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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 | Complex World | Scoop.it

Discovering the large-scale topological features in empirical networks is a crucial tool in understanding how complex systems function. However most existing methods used to obtain the modular structure of networks suffer from serious problems, such as the resolution limit on the size of communities, where smaller but well-defined clusters are not detectable when the network becomes large. This phenomenon occurs for the very popular approach of modularity optimization, but also for more principled ones based on statistical inference and model selection. Here we construct a nested generative model which, through a complete description of the entire network hierarchy at multiple scales, is capable of avoiding this limitation, and enables the detection of modular structure at levels far beyond those possible by current approaches. Even with this increased resolution, the method is based on the principle of parsimony, and is capable of separating signal from noise, and thus will not lead to the identification of spurious modules even on sparse networks. Furthermore, it fully generalizes other approaches in that it is not restricted to purely assortative mixing patterns, directed or undirected graphs, and ad hoc hierarchical structures such as binary trees. Despite its general character, the approach is tractable, and can be combined with advanced techniques of community detection to yield an efficient algorithm which scales well for very large networks.

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Complex World
Cutting Edge Research about Complex Systems
Curated by Claudia Mihai
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Are we in danger of losing control of technology?

Are we in danger of losing control of technology? | Complex World | Scoop.it
AI expert Dr Rasmussen from the University of South Denmark has warned of the rise of technology. Companies like Facebook and Google could rob us of our identity (stock image shown)
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How Academia Resembles a Drug Gang

How Academia Resembles a Drug Gang | Complex World | Scoop.it
Academic systems rely on the existence of a supply of “outsiders” ready to forgo wages and employment security in exchange for the prospect of uncertain security, prestige, freedom and reasonably h...
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Credit Default Swaps networks and systemic risk

Credit Default Swaps networks and systemic risk | Complex World | Scoop.it
Credit Default Swaps (CDS) spreads should reflect default risk of the underlying corporate debt. Actually, it has been recognized that CDS spread time series did not anticipate but only followed the increasing risk of default before the financial crisis. In principle, the network of correlations among CDS spread time series could at least display some form of structural change to be used as an early warning of systemic risk. Here we study a set of 176 CDS time series of financial institutions from 2002 to 2011. Networks are constructed in various ways, some of which display structural change at the onset of the credit crisis of 2008, but never before. By taking these networks as a proxy of interdependencies among financial institutions, we run stress-test based on Group DebtRank. Systemic risk before 2008 increases only when incorporating a macroeconomic indicator reflecting the potential losses of financial assets associated with house prices in the US. This approach indicates a promising way to detect systemic instabilities.
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How Wikipedia Data Is Revolutionizing Flu Forecasting | MIT Technology Review

How Wikipedia Data Is Revolutionizing Flu Forecasting | MIT Technology Review | Complex World | Scoop.it
Epidemiologist want to forecast disease like meteorologists forecast rain. And the way people browse Wikipedia could be the key, they say.
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The Scientific Impact of Nations

The Scientific Impact of Nations | Complex World | Scoop.it

International collaboration is becoming increasingly important for the advancement of science. To gain a more precise understanding of how factors such as international collaboration influence publication success, we divide publication success into two categories: journal placement and citation performance. Analyzing all papers published between 1996 and 2012 in eight disciplines, we find that those with more countries in their affiliations performed better in both categories. Furthermore, specific countries vary in their effects both individually and in combination. Finally, we look at the relationship between national output (in papers published) and input (in citations received) over the 17 years, expanding upon prior depictions by also plotting an expected proportion of citations based on Journal Placement. Discrepancies between this expectation and the realized proportion of citations illuminate trends in performance, such as the decline of the Global North in response to rapidly developing countries, especially China. Yet, most countries' show little to no discrepancy, meaning that, in most cases, citation proportion can be predicted by Journal Placement alone. This reveals an extreme asymmetry between the opinions of a few reviewers and the degree to which paper acceptance and citation rates influence career advancement.

 
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Network Theory Reveals The Hidden Link Between Trade And Military Alliances That Leads to Conflict-Free Stability

Network Theory Reveals The Hidden Link Between Trade And Military Alliances That Leads to Conflict-Free Stability | Complex World | Scoop.it
The first game-theoretical study of military alliances shows that they cannot alone lead to global stability.

The study of modern history is currently undergoing a revolution. That is largely because historians are beginning to apply the ideas in network theory to the complex interactions that have forged our past.

There was a time when historians focused largely on events as the be all and end all of history. But in recent years, there has been a growing understanding that a complex network of links, alliances, trade agreements and so on play a hugely important role in creating an environment in which conflict (or peace) can spread.

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Snowflake-shaped networks are easiest to mend

Snowflake-shaped networks are easiest to mend | Complex World | Scoop.it
Power grids and other networks with the branching quality of snowflakes are easiest to fix when damaged links can't simply be restored in the same place
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Explaining the Power-law Distribution of Human Mobility Through Transportation Modality Decomposition

Explaining the Power-law Distribution of Human Mobility Through Transportation Modality Decomposition | Complex World | Scoop.it

Human mobility has been empirically observed to exhibit Levy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Levy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. We show that
human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Levy Walk patterns that characterize human mobility patterns.

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Punctuated Equilibrium in the Large Scale Evolution of Programming Languages

Punctuated Equilibrium in the Large Scale Evolution of Programming Languages | Complex World | Scoop.it

The analogies and differences between biological and cultural evolution have been explored by evolutionary biologists, historians, engineers and linguists alike. Two well known domains of cultural change are language and technology. Both share some traits relating the evolution of species, but technological change is very difficult to study. A major challenge in our way towards a scientific theory of technological evolution is how to properly define evolutionary trees or clades and how to weight the role played by horizontal transfer of information. Here we study the large scale historical development of programming languages, which have deeply marked social and technological advances in the last half century. We analyse their historical connections using network theory and reconstructed phylogenetic networks. Using both data analysis and network modelling, it is shown that their evolution is highly uneven, marked by innovation events where new languages are created out of improved combinations of different structural components belonging
to previous languages. These radiation events occur in a bursty pattern and are tied to novel technological and social niches. The method can be extrapolated to other systems and consistently captures the major classes of languages and the widespread horizontal design exchanges, revealing a punctuated evolutionary path.

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Bayesian Inference of Natural Rankings in Incomplete Competition Networks

Bayesian Inference of Natural Rankings in Incomplete Competition Networks | Complex World | Scoop.it
Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest - essential in determining reward and penalty - is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the [ldquo]Natural Ranking,[rdquo] an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks.
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The small-world effect is a modern phenomenon

The small-world effect is a modern phenomenon | Complex World | Scoop.it

The "small-world effect" is the observation that one can find a short chain of acquaintances, often of no more than a handful of individuals, connecting almost any two people on the planet. It is often expressed in the language of networks, where it is equivalent to the statement that most pairs of individuals are connected by a short path through the acquaintance network. Although the small-world effect is well-established empirically for contemporary social networks, we argue here that it is a relatively recent phenomenon, arising only in the last few hundred years: for most of mankind's tenure on Earth the social world was large, with most pairs of individuals connected by relatively long chains of acquaintances, if at all. Our conclusions are based on observations about the spread of diseases, which travel over contact networks between individuals and whose dynamics can give us clues to the structure of those networks even when direct network measurements are not available. As an example we consider the spread of the Black Death in 14th-century Europe, which is known to have traveled across the continent in well-defined waves of infection over the course of several years. Using established epidemiological models, we show that such wave-like behavior can occur only if contacts between individuals living far apart are exponentially rare. We further show that if long-distance contacts are exponentially rare, then the shortest chain of contacts between distant individuals is on average a long one. The observation of the wave-like spread of a disease like the Black Death thus implies a network without the small-world effect.

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Sand Pile Model of the Mind Grows in Popularity

Sand Pile Model of the Mind Grows in Popularity | Complex World | Scoop.it
Support is growing for a decades-old physics idea suggesting that localized episodes of disordered brain activity help keep the overall system in healthy balance
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Even online, you can't have more than 150 friends

Even online, you can't have more than 150 friends | Complex World | Scoop.it
Sci-fi game allows researchers to test the limits of our human relationships
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Underestimating extreme events in power-law behavior due to machine-dependent cutoffs

Underestimating extreme events in power-law behavior due to machine-dependent cutoffs | Complex World | Scoop.it
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law distributions. The task is usually performed through standard methods that map uniform random variates into the desired probability space. Whereas all these algorithms are theoretically solid, in this paper we show that they are subject to severe machine-dependent limitations. As a result, two dramatic consequences arise: (i) the sampling in the tail of the distribution is not random but deterministic; (ii) the moments of the sample distribution, which are theoretically expected to diverge as functions of the sample sizes, converge instead to finite values. We provide quantitative indications for the range of distribution parameters that can be safely handled by standard libraries used in computational analyses. Whereas our findings indicate possible reinterpretations of numerical results obtained through flawed sampling methodologies, they also pave the way for the search for a concrete solution to this central issue shared by all quantitative sciences dealing with complexity.
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Twitter usage reveals ebbs and flows of life in NYC

Twitter usage reveals ebbs and flows of life in NYC | Complex World | Scoop.it

Social media data could be used to design more efficient cities.

Next time you’re in New York City and wondering where the party’s at, or if you’re going to get stuck on 8th Avenue in traffic from the Rangers’ game, you might do well to consult an unlikely ally: Twitter. Scientists have analyzed 6 million geolocated, time-stamped tweets from New York City and the surrounding area and discovered a “heartbeat” that says a lot about how New Yorkers live

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Can Government Be Self-Organized? A Mathematical Model of the Collective Social Organization of Ancient Teotihuacan, Central Mexico

Can Government Be Self-Organized? A Mathematical Model of the Collective Social Organization of Ancient Teotihuacan, Central Mexico | Complex World | Scoop.it

Teotihuacan was the first urban civilization of Mesoamerica and one of the largest of the ancient world. Following a tradition in archaeology to equate social complexity with centralized hierarchy, it is widely believed that the city’s origin and growth was controlled by a lineage of powerful individuals. However, much data is indicative of a government of co-rulers, and artistic traditions expressed an egalitarian ideology. Yet this alternative keeps being marginalized because the problems of collective action make it difficult to conceive how such a coalition could have functioned in principle. We therefore devised a mathematical model of the city’s hypothetical network of representatives as a formal proof of concept that widespread cooperation was realizable in a fully distributed manner. In the model, decisions become self-organized into globally optimal configurations even though local representatives behave and modify their relations in a rational and selfish manner. This self-optimization crucially depends on occasional communal interruptions of normal activity, and it is impeded when sections of the network are too independent. We relate these insights to theories about community-wide rituals at Teotihuacan and the city’s eventual disintegration.

 

Froese, T., Gershenson, C., and Manzanilla, L. R. (2014). Can government be self-organized? a mathematical model of the collective social organization of ancient teotihuacan, central mexico.PLoS ONE 9 (10) (10): e109966.


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Memory effect of the online user preference

Memory effect of the online user preference | Complex World | Scoop.it
The mechanism of the online user preference evolution is of great significance for understanding the online user behaviors and improving the quality of online services. Since users are allowed to rate on objects in many online systems, ratings can well reflect the users' preference. With two benchmark datasets from online systems, we uncover the memory effect in users' selecting behavior which is the sequence of qualities of selected objects and the rating behavior which is the sequence of ratings delivered by each user. Furthermore, the memory duration is presented to describe the length of a memory, which exhibits the power-law distribution, i.e., the probability of the occurring of long-duration memory is much higher than that of the random case which follows the exponential distribution. We present a preference model in which a Markovian process is utilized to describe the users' selecting behavior, and the rating behavior depends on the selecting behavior. With only one parameter for each of the user's selecting and rating behavior, the preference model could regenerate any duration distribution ranging from the power-law form (strong memory) to the exponential form (weak memory).
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​There Are Only Four Types of City in the World, Says Math

​There Are Only Four Types of City in the World, Says Math | Complex World | Scoop.it
Physicists discover that Brooklyn has a touch of Brussels and that Buenos Aires is in a class all its own.

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Network-based statistical comparison of citation topology of bibliographic databases

Network-based statistical comparison of citation topology of bibliographic databases | Complex World | Scoop.it
Modern bibliographic databases provide the basis for scientific research and its evaluation. While their content and structure differ substantially, there exist only informal notions on their reliability. Here we compare the topological consistency of citation networks extracted from six popular bibliographic databases including Web of Science, CiteSeer and arXiv.org. The networks are assessed through a rich set of local and global graph statistics. We first reveal statistically significant inconsistencies between some of the databases with respect to individual statistics. For example, the introduced field bow-tie decomposition of DBLP Computer Science Bibliography substantially differs from the rest due to the coverage of the database, while the citation information within arXiv.org is the most exhaustive. Finally, we compare the databases over multiple graph statistics using the critical difference diagram. The citation topology of DBLP Computer Science Bibliography is the least consistent with the rest, while, not surprisingly, Web of Science is significantly more reliable from the perspective of consistency. This work can serve either as a reference for scholars in bibliometrics and scientometrics or a scientific evaluation guideline for governments and research agencies.
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Scientists Cannot Explain This Crazy Ant Behavior, but They Love It

Scientists Cannot Explain This Crazy Ant Behavior, but They Love It | Complex World | Scoop.it
Watch as this colony forms a daisy chain to pull a millipede—a behavior researchers have never seen before.
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Percolation and cooperation with mobile agents: Geometric and strategy clusters

Percolation and cooperation with mobile agents: Geometric and strategy clusters | Complex World | Scoop.it
We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius ${r}_{P}$, which accounts for the population viscosity, and an interaction radius ${r}_{\mathrm{int}}$, which defines the instantaneous contact network for the game dynamics. We show that, differently from the ${r}_{P}=0$ case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.
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Controlling extreme events on complex networks

Controlling extreme events on complex networks | Complex World | Scoop.it
Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network [ldquo]mobile[rdquo] can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.
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Scaling of Chaos versus Periodicity: How Certain is it that an Attractor is Chaotic?

Scaling of Chaos versus Periodicity: How Certain is it that an Attractor is Chaotic? | Complex World | Scoop.it
A small perturbation in a system's parameter can convert its attractor from chaotic to periodic, where the probability of obtaining a chaotic regime scales as a power law with respect to the perturbation size.
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A Brazilian Wunderkind Who Calms Chaos

A Brazilian Wunderkind Who Calms Chaos | Complex World | Scoop.it
Artur Avila’s solutions to ubiquitous problems in chaos theory have “changed the face of the field,” earning him Brazil’s first Fields Medal.
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