Statistical physics is the natural framework to model complex networks. In the last twenty years, it has brought novel physical insights on a variety of emergent phenomena, such as self-organisation, scale invariance, mixed distributions and ensemble non-equivalence, which cannot be deduced from the behaviour of the individual constituents. At the same time, thanks to its deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models reproducing some features of empirical networks, but otherwise as random as possible. We review here the statistical physics approach for complex networks and the null models for the various physical problems, focusing in particular on the analytic frameworks reproducing the local features of the network. We show how these models have been used to detect statistically significant and predictive structural patterns in real-world networks, as well as to reconstruct the network structure in case of incomplete information. We further survey the statistical physics frameworks that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, and the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes.
Comments: To appear on Nature Reviews Physics. The revised accepted version will be posted 6 months after publication
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
h/t Disconnected, fragmented, or united? a trans-disciplinary review of network science by César A. Hidalgo (Applied Network Science | SpringerLink)
During decades the study of networks has been divided between the efforts of social scientists and natural scientists, two groups of scholars who often do not see eye to eye. In this review I present an effort to mutually translate the work conducted by scholars from both of these academic fronts hoping to continue to unify what has become a diverging body of literature. I argue that social and natural scientists fail to see eye to eye because they have diverging academic goals. Social scientists focus on explaining how context specific social and economic mechanisms drive the structure of networks and on how networks shape social and economic outcomes. By contrast, natural scientists focus primarily on modeling network characteristics that are independent of context, since their focus is to identify universal characteristics of systems instead of context specific mechanisms. In the following pages I discuss the differences between both of these literatures by summarizing the parallel theories advanced to explain link formation and the applications used by scholars in each field to justify their approach to network science. I conclude by providing an outlook on how these literatures can be further unified.
Highlights, Quotes, Annotations, & Marginalia
Social scientists focus on explaining how context specific social and economic mechanisms drive the structure of networks and on how networks shape social and economic outcomes. By contrast, natural scientists focus primarily on modeling network characteristics that are independent of context, since their focus is to identify universal characteristics of systems instead of context specific mechanisms. ❧
August 25, 2018 at 10:18PM
Science and Complexity (Weaver 1948); explained the three eras that according to him defined the history of science. These were the era of simplicity, disorganized complexity, and organized complexity. In the eyes of Weaver what separated these three eras was the development of mathematical tools allowing scholars to describe systems of increasing complexity. ❧
August 25, 2018 at 10:19PM
Problems of disorganized complexity are problems that can be described using averages and distributions, and that do not depend on the identity of the elements involved in a system, or their precise patterns of interactions. A classic example of a problem of disorganized complexity is the statistical mechanics of Ludwig Boltzmann, James-Clerk Maxwell, and Willard Gibbs, which focuses on the properties of gases. ❧
August 25, 2018 at 10:20PM
Soon after Weaver’s paper, biologists like Francois Jacob (Jacob and Monod 1961), (Jacob et al. 1963) and Stuart Kaufmann (Kauffman 1969), developed the idea of regulatory networks. Mathematicians like Paul Erdos and Alfred Renyi, advanced graph theory (Erdős and Rényi 1960) while Benoit Mandelbrot worked on Fractals (Mandelbrot and Van Ness 1968), (Mandelbrot 1982). Economists like Thomas Schelling (Schelling 1960) and Wasily Leontief (Leontief 1936), (Leontief 1936), respectively explored self-organization and input-output networks. Sociologists, like Harrison White (Lorrain and White 1971) and Mark Granovetter (Granovetter 1985), explored social networks, while psychologists like Stanley Milgram (Travers and Milgram 1969) explored the now famous small world problem. ❧
Some excellent references
August 25, 2018 at 10:24PM
First, I will focus in these larger groups because reviews that transcend the boundary between the social and natural sciences are rare, but I believe them to be valuable. One such review is Borgatti et al. (2009), which compares the network science of natural and social sciences arriving at a similar conclusion to the one I arrived. ❧
August 25, 2018 at 10:27PM
Links are the essence of networks. So I will start this review by comparing the mechanisms used by natural and social scientists to explain link formation. ❧
August 25, 2018 at 10:32PM
When connecting the people that acted in the same movie, natural scientists do not differentiate between people in leading or supporting roles. ❧
But they should because it’s not often the case that these are relevant unless they are represented by the same agent or agency.
August 25, 2018 at 10:51PM
For instance, in the study of mobile phone networks, the frequency and length of interactions has often been used as measures of link weight (Onnela et al. 2007), (Hidalgo and Rodriguez-Sickert 1008), (Miritello et al. 2011). ❧
And they probably shouldn’t because typically different levels of people are making these decisions. Studio brass and producers typically have more to say about the lead roles and don’t care as much about the smaller ones which are overseen by casting directors or sometimes the producers. The only person who has oversight of all of them is the director, and even then they may quit caring at some point.
August 25, 2018 at 10:52PM
Social scientists explain link formation through two families of mechanisms; one that finds it roots in sociology and the other one in economics. The sociological approach assumes that link formation is connected to the characteristics of individuals and their context. Chief examples of the sociological approach include what I will call the big three sociological link-formation hypotheses. These are: shared social foci, triadic closure, and homophily. ❧
August 25, 2018 at 10:55PM
The social foci hypothesis predicts that links are more likely to form among individuals who, for example, are classmates, co-workers, or go to the same gym (they share a social foci). The triadic closure hypothesis predicts that links are more likely to form among individuals that share “friends” or acquaintances. Finally, the homophily hypothesis predicts that links are more likely to form among individuals who share social characteristics, such as tastes, cultural background, or physical appearance (Lazarsfeld and Merton 1954), (McPherson et al. 2001). ❧
definitions of social foci, triadic closure, and homophily within network science.
August 26, 2018 at 11:39AM
Yet, strategic games look for equilibrium in the formation and dissolution of ties in the context of the game theory advanced first by (Von Neumann et al. 2007), and later by (Nash 1950). ❧
August 25, 2018 at 10:58PM
Preferential attachment is the idea that connectivity begets connectivity. ❧
August 25, 2018 at 10:59PM
Preferential attachment is an idea advanced originally by the statisticians John Willis and Udny Yule in (Willis and Yule 1922), but has been rediscovered numerous times during the twentieth century. ❧
August 25, 2018 at 11:00PM
Rediscoveries of this idea in the twentieth century include the work of (Simon 1955) (who did cite Yule), (Merton 1968), (Price 1976) (who studied citation networks), and (Barabási and Albert 1999), who published the modern reference for this model, which is now widely known as the Barabasi-Albert model. ❧
August 25, 2018 at 11:01PM
preferential attachment. In the eyes of the social sciences, however, understanding which of all of these hypotheses drives the formation of the network is what one needs to explore. ❧
For example what drives attachment of political candidates?
August 26, 2018 at 08:15AM
Finally it is worth noting that trust, through the theory of social capital, has been connected with long-term economic growth—even though these results are based on regressions using extremely sparse datasets. ❧
And this is an example of how Trump is hurting the economy.
August 26, 2018 at 08:33AM
Nevertheless, the evidence suggests that social capital and social institutions are significant predictors of economic growth, after controlling for the effects of human capital and initial levels of income (Knack and Keefer 1997), (Knack 2002).4 So trust is a relevant dimension of social interactions that has been connected to individual dyads, network formation, labor markets, and even economic growth. ❧
August 26, 2018 at 08:35AM
Social scientist, on the other hand, have focused on what ties are more likely to bring in new information, which are primarily weak ties (Granovetter 1973), and on why weak ties bring new information (because they bridge structural holes (Burt 2001), (Burt 2005)). ❧
August 26, 2018 at 09:45AM
heterogeneous networks have been found to be effective promoters of the evolution of cooperation, since there are advantages to being a cooperator when you are a hub, and hubs tend to stabilize networks in equilibriums where levels of cooperation are high (Ohtsuki et al. 2006), (Pacheco et al. 2006), (Lieberman et al. 2005), (Santos and Pacheco 2005). ❧
August 26, 2018 at 09:49AM
These results, however, have also been challenged by human experiments finding no such effect (Gracia-Lázaro et al. 2012). The study of cooperation in networks has also been performed in dynamic settings, where individuals are allowed to cut ties (Wang et al. 2012), promoting cooperation, and are faced with different levels of knowledge about the reputation of peers in their network (Gallo and Yan 2015). Moreover, cooperating behavior has seen to spread when people change the networks where they participate in (Fowler and Christakis 2010). ❧
August 26, 2018 at 09:50AM
Given the statement he makes I honestly wonder if he’s considered taking Malcolm Gladwell’s advice about where to best focus his money for the best outcome based on statistical mechanics–particularly given his stated background?
I once taught an 8 am college class. So many grandparents died that semester. I then moved my class to 3 pm. No more deaths. And that, my friends, is how I save lives.— Viorica Marian (@VioricaMarian1) May 5, 2018
I wonder what a statistical analysis would do to improve peoples’ lives if registrars attempted to put the mass of classes in the middle of the day? Would educational outcomes improve along with peoples’ psyches? Many schedulers are trying to maximize based on the scarcity of classroom resources. What if they maximized on mental health and classroom performance? Is classroom scheduling potentially a valuable public health tool?
In 1984, Elvis Costello released what he would say later was his worst record: Goodbye Cruel World. Among the most discordant songs on the album was the forgettable “The Deportees Club.” But then, years later, Costello went back and re-recorded it as “Deportee,” and today it stands as one of his most sublime achievements.
“Hallelujah” is about the role that time and iteration play in the production of genius, and how some of the most memorable works of art had modest and undistinguished births.
And here I thought I knew a lot about the story of Hallelujah. I haven’t read any of the books on its history, nor written any myself, but this short story does have a good bit I’ve not heard before in the past. I did read quite a bit when Cohen passed away, and even spent some time making a Spotify playlist with over five hours of covers.
The bigger idea here of immediate genius versus “slow cooked” genius is the fun one to contemplate. I’ve previously heard stories about Mozart’s composing involved his working things out in his head and then later putting them on paper much the same way that a “cow pees” (i.e. all in one quick go or a fast flood.)
Another interesting thing I find here is the insanely small probability that the chain of events that makes the song popular actually happens. It seems worthwhile to look at the statistical mechanics of the production of genius. Perhaps applying Ridley’s concepts of “Ideas having sex” and Dawkin’s “meme theory” (aka selfish gene) could be interestingly useful. What does the state space of genius look like?
In the early ’90s, Hank Rowan gave $100 million to a university in New Jersey, an act of extraordinary generosity that helped launch the greatest explosion in educational philanthropy since the days of Andrew Carnegie and the Rockefellers. But Rowan gave his money to Glassboro State University, a tiny, almost bankrupt school in South Jersey, while almost all of the philanthropists who followed his lead made their donations to elite schools such as Harvard and Yale. Why did no one follow Rowan’s example?
“My Little Hundred Million” is the third part of Revisionist History’s educational miniseries. It looks at the hidden ideologies behind giving and how a strange set of ideas has hijacked educational philanthropy.
The key idea laid out stunningly here is strong links versus weak links.
I’m generally flabbergasted by the general idea proposed here and will have to do some more research in the near future to play around further with the ideas presented. Fortunately, in addition to the education specific idea presented, Gladwell also comes up with an additional few examples in sports by using the differences between soccer and basketball to show the subtle differences.
If he and his lab aren’t aware of the general concept, I would recommend this particular podcast and the concept of strong and weak links to César Hidalgo (t) who might actually have some troves of economics data to use to play around with some general modeling to expand upon these ideas. I’ve been generally enamored of Hidalgo’s general thesis about the overall value of links as expressed in Why Information Grows: The Evolution of Order, from Atoms to Economies1. I often think of it with relation to political economies and how the current administration seems to be (often quietly) destroying large amounts of value by breaking down a variety of economic, social, and political links within the United States as well as between our country and others.
I wonder if the additional ideas about the differences between strong and weak links might further improve these broader ideas. The general ideas behind statistical mechanics and statistics make me think that Gladwell, like Hidalgo, is certainly onto a strong idea which can be continued to be refined to improve billions of lives. I’ll have to start some literature searches now…
Carlos is a brilliant student from South Los Angeles. He attends an exclusive private school on an academic scholarship. He is the kind of person the American meritocracy is supposed to reward. But in the hidden details of his life lies a cautionary tale about how hard it is to rise from the bottom to the top—and why the American school system, despite its best efforts, continues to leave an extraordinary amount of talent on the table.
Eric Eisner and students from his YES Program featured above. Photo credit: David Lauridsen and Los Angeles Magazine “Carlos Doesn’t Remember” is the first in a three-part Revisionist History miniseries taking a critical look at the idea of capitalization—the measure of how well America is making use of its human potential.
Certainly a stunning episode! Some of this is just painful to hear though.
We should easily be able to make things simpler, fairer, and more resilient for a lot of the poor we’re overlooking in society. As a larger group competing against other countries, we’re heavily undervaluing a major portion of our populace, and we’re going to need them just to keep pace. America can’t be the “greatest” country without them.
This article provides answers to the two questions posed in the title. It is argued that, contrary to many statements made in the literature, neither entropy, nor the Second Law may be used for the entire universe. The origin of this misuse of entropy and the second law may be traced back to Clausius himself. More resent (erroneous) justification is also discussed.
The Santa Fe Institute, in New Mexico, is a place for studying complex systems. I’ve never been there! Next week I’ll go there to give a colloquium on network theory, and also to participate in this workshop.
I just found out about this from John Carlos Baez and wish I could go! How have I not managed to have heard about it?
Syndicated copies to:
November 16, 2016 – November 18, 2016
Noyce Conference Room
This workshop will address a fundamental question in theoretical biology: Does the relationship between statistical physics and the need of biological systems to process information underpin some of their deepest features? It recognizes that a core feature of biological systems is that they acquire, store and process information (i.e., perform computation). However to manipulate information in this way they require a steady flux of free energy from their environments. These two, inter-related attributes of biological systems are often taken for granted; they are not part of standard analyses of either the homeostasis or the evolution of biological systems. In this workshop we aim to fill in this major gap in our understanding of biological systems, by gaining deeper insight in the relation between the need for biological systems to process information and the free energy they need to pay for that processing.
The goal of this workshop is to address these issues by focusing on a set three specific question:
- How has the fraction of free energy flux on earth that is used by biological computation changed with time?;
- What is the free energy cost of biological computation / function?;
- What is the free energy cost of the evolution of biological computation / function.
In all of these cases we are interested in the fundamental limits that the laws of physics impose on various aspects of living systems as expressed by these three questions.
Purpose: Research Collaboration
SFI Host: David Krakauer, Michael Lachmann, Manfred Laubichler, Peter Stadler, and David Wolpert
I ran across a link to this textbook by way of a standing Google alert, and was excited to check it out. I was immediately disappointed to think that I would have to wait another month and change for the physical textbook to be released, but made my pre-order directly. Then with a bit of digging around, I realized that individual chapters are available immediately to quench my thirst until the physical text is printed next month.
If you’re not already doing so, you should follow Barabási on Twitter.
Syndicated copies to:
— Laszlo Barabasi (@barabasi) August 3, 2016
Went on vacation or fell asleep at the internet wheel this week? Here’s some of the interesting stuff you missed.
Science & Math
- Context Specific and Differential Gene Co-expression Networks via Bayesian Biclustering | PLOS Computational Biology
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- The Water Kingdom: A Secret History of China by Philip Ball (review)
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- One-sentence proof of Fermat’s theorem on sums of two squares | Fermat’s Library
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- *Disconnected, fragmented, or united? a trans-disciplinary review of network
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- What is a “Neutral Network” Anyway? An Exploration and Rediscovery of the Aims of Net Neutrality in Theory and Practice
- The Brachistochrone Curve: The Problem of Quickest Descent | Fermat’s Library
- In what sense is Quantum Mechanics a theory of information? | Quora
- Major transitions in information technology | Philosophical Transactions of
- Human brain mapped in unprecedented detail: Nearly 100 previously unidentified brain areas revealed by examination of the cerebral cortex. | Nature
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- How a Guy From a Montana Trailer Park Overturned 150 Years of Biology | The Atlantic
- People can sense single photons | Nature News & Comment
- Defining synergy thermodynamically using quantitative measurements of entropy and free energy
- A Prime Case of Chaos | AMS.org
- Murray Gell-Mann (video interviews) – YouTube
- Mathematics & Chalk: A teary goodbye to Hagomoro | Jeremy Kun
- Want to Change Academic Publishing? Just Say No | Chronicle
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Indieweb, Internet, Identity, Blogging, Social Media
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Information is a precise concept that can be defined mathematically, but its relationship to what we call "knowledge" is not always made clear. Furthermore, the concepts "entropy" and "information", while deeply related, are distinct and must be used with care, something that is not always achieved in the literature. In this elementary introduction, the concepts of entropy and information are laid out one by one, explained intuitively, but defined rigorously. I argue that a proper understanding of information in terms of prediction is key to a number of disciplines beyond engineering, such as physics and biology.
A proper understanding of information in terms of prediction is key to a number of disciplines beyond engineering, such as physics and biology.
Comments: 19 pages, 2 figures. To appear in Philosophical Transaction of the Royal Society A
Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Information Theory (cs.IT); Biological Physics (physics.bio-ph); Quantitative Methods (q-bio.QM)
Cite as:arXiv:1601.06176 [nlin.AO] (or arXiv:1601.06176v1 [nlin.AO] for this version)