Libros y Papers s...
1.4K views | +6 today
 Rescooped by Complejidady Economía from Papers onto Libros y Papers sobre Complejidad - Sistemas Complejos

# Virality Prediction and Community Structure in Social Networks

How does network structure affect diffusion? Recent studies suggest that the answer depends on the type of contagion. Complex contagions, unlike infectious diseases (simple contagions), are affected by social reinforcement and homophily.

Via Complexity Digest
No comment yet.

# Libros y Papers sobre Complejidad - Sistemas Complejos

Publicaciones sobre Complejidad y Sistemas Complejos
 Rescooped by Complejidady Economía from Non-Equilibrium Social Science

## Topics in social network analysis and network science

This chapter introduces statistical methods used in the analysis of social networks and in the rapidly evolving parallel-field of network science. Although several instances of social network analysis in health services research have appeared recently, the majority involve only the most basic methods and thus scratch the surface of what might be accomplished. Cutting-edge methods using relevant examples and illustrations in health services research are provided.

by A. James O'Malley, Jukka-Pekka Onnela

arXiv:1404.0067 [physics.soc-ph]

Via NESS
Eli Levine's curator insight,

A very cool and comprehensive look at how networks can be analyzed, studied and examined.

Way cool science!

 Rescooped by Complejidady Economía from Papers

## Towards a Methodology for Validation of Centrality Measures in Complex Networks

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

Via Complexity Digest
Liz Rykert's curator insight,

Love this stuff.

 Rescooped by Complejidady Economía from Complexity - Complex Systems Theory

## 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.

Via Bernard Ryefield
No comment yet.
 Rescooped by Complejidady Economía from Papers

## The Ecology of Collective Behavior

Similar patterns of interaction, such as network motifs and feedback loops, are used in many natural collective processes, probably because they have evolved independently under similar pressures. Here I consider how three environmental constraints may shape the evolution of collective behavior: the patchiness of resources, the operating costs of maintaining the interaction network that produces collective behavior, and the threat of rupture of the network. The ants are a large and successful taxon that have evolved in very diverse environments. Examples from ants provide a starting point for examining more generally the fit between the particular pattern of interaction that regulates activity, and the environment in which it functions.

Gordon DM (2014) The Ecology of Collective Behavior. PLoS Biol 12(3): e1001805. http://dx.doi.org/10.1371/journal.pbio.1001805

Via Complexity Digest
No comment yet.
 Rescooped by Complejidady Economía from Complexity in Education

## Complexity Theory and the Philosophy of Educatioin

Via Keith Hamon
Keith Hamon's curator insight,

An early collection of essays about the influence of complexity theory on education.

 Rescooped by Complejidady Economía from Non-Equilibrium Social Science

## An agent based decentralized matching macroeconomic model

In this paper we present a macroeconomic microfounded framework with heterogeneous agents—individuals, firms, banks—which interact through a decentralized matching process presenting common features across four markets—goods, labor, credit and deposit. We study the dynamics of the model by means of computer simulation. Some macroeconomic properties emerge such as endogenous business cycles, nominal GDP growth, unemployment rate fluctuations, the Phillips curve, leverage cycles and credit constraints, bank defaults and financial instability, and the importance of government as an acyclical sector which stabilize the economy. The model highlights that even extended crises can endogenously emerge. In these cases, the system may remain trapped in a large unemployment status, without the possibility to quickly recover unless an exogenous intervention takes place.

by Luca Riccetti, Alberto Russo, Mauro Gallegati

Via NESS
Eli Levine's curator insight,

"...the system may remain trapped in a large unemployment status, without the possibility to quickly recover unless an exogenous intervention takes place."

What the government should do, in times of financial crisis, is to bail out businesses and people rather than banks.  If people are guaranteed, the economy can carry on, while the banks can fail for their actions and be over taken by their smaller, less effected competitors.  It is society that is too large to fail, not a specific company or set of companies in the economy.

Also, funny how it is that those conservatives who love order and stability are so inclined to get rid of it for the sake of ideology and small-self greed.  Otherwise, they wouldn't be supporting government deregulation and a lack of social support, now would they?

 Rescooped by Complejidady Economía from Complexity - Complex Systems Theory

## Emergence of Criticality in the Transportation Passenger Flow: Scaling and Renormalization in the Seoul Bus System

Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) “block stop” and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

Via Bernard Ryefield
No comment yet.
 Rescooped by Complejidady Economía from Papers

## Information Evolution in Social Networks

Social networks readily transmit information, albeit with less than perfect fidelity. We present a large-scale measurement of this imperfect information copying mechanism by examining the dissemination and evolution of thousands of memes, collectively replicated hundreds of millions of times in the online social network Facebook. The information undergoes an evolutionary process that exhibits several regularities. A meme's mutation rate characterizes the population distribution of its variants, in accordance with the Yule process. Variants further apart in the diffusion cascade have greater edit distance, as would be expected in an iterative, imperfect replication process. Some text sequences can confer a replicative advantage; these sequences are abundant and transfer "laterally" between different memes. Subpopulations of the social network can preferentially transmit a specific variant of a meme if the variant matches their beliefs or culture. Understanding the mechanism driving change in diffusing information has important implications for how we interpret and harness the information that reaches us through our social networks.

Information Evolution in Social Networks

http://arxiv.org/abs/1402.6792

Via Complexity Digest
António F Fonseca's curator insight,

Memes are the information science counterpath of particles to physics.

 Rescooped by Complejidady Economía from Complexity - Complex Systems Theory

## PLOS ONE Complex systems articles

PLOS ONE: an inclusive, peer-reviewed, open-access resource from the PUBLIC LIBRARY OF SCIENCE. Reports of well-performed scientific studies from all disciplines freely available to the whole world.

Via Bryan Knowles, Bernard Ryefield
No comment yet.
 Rescooped by Complejidady Economía from Papers

## Zipf's Law for All the Natural Cities around the World

Two fundamental issues surrounding research on Zipf's law regarding city sizes are whether and why Zipf's law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf's law holds in a global setting, thus involving all cities around the world. Unlike previous studies, which have mainly relied on conventional census data, and census- bureau-imposed definitions of cities, we adopt naturally and objectively delineated cities, or natural cities, to be more precise, in order to examine Zipf's law. We find that Zipf's law holds remarkably well for all natural cities at the global level, and remains almost valid at the continental level except for Africa at certain time instants. We further examine the law at the country level, and note that Zipf's law is violated from country to country or from time to time. This violation is mainly due to our limitations; we are limited to individual countries, and to a static view on city-size distributions. The central argument of this paper is that Zipf's law is universal, and we therefore must use the correct scope in order to observe it. We further find that this law is reflected in the distribution of cities: the number of cities in individual countries follows an inverse power relationship; the number of cities in the first largest country is twice as many as that in the second largest country, three times as many as that in the third largest country, and so on.

Zipf's Law for All the Natural Cities around the World
Bin Jiang, Junjun Yin, Qingling Liu

http://arxiv.org/abs/1402.2965

Via Complexity Digest
António F Fonseca's curator insight,

This is a problem almost a century old, Zip's law was formulated in the 40's with English words.

 Rescooped by Complejidady Economía from Papers

## Damage spreading in spatial and small-world random Boolean networks

The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean networks (RBNs) are commonly used as a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other nonrandom connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the Hamming distance at very low connectivities ($\bar{K} << 1$) and that the critical connectivity of stability $\bar{K}$ changes compared to random networks. At higher $\bar{K}$, this scaling remains unchanged. We also show that the Hamming distance of spatially local networks scales with a power law as the system size $N$ increases, but with a different exponent for local and small-world networks. The scaling arguments for small-world networks are obtained with respect to the system sizes and strength of spatially local connections. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.

Qiming Lu and Christof Teuscher
Damage spreading in spatial and small-world random Boolean networks
Phys. Rev. E 89, 022806 (2014)

http://pre.aps.org/abstract/PRE/v89/i2/e022806

Via Complexity Digest
No comment yet.

## [1310.5360] A Bottom-Up Model of Self-Organized Criticality on Networks

Costas Bouyioukos's curator insight,

Potential groundbreaking findings!

 Rescooped by Complejidady Economía from Papers

## From Schelling to Schools

We address theoretically whether and under what conditions Schelling's celebrated result of 'self-organized' unintended residential segregation may also apply to school segregation. We propose here a computational model of school segregation that is aligned with a corresponding Schelling-type model of residential segregation. To adapt the model for application to school segregation, we move beyond previous work by combining two preference arguments in modeling parents' school choice, preferences for the ethnic composition of a school and preferences for minimizing the travelling distance to the school. In a set of computational experiments we assessed the effects of population composition and distance preferences in the school model. We found that a preference for nearby schools can suppress the trend towards self-organized segregation obtained in a baseline condition where parents were indifferent towards distance. We then investigated the joint effects of the variation of agents' 'tolerance' for out-group members and distance preference. We found that integrated distributions were preserved under a much broader range of conditions than in the absence of a preference for nearby schools. We conclude that parents' preferences for nearby schools may be an important factor in tempering for school choice the segregation dynamics known from models of residential segregation.

From Schelling to Schools: A Comparison of a Model of Residential Segregation with a Model of School Segregation

Victor Ionut Stoica and Andreas Flache

Journal of Artificial Societies and Social Simulation 17 (1) 5

Via Complexity Digest
Eli Levine's curator insight,

It appears as if racial segregation begins with where you live and are able to live.  This then helps to perpetuate misunderstandings, bigotry and biases against people from other racial, ethnic and social backgrounds than yourself in many individual cases across the human spectrum.

It's a shame that, even now, we're still so tribal, just like our chimp ancestors.

 Rescooped by Complejidady Economía from CxBooks

## The Social Face of Complexity Science: A Festschrift for Professor Peter M. Allen (by Mark Strathern & James McGlade)

 List Price: $49.95 Price:$47.45 You Save: $2.50 (5%) This work is to honour Professor Peter M. Allen, a seminal figure in the foundation and development of Complexity Science in human systems. From before the time of his joining Nobel Prize winner Ilya Progogine's pioneering group at the Université libre de Bruxelles in 1967 Peter had started publishing on what was then known as Prigogine theory in physics. But it was only after this that his own pioneering work in Complexity Science showed the importance of its applications in evolutionary and human sciences. Since then he has been an influential and guiding figure in this field. The works collected are by admiring colleagues, friends and collaborators, all leaders in their fields, influenced by his seminal ides, and gathered from across a gamut of fields in human systems. This makes this a valuable and unique work, a veritable reader in the influence Complex Systems theory on a wide and diverse range of fields; from archaeology, city design, international banking, economics, policy studies and more. Via Complexity Digest No comment yet.  Rescooped by Complejidady Economía from Papers ## Poverty, Disease, and the Ecology of Complex Systems Understanding why some human populations remain persistently poor remains a significant challenge for both the social and natural sciences. The extremely poor are generally reliant on their immediate natural resource base for subsistence and suffer high rates of mortality due to parasitic and infectious diseases. Economists have developed a range of models to explain persistent poverty, often characterized as poverty traps, but these rarely account for complex biophysical processes. In this Essay, we argue that by coupling insights from ecology and economics, we can begin to model and understand the complex dynamics that underlie the generation and maintenance of poverty traps, which can then be used to inform analyses and possible intervention policies. To illustrate the utility of this approach, we present a simple coupled model of infectious diseases and economic growth, where poverty traps emerge from nonlinear relationships determined by the number of pathogens in the system. These nonlinearities are comparable to those often incorporated into poverty trap models in the economics literature, but, importantly, here the mechanism is anchored in core ecological principles. Coupled models of this sort could be usefully developed in many economically important biophysical systems—such as agriculture, fisheries, nutrition, and land use change—to serve as foundations for deeper explorations of how fundamental ecological processes influence structural poverty and economic development. Ngonghala CN, Pluciński MM, Murray MB, Farmer PE, Barrett CB, et al. (2014) Poverty, Disease, and the Ecology of Complex Systems. PLoS Biol 12(4): e1001827. http://dx.doi.org/10.1371/journal.pbio.1001827 Via Complexity Digest Liz Rykert's curator insight, Essence of this work: In this Essay, we argue that by coupling insights from ecology and economics, we can begin to model and understand the complex dynamics that underlie the generation and maintenance of poverty traps, which can then be used to inform analyses and possible intervention policies. Important insights for cities....  Rescooped by Complejidady Economía from CxBooks ## Hypernetworks in the Science of Complex Systems (by Jeffrey Johnson) ### Hypernetworks in the Science of Complex Systems (Series on Complexity Science) ~ Jeffrey Johnson (author) More about this product  List Price:$128.00 Price: $107.98 You Save:$20.02 (16%)

The modern world is complex beyond human understanding and control. The science of complex systems aims to find new ways of thinking about the many interconnected networks of interaction that defy traditional approaches. Thus far, research into networks has largely been restricted to pairwise relationships represented by links between two nodes. This volume marks a major extension of networks to multidimensional hypernetworks for modeling multi-element relationships, such as companies making up the stock market, the neighborhoods forming a city, people making up committees, divisions making up companies, computers making up the internet, men and machines making up armies, or robots working as teams.

This volume makes an important contribution to the science of complex systems by:
(i) extending network theory to include dynamic relationships between many elements;
(ii) providing a mathematical theory able to integrate multilevel dynamics in a coherent way; (iii)
providing a new methodological approach to analyze complex systems; and
(iv) illustrating the theory with practical examples in the design, management and control of complex systems taken from many areas of application.

Via Complexity Digest
june holley's curator insight,

A little pricey but breakthrough stuff here...

 Rescooped by Complejidady Economía from Non-Equilibrium Social Science

## The Simple Rules of Social Contagion : Scientific Reports : Nature Publishing Group

It is commonly believed that information spreads between individuals like a pathogen, with each exposure by an informed friend potentially resulting in a naive individual becoming infected. However, empirical studies of social media suggest that individual response to repeated exposure to information is far more complex. As a proxy for intervention experiments, we compare user responses to multiple exposures on two different social media sites, Twitter and Digg. We show that the position of exposing messages on the user-interface strongly affects social contagion. Accounting for this visibility significantly simplifies the dynamics of social contagion. The likelihood an individual will spread information increases monotonically with exposure, while explicit feedback about how many friends have previously spread it increases the likelihood of a response. We provide a framework for unifying information visibility, divided attention, and explicit social feedback to predict the temporal dynamics of user behavior.

Via Shaolin Tan, NESS
No comment yet.
 Rescooped by Complejidady Economía from Complex World

## Resilience of Natural Gas Networks during Conflicts, Crises and Disruptions

Human conflict, geopolitical crises, terrorist attacks, and natural disasters can turn large parts of energy distribution networks offline. Europe's current gas supply network is largely dependent on deliveries from Russia and North Africa, creating vulnerabilities to social and political instabilities. During crises, less delivery may mean greater congestion, as the pipeline network is used in ways it has not been designed for. Given the importance of the security of natural gas supply, we develop a model to handle network congestion on various geographical scales. We offer a resilient response strategy to energy shortages and quantify its effectiveness for a variety of relevant scenarios. In essence, Europe's gas supply can be made robust even to major supply disruptions, if a fair distribution strategy is applied.

Via Claudia Mihai
No comment yet.
 Rescooped by Complejidady Economía from Papers

## Netconomics: Novel Forecasting Techniques from the Combination of Big Data, Network Science and Economics

The combination of the network theoretic approach with recently available abundant economic data leads to the development of novel analytic and computational tools for modelling and forecasting key economic indicators. The main idea is to introduce a topological component into the analysis, taking into account consistently all higher-order interactions. We present three basic methodologies to demonstrate different approaches to harness the resulting network gain. First, a multiple linear regression optimisation algorithm is used to generate a relational network between individual components of national balance of payment accounts. This model describes annual statistics with a high accuracy and delivers good forecasts for the majority of indicators. Second, an early-warning mechanism for global financial crises is presented, which combines network measures with standard economic indicators. From the analysis of the cross-border portfolio investment network of long-term debt securities, the proliferation of a wide range of over-the-counter-traded financial derivative products, such as credit default swaps, can be described in terms of gross-market values and notional outstanding amounts, which are associated with increased levels of market interdependence and systemic risk. Third, considering the flow-network of goods traded between G-20 economies, network statistics provide better proxies for key economic measures than conventional indicators. For example, it is shown that a country's gate-keeping potential, as a measure for local power, projects its annual change of GDP generally far better than the volume of its imports or exports.

Netconomics: Novel Forecasting Techniques from the Combination of Big Data, Network Science and Economics
Andreas Joseph, Irena Vodenska, Eugene Stanley, Guanrong Chen

http://arxiv.org/abs/1403.0848

Via Complexity Digest
Eli Levine's curator insight,

In other words, the more interconnected, bound of and valuable a bank is, the more likely that its failure will result in a global financial crisis.  These banks probably should be broken up, such that there are more nodes and less valuable interconnectivity amongst the banks.

The second part, in plain English, basically stated that a country's relative interconnectivity as a node in international trade and the strength of that interconnected trade are greater predictions of economic success than of simple net import/export data.

It seems to me that many political leaders and policy makers are not up to date with these latest insights.  This is probably how it is that we're getting the same unevolved, unadapted and negatively effective policies that are driving this country, and the world, into the ground.  On top of that, it's still not addressing our chief problem of being addicted to something that we don't really use and shouldn't really want in excess quantities (money), especially when it's purchased with the opportunity to be well, healthy and survivable as an individual and collective species.

It's sad that such a species with such potential should go to waste at this moment over a little ignorance and a very powerful attachment to something that has no bearing on our well being and actual quality of life.

 Rescooped by Complejidady Economía from Papers

## The Relative Ineffectiveness of Criminal Network Disruption

Researchers, policymakers and law enforcement agencies across the globe struggle to find effective strategies to control criminal networks. The effectiveness of disruption strategies is known to depend on both network topology and network resilience. However, as these criminal networks operate in secrecy, data-driven knowledge concerning the effectiveness of different criminal network disruption strategies is very limited. By combining computational modeling and social network analysis with unique criminal network intelligence data from the Dutch Police, we discovered, in contrast to common belief, that criminal networks might even become ‘stronger’, after targeted attacks. On the other hand increased efficiency within criminal networks decreases its internal security, thus offering opportunities for law enforcement agencies to target these networks more deliberately. Our results emphasize the importance of criminal network interventions at an early stage, before the network gets a chance to (re-)organize to maximum resilience. In the end disruption strategies force criminal networks to become more exposed, which causes successful network disruption to become a long-term effort.

The Relative Ineffectiveness of Criminal Network Disruption
Paul A. C. Duijn, Victor Kashirin & Peter M. A. Sloot

Scientific Reports 4, Article number: 4238 http://dx.doi.org/10.1038/srep04238 ;

Via Complexity Digest
Eli Levine's curator insight,

My only critique of this, is that even by successfully disrupting the social networks, you will ont get rid of the foundations of crime within a society.

Greed, lust, violence, all of these things come from the brain and can be seen as mental health problems, rather than necessarily just societal problems.  I think we've got to begin ori sorting th the convected and post conicted crowd, such tht we can understand how their brains work and then, how to help heal them, such that we eliminate criminality and crime inspited lifestyles.  I understand there are dozens of easy ways to be opposed to this and that there are dozes more ways th work (especially here, in america, where we are soc focused on our small "selves" to forget that there is a much much much much larger world out thre, and that of ourselves as well.  We are connected to everyone and everything.  That's science.  To deny that it is otherwise is to invite delusion and hallucinations about reality and to invite other problems into your life and the rest of ours for your deliberate ignorance and unwillingness to escape to where reality simply is unoffensive and not politically motivated other than to help other people.

Therefore, let's overcome this monkey need to punish people for crimes they really didn't have much say in (thankst o the primacy of the brain) and start doing some research on these people (even though they should be confined from the rest of the population until treatments and diagnoses have been developed and concluded upon).

 Rescooped by Complejidady Economía from Complexity - Complex Systems Theory

## PLOS ONE Nonlinear dynamics articles

PLOS ONE: an inclusive, peer-reviewed, open-access resource from the PUBLIC LIBRARY OF SCIENCE. Reports of well-performed scientific studies from all disciplines freely available to the whole world.

Via Bryan Knowles, Bernard Ryefield
No comment yet.
 Rescooped by Complejidady Economía from Complexity - Complex Systems Theory

## How to Save Human Lives with Complexity Science

We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are not effective and sufficient to contain them. The failure of many conventional approaches results from their neglection of feedback loops, instabilities and/or cascade effects, due to which equilibrium models do often not provide a good picture of the actual system behavior. However, the complex and often counter-intuitive behavior of social systems and their macro-level collective dynamics can be understood by means of complexity science, which enables one to address the aforementioned problems more successfully. We highlight that a suitable system design and management can help to stop undesirable cascade effects and to enable favorable kinds of self-organization in the system. In such a way, complexity science can help to save human lives.

Via Bernard Ryefield
No comment yet.
 Rescooped by Complejidady Economía from Papers

## Controlling Chaos Faster

Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original Predictive Feedback Control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.

Controlling Chaos Faster
Christian Bick, Christoph Kolodziejski, Marc Timme

http://arxiv.org/abs/1402.4763

Via Complexity Digest
No comment yet.
 Rescooped by Complejidady Economía from Papers

## The complex architecture of primes and natural numbers

Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cram\'er's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cram\'er's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help not only to conjecture but also to prove results about primes and the complex architecture of natural numbers.

The complex architecture of primes and natural numbers
Guillermo Garcia-Perez, M. Angeles Serrano, Marian Boguna

http://arxiv.org/abs/1402.3612

Via Complexity Digest
No comment yet.