstrate that the result holds for networks of finite sizes, and provides a convenient measure of the extent to which an evolving family of networks belongs to the same power-law class.


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Complex Thinking for a Complex World – About Reductionism, Disjunction and Systemism | Morin | Systema: connecting matter, life, culture and technology

Complex Thinking for a Complex World – About Reductionism, Disjunction and Systemism | Morin | Systema: connecting matter, life, culture and technology | collectibles from scoop.it | Scoop.it

This article is based on the keynote address presented to the European Meetings on Cybernetics and Systems Research (EMCSR) in 2012, on the occasion of Edgar Morin receiving the Bertalanffy Prize in Complexity Thinking, awarded by the Bertalanffy Centre for the Study of Systems Science(BCSSS).

The following theses will be elaborated on: (a) The whole is at the same time more and less than its parts; (b) We must abandon the term "object" for systems because all the objects are systems and parts of systems; (c) System and organization are the two faces of the same reality; (d) Eco-systems illustrate self-organization.


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Chaotic and non-chaotic phases in experimental responses of a single neuron

Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron do not increase with the number of stimulations. A chaotic neuronal phase emerges at a transition to convex latency profiles which diverge exponentially, indicating irreproducible response timings. Our findings are supported by a quantitative mathematical framework and found robust to periodic and random stimulation patterns. In addition, these results put a bound on the neuronal temporal resolution which can be enhanced below a millisecond using neuronal chains.


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C.G. Jung: “We Are Living in What the Greeks Called the Right Time for a “Metamorphosis of the Gods….”

C.G. Jung: “We Are Living in What the Greeks Called the Right Time for a “Metamorphosis of the Gods….” | collectibles from scoop.it | Scoop.it
 
 

We are living in what the Greeks called the right time for a "metamorphosis of the gods," i.e. of the fundamental principles and symbols.

This peculi(...) (C.G. Jung: “We Are Living in What the Greeks Called the Right Time...

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Ants Swarm Like Brains Think

Ants Swarm Like Brains Think | collectibles from scoop.it | Scoop.it

Both ants and brains actually rely on two types of feedback, held in a delicate balance: negative (or inhibitory) feedback, and positive (or excitatory) feedback. “Negative feedback tends to cause stability. Positive feedback tends to cause runaway behavior,” said Tomer Czaczkes, an ant biologist at the University of Regensburg in Germany. “These two simple rules make something very powerful.”

 

http://nautil.us/issue/12/feedback/ants-swarm-like-brains-think ;


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Eli Levine's curator insight, May 1, 2014 10:14 AM

Small changes in behavior, thought or action can lead to dramatic changes, in time and with persistence, in the overall quality and function of the brain.

 

Imagine if we worked to heal each other and ourselves of our delusions, illusions, false perceptions, misconceptions, anger, depression, anxiety, etc?  What if we invented machines that could help us correct our brains' function, must like how we use glasses or hearing aids to correct our senses?

 

Consciousness must flow through the biological infrastructure of the brain.  You alter that in a majority of the people of this planet, you technically alter the entirety of the universe (although, I would add, that theoretically that higher level of conscious state had always been present, and that it is we who are arriving at it in our perceptions, while the essential universe itself remains unchanged).  This means that we'd simply be adapting to the universe in a more positive fashion, rather than actually altering it; conforming more to its natural law than shifting the paradigm of our existence on this planet, in this place.

 

Cool cool stuff here.

 

Think about it.

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Which forces reduce entropy production?

A real pendulum with friction will oscillate for a while after a short push but will eventually come to rest close to a location where is potential energy has a minimum. If the system is closed, that means, without a source of energy, it will eventually stop moving at a location near a minimum of the potential, no matter what type of friction force acts on the pendulum. This “variation principle” is a simple concept to predict the long-term behavior of mechanical systems, even if the details of the friction forces are unknown.
For many years, scientist tried to find a similarly simple variation principle for systems with a source of energy such as a periodic forcing function or a battery in electrical systems [1]. Prigogine suggested that time rate of entropy production is at a minimum at stationary states [2]. Later the concept of entropy was generalized and used to describe the dynamics and stationary states of open dissipative systems [3-7].

 

Which forces reduce entropy production?
Alfred Hubler
Complexity
http://dx.doi.org/10.1002/cplx.21532 ;

 


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Hierarchical Block Structures and High-Resolution Model Selection in Large Networks

Hierarchical Block Structures and High-Resolution Model Selection in Large Networks | collectibles from scoop.it | Scoop.it

Social, technological, and biological networks are known to organize into modules or “communities.” Characterizing and identifying modules is highly nontrivial and still an outstanding problem in networks research. A new approach uses both the concept of modular hierarchy for network construction and the methods of statistical inference to address this problem, succeeding where the existing approaches see difficulties.

 

Hierarchical Block Structures and High-Resolution Model Selection in Large Networks
Tiago P. Peixoto
Phys. Rev. X 4, 011047 (2014)

http://dx.doi.org/10.1103/PhysRevX.4.011047


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Towards a Methodology for Validation of Centrality Measures in Complex Networks

Towards a Methodology for Validation of Centrality Measures in Complex Networks | collectibles from scoop.it | Scoop.it

Our empirical analysis demonstrates that in the chosen network data sets, nodes which had a high Closeness Centrality also had a high Eccentricity Centrality. Likewise high Degree Centrality also correlated closely with a high Eigenvector Centrality. Whereas Betweenness Centrality varied according to network topology and did not demonstrate any noticeable pattern. In terms of identification of key nodes, we discovered that as compared with other centrality measures, Eigenvector and Eccentricity Centralities were better able to identify important nodes.

 

Batool K, Niazi MA (2014) Towards a Methodology for Validation of Centrality Measures in Complex Networks. PLoS ONE 9(4): e90283. http://dx.doi.org/10.1371/journal.pone.0090283


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Liz Rykert's curator insight, April 15, 2014 10:50 PM

Love this stuff.

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Anima on the wheel – Female Archetypes of Toni Wolff

Anima on the wheel – Female Archetypes of Toni Wolff | collectibles from scoop.it | Scoop.it
Lets say this is not an essay but a fictional story. I was very pleased that good friend of mine, who happens to be a catholic monk and psychoanalyst, accepted to be the god-father of my son.

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Innovations in Statistical Physics

In 1963-71, a group of people, myself included, formulated and perfected a new approach to physics problems, which eventually came to be known under the names of scaling, universality, and renormalization. This work formed the basis of a wide variety of theories ranging from its starting point in critical phenomena, and moving out to particle physics and relativity and then into economics and biology. This work was of transcendental beauty and of considerable intellectual importance.
This left me with a personal problem. What next? Constructing the answer to that question would dominate the next 45 years of my professional life. I would try to:
* Help in finding and constructing new fields of science
* Do research and give talks on science/society borderline
* Provide helpful, constructive criticism of scientific and technical work
* Help students and younger scientists
* Demonstrate scientific leadership

 

Innovations in Statistical Physics
Leo P. Kadanoff

http://arxiv.org/abs/1403.6464


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Contributions and challenges for network models in cognitive neuroscience

Contributions and challenges for network models in cognitive neuroscience | collectibles from scoop.it | Scoop.it

The confluence of new approaches in recording patterns of brain connectivity and quantitative analytic tools from network science has opened new avenues toward understanding the organization and function of brain networks. Descriptive network models of brain structural and functional connectivity have made several important contributions; for example, in the mapping of putative network hubs and network communities. Building on the importance of anatomical and functional interactions, network models have provided insight into the basic structures and mechanisms that enable integrative neural processes. Network models have also been instrumental in understanding the role of structural brain networks in generating spatially and temporally organized brain activity. Despite these contributions, network models are subject to limitations in methodology and interpretation, and they face many challenges as brain connectivity data sets continue to increase in detail and complexity.

 

Contributions and challenges for network models in cognitive neuroscience
• Olaf Sporns
Nature Neuroscience (2014) http://dx.doi.org/10.1038/nn.3690


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Synchronicity and quantum entanglement - YouTube

On the trail of the dialogue by W. Pauli and C.G. Jung An even more neglected correspondence (1932-58) of the Nobel Prize winner and pioneer of quantum theor... (Synchronicity and quantum entanglement, W.

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Philippe Vallat's curator insight, April 6, 2014 3:35 AM

Always interesting to listen to open-minded and curious scientists

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Behavioral and Network Origins of Wealth Inequality: Insights from a Virtual World

Almost universally, wealth is not distributed uniformly within societies or economies. Even though wealth data have been collected in various forms for centuries, the origins for the observed wealth-disparity and social inequality are not yet fully understood. Especially the impact and connections of human behavior on wealth could so far not be inferred from data. Here we study wealth data from the virtual economy of the massive multiplayer online game (MMOG) Pardus. This data not only contains every player's wealth at every point in time, but also all actions of every player over a timespan of almost a decade. We find that wealth distributions in the virtual world are very similar to those in western countries. In particular we find an approximate exponential for low wealth and a power-law tail. The Gini index is found to be 0.65, which is close to the indices of many Western countries. We find that wealth-increase rates depend on the time when players entered the game. Players that entered the game early on tend to have remarkably higher wealth-increase rates than those who joined later. Studying the players' positions within their social networks, we find that the local position in the trade network is most relevant for wealth. Wealthy people have high in- and out-degree in the trade network, relatively low nearest-neighbor degree and a low clustering coefficient. Wealthy players have many mutual friendships and are socially well respected by others, but spend more time on business than on socializing. We find that players that are not organized within social groups with at least three members are significantly poorer on average. We observe that high `political' status and high wealth go hand in hand. Wealthy players have few personal enemies, but show animosity towards players that behave as public enemies.


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Eli Levine's curator insight, April 5, 2014 10:53 AM

When you let laissez-faire take its course, only a few individuals really end up on top.  That's not to say that markets shouldn't be allowed and enabled to exist, for the sake of the free exchange of goods, services, knowledge, wealth, etc.  It is saying that we need non-intrusive mechanisms to help make sure that the wealth that is produced is enjoyed by everyone who produced it.

 

Some people will always have more than others, for behavioral reasons and for circumstantial reasons.  That is not a problem, in my own view.  The problem comes, for me, when their focus on wealth becomes so great that they lose sight of their human needs on the individual as well as social and environmental levels, such that they choose wealth that they will not use over that which they need for survival and physical/psychological well being.

 

It's a form of being disconnected with the real world, kind of like schizophrenia.  The brain isn't functioning properly when  greed is and has taken over, for one reason or another.  It should be considered a mental illness that we could, potentially in time, treat, such that these individuals who are not aware and do not care to be aware of their actual place in the universe can lead normal, happy, healthy and appropriately placed lives in our societies.

 

So, we're left with the present situation in which work is undervalued, relative to what it produces, while executive management is way overvalued relative to its healthy role in the economy and society.  I'm not saying that pure equality is desirable, because sometimes people do work harder than others and deserve a greater share of wealth than someone who didn't work when they honestly could have.  What I'm saying, is that indulging the elite's fantasy of the ego is detrimental to themselves and to others, and that I don't think it should be accepted or tolerated within our social world.

 

If you want equality of opportunities, you must have more equality of outcomes.  That is yet another fact about our world that conservatives fail to accept and appreciate, if they're attempting to realize a world in which we are all together as one, rather than a world where we are heavily stratified according to an artificial hierarchy.  That is the difference between a conservative and a progressive.  One wants us all to be living together in peace, harmony, stability and, for want of a better word, love, while the other just wants everyone in a specific place according to birth.  One promotes democracy and inclusivity, the other, discourages it.  One works better for humanity on the tangible level, the other, does not.

 

And it's just a difference in brain type/values that makes them be something so antithetical to what Western civilization has stood for.

 

Think about it.

Rescooped by Vasileios Basios from Complexity - Complex Systems Theory
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Pattern and Process | Spatial Simulation: Exploring Pattern and Process

Pattern and Process | Spatial Simulation: Exploring Pattern and Process | collectibles from scoop.it | Scoop.it

Across broad areas of the environmental and social sciences, simulation models are an important way to study systems inaccessible to scientific experimental and observational methods, and also an essential complement of those more conventional approaches.  The contemporary research literature is teeming with abstract simulation models whose presentation is mathematically demanding and requires a high level of knowledge of quantitative and computational methods and approaches.  Furthermore, simulation models designed to represent specific systems and phenomena are often complicated, and, as a result, difficult to reconstruct from their descriptions in the literature.  Spatial Simulation: Exploring Pattern and Process aims to provide a practical and accessible account of dynamic spatial modelling, while also equipping readers with a sound conceptual foundation in the subject, and a useful introduction to the wide-ranging literature.


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What’s the use of “econo-physics”? — The Physics of Finance — Medium

What’s the use of “econo-physics”? — The Physics of Finance — Medium | collectibles from scoop.it | Scoop.it

About 20 years ago, a few physicists got interested in applying some ideas and concepts from physics to problems in finance and economics. The area is sometimes called "econophysics" – I actually don't like the name – and it tends to be controversial. Some economists find it annoying, although a few others either work in the area or do work that is closely associated conceptually. On occasion, you'll find people suggesting that research in econophysics has never achieved anything worthwhile (this was seven years ago, and that writer may possibly have changed his mind by now).


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Markers of criticality in phase synchronisation

The concept of the brain as a critical system is very attractive because systems close to criticality are thought to maximise their dynamic range of information processing and communication. To date, there have been two key experimental observations supporting this hypothesis: i) neuronal avalanches with power law distribution of size and ii) long-range temporal correlations (LRTCs) in the amplitude of neural oscillations. The case for how these maximise dynamic range of information processing and communication is still being made and because a significant substrate for information coding and transmission is neural synchrony it is of interest to link synchronisation measures with those of criticality. We propose a framework for characterising criticality in synchronisation based on a new metric of phase synchronisation (rate of change of phase difference) and a set of methods we have developed for detecting LRTCs. We test this framework against two classical models of criticality (Ising and Kuramoto) and recently described variants of these models aimed to more closely represent human brain dynamics. From these simulations we determine the parameters at which these systems show evidence of LRTCs in phase synchronisation. We demonstrate proof of principle by analysing pairs of human simultaneous EEG and EMG time series, suggesting that LRTCs of corticomuscular phase synchronisation can be detected in the resting state. The existence of LRTCs in fluctuations of phase synchronisation suggests that these fluctuations are governed by non-local behaviour. This has important implications regarding the conditions under which one should expect to see LRTCs in phase synchronisation. Specifically, brain resting states may exhibit LRTCs reflecting a state of readiness facilitating rapid task-dependent shifts towards and away from synchronous states that abolish LRTCs.

 

Markers of criticality in phase synchronisation
Maria Botcharova, Simon F. Farmer, Luc Berthouze

http://arxiv.org/abs/1404.5774


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C.G. Jung: “We Are Living in What the Greeks Called the Right Time for a “Metamorphosis of the Gods….”

C.G. Jung: “We Are Living in What the Greeks Called the Right Time for a “Metamorphosis of the Gods….” | collectibles from scoop.it | Scoop.it
 
 

We are living in what the Greeks called the right time for a "metamorphosis of the gods," i.e. of the fundamental principles and symbols.

This peculi(...) (C.G. Jung: “We Are Living in What the Greeks Called the Right Time...

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Flow, Conflux | Smart Cities

Flow, Conflux | Smart Cities | collectibles from scoop.it | Scoop.it

“The city is not only a community, it is a conflux. ….The real city, as a center of industry, is a conflux of streams of traffic; as a center of culture, it is conflux of streams of thought.” So wrote Benton MacKaye in 1928 in his book The New Exploration: A Philosophy of Regional Planning. When I sent a copy of my own recent book The New Science of Cities to my erstwhile colleague and old friend Lionel March, he quickly scowered it and said: “I see in your Preamble that you cite Castells’ ‘space of flows’ and that your approach makes much of flows and networks. I immediately turned to your bibliography to search for the name Benton MacKaye. It is not there! The author of The New Exploration (1928) is my hero of metropolitan/regional development. I’m sure you know of him”.


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Eli Levine's curator insight, April 17, 2014 12:00 PM

Location, location, location.

 

The natural geography has to fit with the demands of the population and the society.  It's not something that someone on high chooses, but rather one where things grow up naturally according to the relative advantages and disadvantages of the area.  Then you build and with building in these geographically advantageous (or, sometimes, just convenient) areas you reinforce their advantages as centers of commerce, trade and "flows" as Batty would put it.

 

It makes sense to have it be on the regional, national and/or international scale, such that we, as humans, take advantage of the most strategic places and the most strategic resources that are available.  With this comes the flourishing of new life, happiness and possible/hopefully sustainable prosperity for the present and for the future well being of our civilizations.

 

The climate is changing and that's going to force a lot of changes on our part.  If we can survive the environmental tumult, and the economic and social tumult that it is going to cause, we could potentially, get off on a better footing than before, in spite of the losses which we incur as a result of the present silliness of our political, social and economic "leadership".

 

Good stuff!

 

Think about it.

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Information Flow in Animal-Robot Interactions

The nonverbal transmission of information between social animals is a primary driving force behind their actions and, therefore, an important quantity to measure in animal behavior studies. Despite its key role in social behavior, the flow of information has only been inferred by correlating the actions of individuals with a simplifying assumption of linearity. In this paper, we leverage information-theoretic tools to relax this assumption. To demonstrate the feasibility of our approach, we focus on a robotics-based experimental paradigm, which affords consistent and controllable delivery of visual stimuli to zebrafish. Specifically, we use a robotic arm to maneuver a life-sized replica of a zebrafish in a predetermined trajectory as it interacts with a focal subject in a test tank. We track the fish and the replica through time and use the resulting trajectory data to measure the transfer entropy between the replica and the focal subject, which, in turn, is used to quantify one-directional information flow from the robot to the fish. In agreement with our expectations, we find that the information flow from the replica to the zebrafish is significantly more than the other way around. Notably, such information is specifically related to the response of the fish to the replica, whereby we observe that the information flow is reduced significantly if the motion of the replica is randomly delayed in a surrogate dataset. In addition, comparison with a control experiment, where the replica is replaced by a conspecific, shows that the information flow toward the focal fish is significantly more for a robotic than a live stimulus. These findings support the reliability of using transfer entropy as a measure of information flow, while providing indirect evidence for the efficacy of a robotics-based platform in animal behavioral studies.

 

Information Flow in Animal-Robot Interactions
by Sachit Butail, Fabrizio Ladu, Davide Spinello and Maurizio Porfiri
Entropy 2014, 16(3), 1315-1330; doi:10.3390/e16031315
http://www.mdpi.com/1099-4300/16/3/1315/


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Complex Thinking for a Complex World – About Reductionism, Disjunction and Systemism, by Edgar Morin

This article is based on the keynote address presented to the European Meetings on Cybernetics and Systems Research (EMCSR) in 2012, on the occasion of Edgar Morin receiving the Bertalanffy Prize in Complexity Thinking, awarded by the Bertalanffy Centre for the Study of Systems Science (BCSSS).
The following theses will be elaborated on: (a) The whole is at the same time more and less than its parts; (b) We must abandon the term "object" for systems because all the objects are systems and parts of systems; (c) System and organization are the two faces of the same reality; (d) Eco-systems illustrate self-organization.

 

Complex Thinking for a Complex World – About Reductionism, Disjunction and Systemism
Edgar Morin

Systema: connecting matter, life, culture and technology Vol 2, No 1 (2014)

http://www.systema-journal.org/article/view/257


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Eli Levine's curator insight, April 13, 2014 10:21 PM

There is a kind of meditation in Buddhist practice known as analytical meditation.  It's purpose is to inform us about an object, all of its properties and all of the associations, connections and contexts that it can have in the individual and collective sense. 

 

We're not going to be perfect coming up with all of the connections all of the time.  However, I think it's a good starting basis for the purposes of analyzing complex systems and all of the layered, interconnected parts.  We are one, and one is all.

 

The universe is us as well as around us.


And that's a scientific fact, it seems.

 

Think about it.

Luciano Lampi's curator insight, April 14, 2014 2:37 PM

objects versus systems?

luiy's curator insight, May 1, 2014 9:20 PM

In this light is interesting to consider the nature of life. Living systems represent a complex type of organization. The organization of a living system is more complex than the  organization of the molecules of which it is composed. However, this organization is  achieved using only molecules from the physical universe – living systems are not made from something like ‘living matter’, but from ordinary physical and chemical substances.


“Life” is a property created through complex self-organisation. Life is characterized by processes of self-reproduction and self-repair, processes that involve knowledge and  memory. The central feature of a living system is the self-organizational capacity to produce
and reproduce itself. However, as von Foerster noted, calling this self-organisation is paradoxical, because the organizational processes of life require a continuous input of energy. We need energy even when we sleep – energy to drive our heartbeat, our digestion, our breathing. We use energy in all moments of life. However, we also need to compensate for the dissipation of energy in line with the second law of thermodynamics, and this means we must take in energy from the environment. We do this by ingesting material  that contains energy, and to this we need knowledge of the environment, and in particular knowledge of the organization of the environment. So self-organisation requires an interplay between the knowledge of how to organize the self and the knowledge of how the environment is organized.

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Crisis Responses and Crisis Management: what can we learn from Biological Networks?

The generality of network properties allows the utilization of the ‘wisdom’ of biological systems surviving crisis events for many millions of years. Yeast protein-protein interaction network shows a decrease in community-overlap (an increase in community cohesion) in stress. Community rearrangement seems to be a cost-efficient, general crisis-management response of complex systems. Inter-community bridges, such as the highly dynamic ‘creative nodes’ emerge as crucial determinants helping crisis survival.

 

Crisis Responses and Crisis Management: what can we learn from Biological Networks?
Péter Csermely, Agoston Mihalik, Zsolt Vassy, András London

Systema: connecting matter, life, culture and technology

Vol 2, No 1 (2014)

http://www.systema-journal.org/article/view/115 ;


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Liz Rykert's curator insight, April 13, 2014 10:46 AM

Love the insights generated by looking at existing systems and how one could apply or learn from how they function in a different context - rich with insight and ideas.

Eli Levine's curator insight, April 13, 2014 6:54 PM

Interesting.

 

Check it out.

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Noise induces explosive synchronization

We study explosive synchronization of network-coupled oscillators. Despite recent advances it remains unclear how robust explosive synchronization is in view of realistic structural and dynamical properties. Here we show that explosive synchronization can be induced simply by adding uncorrelated noise to the oscillators' frequencies, demonstrating it is not only robust to, but moreover promoted by, this natural mechanism. We support these results numerically and analytically, presenting simulations of a real neural network as well as a self consistency theory used to study synthetic networks.

 

Noise induces explosive synchronization
Per Sebastian Skardal, Alex Arenas

http://arxiv.org/abs/1404.0883


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Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks, and we focus in particular on ``simple" situations that are tractable analytically. We briefly motivate why examining dynamical systems on networks is interesting and important. We then give several fascinating examples and discuss some theoretical results. We also discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give our outlook on the field.

 

Dynamical Systems on Networks: A Tutorial
Mason A. Porter, James P. Gleeson

http://arxiv.org/abs/1403.7663


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Synchronicity and quantum entanglement - YouTube

On the trail of the dialogue by W. Pauli and C.G. Jung An even more neglected correspondence (1932-58) of the Nobel Prize winner and pioneer of quantum theor... (Synchronicity and quantum entanglement, W.

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Philippe Vallat's curator insight, April 6, 2014 3:35 AM

Always interesting to listen to open-minded and curious scientists

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Noise in biology

Noise permeates biology on all levels, from the most basic molecular, sub-cellular processes to the dynamics of tissues, organs, organisms and populations. The functional roles of noise in biological processes can vary greatly. Along with standard, entropy-increasing effects of producing random mutations, diversifying phenotypes in isogenic populations, limiting information capacity of signaling relays, it occasionally plays more surprising constructive roles by accelerating the pace of evolution, providing selective advantage in dynamic environments, enhancing intracellular transport of biomolecules and increasing information capacity of signaling pathways. This short review covers the recent progress in understanding mechanisms and effects of fluctuations in biological systems of different scales and the basic approaches to their mathematical modeling.

 

Lev S Tsimring 2014 Rep. Prog. Phys. 77 026601
http://dx.doi.org/10.1088/0034-4885/77/2/026601


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