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Faster Adaptation in Smaller Populations: Counterintuitive Evolution of HIV during Childhood Infection

Since some common approaches to the study of molecular adaptation may not be optimal for answering questions regarding within-host virus evolution, we have developed an alternative approach that estimates an absolute rate of molecular adaptation from serially-sampled viral populations. Here, we extend this framework to include sampling error when estimating the rate of adaptation, which is an important addition when analyzing historical data sets obtained in the pre-HAART era, for which the number of sequences per time point is often limited. We applied this extended method to a cohort of 24 pediatric HIV-1 patients and discovered that viral adaptation is strongly associated with the rate of disease progression, which is in contrast to previous analyses of these data that did not find a significant association. Strikingly, this results in a negative relationship between the rate of viral adaptation and viral population size, which is unexpected under standard micro-evolutionary models since larger populations are predicted to fix more mutations per unit time than smaller populations. Our findings indicate that the negative correlation is unlikely to be driven by relaxation of selective constraint, but instead by significant variation in host immune responses. Consequently, this supports a previously proposed non-linear model of viral adaptation in which host immunity imposes counteracting effects on population size and selection.


Raghwani J, Bhatt S, Pybus OG (2016) Faster Adaptation in Smaller Populations: Counterintuitive Evolution of HIV during Childhood Infection. PLoS Comput Biol 12(1): e1004694. http://dx.doi.org/10.1371/journal.pcbi.1004694 ;

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The angular nature of road networks

Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore, spatially constrained, to fully understand the role that each road plays in the system it is fundamental to characterize the influence that geometrical properties have over the network's behaviour. In this work, we percolate the UK's road network using the relative angle between street segments as the occupation probability. We argue that road networks undergo a non-equilibrium first-order phase transition at the moment the main roads start to interconnect forming the spanning percolation cluster. The percolation process uncovers the hierarchical structure of the roads in the network, and as such, its classification. Furthermore, this technique serves to extract the set of most important roads of the network and to create a hierarchical index for each road in the system.


The angular nature of road networks
Carlos Molinero, Roberto Murcio, Elsa Arcaute

http://arxiv.org/abs/1512.05659

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On the origin of burstiness in human behavior: The wikipedia edits case

A number of human activities exhibit a bursty pattern, namely periods of very high activity that are followed by rest periods. Records of this process generate time series of events whose inter-event times follow a probability distribution that displays a fat tail. The grounds for such phenomenon are not yet clearly understood. In the present work we use the freely available Wikipedia's editing records to tackle this question by measuring the level of burstiness, as well as the memory effect of the editing tasks performed by different editors in different pages. Our main finding is that, even though the editing activity is conditioned by the circadian 24 hour cycle, the conditional probability of an activity of a given duration at a given time of the day is independent from the latter. This suggests that the human activity seems to be related to the high "cost" of starting an action as opposed to the much lower "cost" of continuing that action.


On the origin of burstiness in human behavior: The wikipedia edits case
Yerali Gandica, Joao Carvalho, Fernando Sampaio Dos Aidos, Renaud Lambiotte, and Timoteo Carletti

http://arxiv.org/abs/1601.00864

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Information Flows? A Critique of Transfer Entropies

A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be dominated by the transfer entropy. Via straightforward examples, we show that it and a derivative quantity, the causation entropy, do not, in fact, quantify the flow of information. At one and the same time they can overestimate flow or underestimate influence. We isolate why this is the case and propose alternate measures for information flow. An auxiliary consequence reveals that the proliferation of networks as a now-common theoretical model for large-scale systems in concert with the use of transfer-like entropies has shoehorned dyadic relationships into our structural interpretation of the organization and behavior of complex systems, despite the occurrence of polyadic dependencies. The net result is that much of the sophisticated organization of complex systems goes undetected.


Information Flows? A Critique of Transfer Entropies
Ryan G. James, Nix Barnett, James P. Crutchfield

http://arxiv.org/abs/1512.06479

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Stigmergy as a Universal Coordination Mechanism I: Definition and Components

Stigmergy as a Universal Coordination Mechanism I: Definition and Components | Papers | Scoop.it

The concept of stigmergy has been used to analyze self-organizing activities in an ever-widening range of domains, including social insects, robotics, web communities and human society. Yet, it is still poorly understood and as such its full power remains underappreciated. The present paper clarifies the issue by defining stigmergy as a mechanism of indirect coordination in which the trace left by an action in a medium stimulates subsequent actions. It then analyses the fundamental concepts used in the definition: action, agent, medium, trace and coordination. It clarifies how stigmergy enables complex, coordinated activity without any need for planning, control, communication, simultaneous presence, or even mutual awareness. The resulting self-organization is driven by a combination of positive and negative feedbacks, amplifying beneficial developments while suppressing errors. Thus, stigmergy is applicable to a very broad variety of cases, from chemical reactions to bodily coordination and Internet-supported collaboration in Wikipedia.


Stigmergy as a Universal Coordination Mechanism I: Definition and Components
Leslie Marsh, Ted G. Lewis, Francis Heylighen

Cognitive Systems Research

http://dx.doi.org/10.1016/j.cogsys.2015.12.002 ;

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Dynamical criticality: overview and open questions

In this paper we provide a survey of the most relevant work on dynamical criticality, with particular emphasis on the criticality hypothesis, which states that systems in a dynamical regime between order and chaos have evolutionary advantages with respect to ordered and disordered (chaotic) systems. We review the main contributions concerning dynamics and information processing at the edge of chaos, and we illustrate the main achievements in the detection of critical dynamics in biological systems. Finally, we discuss open questions and outlook future work.


Dynamical criticality: overview and open questions
Andrea Roli, Marco Villani, Alessandro Filisetti, Roberto Serra

http://arxiv.org/abs/1512.05259

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Concurrent Bursty Behavior of Social Sensors in Sporting Events

Concurrent Bursty Behavior of Social Sensors in Sporting Events | Papers | Scoop.it
The advent of social media expands our ability to transmit information and connect with others instantly, which enables us to behave as “social sensors.” Here, we studied concurrent bursty behavior of Twitter users during major sporting events to determine their function as social sensors. We show that the degree of concurrent bursts in tweets (posts) and retweets (re-posts) works as a strong indicator of winning or losing a game. More specifically, our simple tweet analysis of Japanese professional baseball games in 2013 revealed that social sensors can immediately react to positive and negative events through bursts of tweets, but that positive events are more likely to induce a subsequent burst of retweets. We confirm that these findings also hold true for tweets related to Major League Baseball games in 2015. Furthermore, we demonstrate active interactions among social sensors by constructing retweet networks during a baseball game. The resulting networks commonly exhibited user clusters depending on the baseball team, with a scale-free connectedness that is indicative of a substantial difference in user popularity as an information source. While previous studies have mainly focused on bursts of tweets as a simple indicator of a real-world event, the temporal correlation between tweets and retweets implies unique aspects of social sensors, offering new insights into human behavior in a highly connected world.

 

Takeichi Y, Sasahara K, Suzuki R, Arita T (2015) Concurrent Bursty Behavior of Social Sensors in Sporting Events. PLoS ONE 10(12): e0144646. http://dx.doi.org/10.1371/journal.pone.0144646

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Population Dynamics of Self-Replicating Cell-like Structures Emerging from Chaos

We present here a system of self-propelled particles that follow a very simple motion law in continuous space in a deterministic and asynchronous way. This system of particles is capable of producing, depending on the particle density in the habitat, several spatio-temporal patterns emerging from an initial randomized spatial configuration. We found that those structures show specific population dynamics which arise from death (decay) and growth (self-replication) of those structures, thus we call the system Primordial Particle System (PPS), as the model can be interpreted as a simplistic model of emergence of self-replicating chemical structures from initially chaotic mixed components in the "primordial soup" at the beginning of life. We describe the observed dynamics, show the emerging spatio-temporal structures and present a macroscopic top-down model as well as a probabilistic microscopic bottom-up model of the system.


Population Dynamics of Self-Replicating Cell-like Structures Emerging from Chaos
Thomas Schmickl, Martin Stefanec

http://arxiv.org/abs/1512.04478

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Conflict and Computation on Wikipedia: a Finite-State Machine Analysis of Editor Interactions

What is the boundary between a vigorous argument and a breakdown of relations? What drives a group of individuals across it? Taking Wikipedia as a test case, we use a hidden Markov model to approximate the computational structure and social grammar of more than a decade of cooperation and conflict among its editors. Across a wide range of pages, we discover a bursty war/peace structure where the systems can become trapped---sometimes for months---in a computational subspace associated with high levels of rapid-fire conflict. Distinct patterns of behavior sustain the low-conflict subspace, including tit-for-tat reversion. While a fraction of the transitions between these subspaces are associated with top-down actions taken by administrators, the effects are weak and of uncertain valence. Surprisingly, we find no statistical signal that transitions are associated with the appearance of particularly anti-social users, and only weak association with significant news events outside the system. The majority of transitions between high and low conflict states appear to be driven by decentralized processes with no clear locus of control. Our results show how, in a modern sociotechnical system, memory of conflict is delocalized, and conflict management is a bottom-up process. It suggests that policy-makers may be limited in their ability to manage conflict, and that bad actors and exogenous shocks are less effective in causing conflict than is generally believed.


Conflict and Computation on Wikipedia: a Finite-State Machine Analysis of Editor Interactions
Simon DeDeo

http://arxiv.org/abs/1512.04177

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Complex networks as an emerging property of hierarchical preferential attachment

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance, in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality, and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.


Complex networks as an emerging property of hierarchical preferential attachment
Laurent Hébert-Dufresne, Edward Laurence, Antoine Allard, Jean-Gabriel Young, and Louis J. Dubé
Phys. Rev. E 92, 062809

http://dx.doi.org/10.1103/PhysRevE.92.062809

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Maximizing the Adjacent Possible in Automata Chemistries

Automata chemistries are good vehicles for experimentation in open-ended evolution, but they are by necessity complex systems whose low-level properties require careful design. To aid the process of designing automata chemistries, we develop an abstract model that classifies the features of a chemistry from a physical (bottom up) perspective and from a biological (top down) perspective. There are two levels: things that can evolve, and things that cannot. We equate the evolving level with biology and the non-evolving level with physics. We design our initial organisms in the biology, so they can evolve. We design the physics to facilitate evolvable biologies. This architecture leads to a set of design principles that should be observed when creating an instantiation of the architecture. These principles are Everything Evolves, Everything's Soft, and Everything Dies. To evaluate these ideas, we present experiments in the recently developed Stringmol automata chemistry. We examine the properties of Stringmol with respect to the principles, and so demonstrate the usefulness of the principles in designing automata chemistries.


Maximizing the Adjacent Possible in Automata Chemistries
Simon Hickinbotham, et al.

Artificial Life

http://dx.doi.org/10.1162/ARTL_a_00180

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Untangling Performance from Success

Fame, popularity and celebrity status, frequently used tokens of success, are often loosely related to, or even divorced from professional performance. This dichotomy is partly rooted in the difficulty to distinguish performance, an individual measure that captures the actions of a performer, from success, a collective measure that captures a community's reactions to these actions. Yet, finding the relationship between the two measures is essential for all areas that aim to objectively reward excellence, from science to business. Here we quantify the relationship between performance and success by focusing on tennis, an individual sport where the two quantities can be independently measured. We show that a predictive model, relying only on a tennis player's performance in tournaments, can accurately predict an athlete's popularity, both during a player's active years and after retirement. Hence the model establishes a direct link between performance and momentary popularity. The agreement between the performance-driven and observed popularity suggests that in most areas of human achievement exceptional visibility may be rooted in detectable performance measures.


Untangling Performance from Success
Burcu Yucesoy, Albert-László Barabási

http://arxiv.org/abs/1512.00894

Complexity Digest's insight:

See Also: http://untangling-tennis.net

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The Evolution of Wikipedia's Norm Network

Social norms have traditionally been difficult to quantify. In any particular society, their sheer number and complex interdependencies often limit a system-level analysis. Here, we present the development of the network of norms that sustain the online social system Wikipedia. We do so using a network of pages that establish, describe, and interpret the society's norms. Fifteen years of high-resolution data allow us to study how this network evolves over time. Despite Wikipedia's reputation for ad hoc governance, we find that its normative evolution is highly conservative. The earliest users create norms that dominate the network and persist over time. These core norms govern both content and interpersonal interactions, using abstract principles such as neutrality, verifiability, and assume good faith. As the network grows, norm neighborhoods decouple topologically from each other, while increasing in semantic coherence. Taken together, these results suggest that the evolution of Wikipedia's norm network is akin to bureaucratic systems that predate the information age.


The Evolution of Wikipedia's Norm Network
Bradi Heaberlin, Simon DeDeo

http://arxiv.org/abs/1512.01725

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Tracking Urban Activity Growth Globally with Big Location Data

In recent decades the world has experienced rates of urban growth unparalleled in any other period of history and this growth is shaping the environment in which an increasing proportion of us live. In this paper we use a longitudinal dataset from Foursquare, a location-based social network, to analyse urban growth across 100 major cities worldwide.
Initially we explore how urban growth differs in cities across the world. We show that there exists a strong spatial correlation, with nearby pairs of cities more likely to share similar growth profiles than remote pairs of cities. Subsequently we investigate how growth varies inside cities and demonstrate that, given the existing local density of places, higher-than-expected growth is highly localised while lower-than-expected growth is more diffuse. Finally we attempt to use the dataset to characterise competition between new and existing venues. By defining a measure based on the change in throughput of a venue before and after the opening of a new nearby venue, we demonstrate which venue types have a positive effect on venues of the same type and which have a negative effect. For example, our analysis confirms the hypothesis that there is large degree of competition between bookstores, in the sense that existing bookstores normally experience a notable drop in footfall after a new bookstore opens nearby. Other place categories however, such as Airport Gates or Museums, have a cooperative effect and their presence fosters higher traffic volumes to nearby places of the same type.


Tracking Urban Activity Growth Globally with Big Location Data
Matthew Daggitt, Anastasios Noulas, Blake Shaw, Cecilia Mascolo

http://arxiv.org/abs/1512.05819

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Understanding the group dynamics and success of teams

Complex problems often require coordinated group effort and can consume significant resources, yet our understanding of how teams form and succeed has been limited by a lack of large-scale, quantitative data. We analyze activity traces and success levels for ~150,000 self-organized, online team projects. While larger teams tend to be more successful, workload is highly focused across the team, with only a few members performing most work. We find that highly successful teams are significantly more focused than average teams of the same size, that their members have worked on more diverse sets of projects, and the members of highly successful teams are more likely to be core members or 'leads' of other teams. The relations between team success and size, focus and especially team experience cannot be explained by confounding factors such as team age or external contributions from non-team members nor by group mechanisms such as social loafing. Taken together, these features point to organizational principles that may maximize the success of collaborative endeavors.


Understanding the group dynamics and success of teams
Michael Klug, James P. Bagrow

http://arxiv.org/abs/1407.2893

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Interacting Behavior and Emerging Complexity

Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited available resources. We implement Global Rules that determine the interaction between two Elementary Cellular Automata on the same grid. Global Rules change the complexity of the state evolution output which suggests that some complexity is intrinsic to the interaction rules themselves. The largest increases in complexity occurred when the interacting elementary rules had very little complexity, suggesting that they are able to accept complexity through interaction only. We also found that some Class 3 or 4 CA rules are more fragile than others to Global Rules, while others are more robust, hence suggesting some intrinsic properties of the rules independent of the Global Rule choice. We provide statistical mappings of Elementary Cellular Automata exposed to Global Rules and different initial conditions onto different complexity classes.


Interacting Behavior and Emerging Complexity
Alyssa Adams, Hector Zenil, Eduardo Hermo Reyes, Joost Joosten

http://arxiv.org/abs/1512.07450

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Fisher transfer entropy: quantifying the gain in transient sensitivity

We introduce a novel measure, Fisher transfer entropy (FTE), which quantifies a gain in sensitivity to a control parameter of a state transition, in the context of another observable source. The new measure captures both transient and contextual qualities of transfer entropy and the sensitivity characteristics of Fisher information. FTE is exemplified for a ferromagnetic two-dimensional lattice Ising model with Glauber dynamics and is shown to diverge at the critical point.


Fisher transfer entropy: quantifying the gain in transient sensitivity
Mikhail Prokopenko, Lionel Barnett, Michael Harré, Joseph T. Lizier, Oliver Obst, X. Rosalind Wang
Royal Society Proceedings A

December 2015
Volume: 471 Issue: 2184

http://dx.doi.org/10.1098/rspa.2015.0610 

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Stigmergy as a Universal Coordination Mechanism II: Varieties and evolution

The concept of stigmergy, a mechanism for the coordination of actions via the trace they leave in a medium, can explain self-organizing activities in a broad range of domains, including social insects, collaborative websites, and human institutions. The present paper attempts to bring some order to these diverse applications by classifying varieties of stigmergy according to general aspects: the number of agents involved, the relative persistence or transience of the trace, the use of sematectonic or marker-based traces, and the quantitative or qualitative characteristics of traces. The resulting cases are essentially continuous, as more complex cases can be understood as having evolved out of simpler ones. One application is cognition, which can be viewed as an interiorization of the individual stigmergy that helps an agent to perform a complex project by registering the state of the work in the trace, thus providing an external memory. Another application is the evolution of cooperation, in which agents learn to profit from the synergy produced by the spontaneous stigmergic coordination between their initially independent actions, thus bypassing the problem of “free riders” that exploit the cooperators’ efforts.


Stigmergy as a Universal Coordination Mechanism II: Varieties and evolution
Francis Heylighen

Cognitive Systems Research

http://dx.doi.org/10.1016/j.cogsys.2015.12.007

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Networks of military alliances, wars, and international trade

The incidence of interstate wars has dropped dramatically over time: The number of wars per pair of countries per year from 1950 to 2000 was roughly a 10th as high as it was from 1820 to 1949. This significant decrease in the frequency of wars correlates with a substantial increase in the number of military alliances per country and the stability of those alliances. We show that one possible explanation of this is an accompanying expansion of international trade. Increased trade decreases countries’ incentives to attack each other and increases their incentives to defend each other, leading to a stable and peaceful network of military and trade alliances that is consistent with observed data.


Networks of military alliances, wars, and international trade
Matthew O. Jackson and Stephen Nei

PNAS 112(50):15277–15284

http://dx.doi.org/10.1073/pnas.1520970112 ;

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ukituki's curator insight, December 19, 2015 4:40 PM
Based on the model we also examine some specific relationships, finding that countries with high levels of trade with their allies are less likely to be involved in wars with any other countries (including allies and nonallies), and that an increase in trade between two countries correlates with a lower chance that they will go to war with each other.
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Discovering the laws of urbanisation

In 2012 the world's population exceeded 7 billion, and since 2008 the number of individuals living in urban areas has surpassed that of rural areas. This is the result of an overall increase of life expectancy in many countries that has caused an unprecedented growth of the world's total population during recent decades, combined with a net migration flow from rural villages to urban agglomerations. While it is clear that the rate of natural increase and migration flows are the driving forces shaping the spatial distribution of population, a general consensus on the mechanisms that characterise the urbanisation process is still lacking. Here we present two fundamental laws of urbanisation that are quantitatively supported by empirical evidence: 1) the number of cities in a country is proportional to the country's total population, irrespective of the country's area, and 2) the average distance between cities scales as the inverse of the square root of the country's population density. We study the spatio-temporal evolution of population considering two classes of models, Gravity and Intervening Opportunities, to estimate migration flows and show that they produce different spatial patterns of cities.


Discovering the laws of urbanisation
Filippo Simini, Charlotte James

http://arxiv.org/abs/1512.03747

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Experimental proof of faster-is-slower in systems of frictional particles flowing through constrictions

The “faster-is-slower” (FIS) effect was first predicted by computer simulations of the egress of pedestrians through a narrow exit [D. Helbing, I. J. Farkas, and T. Vicsek, Nature (London) 407, 487 (2000)]. FIS refers to the finding that, under certain conditions, an excess of the individuals' vigor in the attempt to exit causes a decrease in the flow rate. In general, this effect is identified by the appearance of a minimum when plotting the total evacuation time of a crowd as a function of the pedestrian desired velocity. Here, we experimentally show that the FIS effect indeed occurs in three different systems of discrete particles flowing through a constriction: (a) humans evacuating a room, (b) a herd of sheep entering a barn, and (c) grains flowing out a 2D hopper over a vibrated incline. This finding suggests that FIS is a universal phenomenon for active matter passing through a narrowing.


Experimental proof of faster-is-slower in systems of frictional particles flowing through constrictions
José M. Pastor, Angel Garcimartín, Paula A. Gago, Juan P. Peralta, César Martín-Gómez, Luis M. Ferrer, Diego Maza, Daniel R. Parisi, Luis A. Pugnaloni, and Iker Zuriguel
Phys. Rev. E 92, 062817

http://dx.doi.org/10.1103/PhysRevE.92.062817

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Information geometric analysis of phase transitions in complex patterns: the case of the Gray-Scott reaction-diffusion model

The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in complex systems. However, it is unclear whether the Fisher-Rao metric does indeed detect these more general transitions, especially in the absence of a statistical model. In this paper we study the transitions between patterns in the Gray-Scott reaction-diffusion model using Fisher information. We describe the system by a probability density function that represents the size distribution of blobs in the patterns and compute its Fisher information with respect to changing the two rate parameters of the underlying model. We estimate the distribution non-parametrically so that we do not assume any statistical model. The resulting Fisher map can be interpreted as a phase-map of the different patterns. Lines with high Fisher information can be considered as boundaries between regions of parameter space where patterns with similar characteristics appear. These lines of high Fisher information can be interpreted as phase transitions between complex patterns.


Information geometric analysis of phase transitions in complex patterns: the case of the Gray-Scott reaction-diffusion model
Omri Har Shemesh, Rick Quax, Alfons G. Hoekstra, Peter M.A. Sloot

http://arxiv.org/abs/1512.02077 

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Exploring temporal networks with greedy walks

Temporal networks come with a wide variety of heterogeneities, from burstiness of event sequences to correlations between timings of node and link activations. In this paper, we set to explore the latter by using temporal greedy walks as probes of temporal network structure. Given a temporal network (a sequence of contacts), temporal greedy walks proceed from node to node by always following the first available contact. Because of this, their structure is particularly sensitive to temporal-topological patterns involving repeated contacts between sets of nodes. This becomes evident in their small coverage per step taken as compared to a temporal reference model – in empirical temporal networks, greedy walks often get stuck within small sets of nodes because of correlated contact patterns. While this may also happen in static networks that have pronounced community structure, the use of the temporal reference model takes the underlying static network structure out of the equation and indicates that there is a purely temporal reason for the observations. Further analysis of the structure of greedy walks indicates that burst trains, sequences of repeated contacts between node pairs, are the dominant factor. However, there are larger patterns too, as shown with non-backtracking greedy walks. We proceed further to study the entropy rates of greedy walks, and show that the sequences of visited nodes are more structured and predictable in original data as compared to temporally uncorrelated references. Taken together, these results indicate a richness of correlated temporal-topological patterns in temporal networks.


Exploring temporal networks with greedy walks
Jari Saramäki and Petter Holme

Eur. Phys. J. B (2015) 88: 334
http://dx.doi.org/10.1140/epjb/e2015-60660-9

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‘Novel, amazing, innovative’: positive words on the rise in science papers

‘Novel, amazing, innovative’: positive words on the rise in science papers | Papers | Scoop.it

Analysis suggests an increasing tendency to exaggerate and polarize results.


‘Novel, amazing, innovative’: positive words on the rise in science papers

Philip Ball

Nature News

http://dx.doi.org/10.1038/nature.2015.19024 ;

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Undecidability of the spectral gap

In quantum many-body physics, the spectral gap is the energy difference between the ground state of a system and its first excited state. Establishing whether it is possible to make a decision about the system being gapped or gapless, given a specific model Hamiltonian, is a long-standing problem in physics known as the spectral gap problem. Here, Toby Cubitt et al. prove that the spectral gap problem is undecidable. Although it had been known before that deciding about the existence of a spectral gap is difficult, this result proves the strongest possible form of algorithmic difficulty for a core problem of many-body physics.


Undecidability of the spectral gap
Toby S. Cubitt, David Perez-Garcia & Michael M. Wolf

Nature 528, 207–211 (10 December 2015) http://dx.doi.org/10.1038/nature16059 ;

Complexity Digest's insight:

This result is similar to those of Gödel, Turing, and Chaitin, but for physics, proving that not every macroscopic property can be derived from microscopic properties, i.e. non-reductionism.

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