112 research outputs found
Projective and Coarse Projective Integration for Problems with Continuous Symmetries
Temporal integration of equations possessing continuous symmetries (e.g.
systems with translational invariance associated with traveling solutions and
scale invariance associated with self-similar solutions) in a ``co-evolving''
frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with
the evolving solution) leads to improved accuracy because of the smaller time
derivative in the new spatial frame. The slower time behavior permits the use
of {\it projective} and {\it coarse projective} integration with longer
projective steps in the computation of the time evolution of partial
differential equations and multiscale systems, respectively. These methods are
also demonstrated to be effective for systems which only approximately or
asymptotically possess continuous symmetries. The ideas of projective
integration in a co-evolving frame are illustrated on the one-dimensional,
translationally invariant Nagumo partial differential equation (PDE). A
corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is
used to illustrate the coarse-grained method. A simple, one-dimensional
diffusion problem is used to illustrate the scale invariant case. The
efficiency of projective integration in the co-evolving frame for both the
macroscopic diffusion PDE and for a random-walker particle based model is again
demonstrated
Delineating Geographical Regions with Networks of Human Interactions in an Extensive Set of Countries
Large-scale networks of human interaction, in particular country-wide telephone call networks, can be used to redraw geographical maps by applying algorithms of topological community detection. The geographic projections of the emerging areas in a few recent studies on single regions have been suggested to share two distinct properties: first, they are cohesive, and second, they tend to closely follow socio-economic boundaries and are similar to existing political regions in size and number. Here we use an extended set of countries and clustering indices to quantify overlaps, providing ample additional evidence for these observations using phone data from countries of various scales across Europe, Asia, and Africa: France, the UK, Italy, Belgium, Portugal, Saudi Arabia, and Ivory Coast. In our analysis we use the known approach of partitioning country-wide networks, and an additional iterative partitioning of each of the first level communities into sub-communities, revealing that cohesiveness and matching of official regions can also be observed on a second level if spatial resolution of the data is high enough. The method has possible policy implications on the definition of the borderlines and sizes of administrative regions.National Science Foundation (U.S.)Singapore-MIT Alliance for Research and Technolog
Predicting language diversity with complex network
Evolution and propagation of the world's languages is a complex phenomenon,
driven, to a large extent, by social interactions. Multilingual society can be
seen as a system of interacting agents, where the interaction leads to a
modification of the language spoken by the individuals. Two people can reach
the state of full linguistic compatibility due to the positive interactions,
like transfer of loanwords. But, on the other hand, if they speak entirely
different languages, they will separate from each other. These simple
observations make the network science the most suitable framework to describe
and analyze dynamics of language change. Although many mechanisms have been
explained, we lack a qualitative description of the scaling behavior for
different sizes of a population. Here we address the issue of the language
diversity in societies of different sizes, and we show that local interactions
are crucial to capture characteristics of the empirical data. We propose a
model of social interactions, extending the idea from, that explains the growth
of the language diversity with the size of a population of country or society.
We argue that high clustering and network disintegration are the most important
characteristics of models properly describing empirical data. Furthermore, we
cancel the contradiction between previous models and the Solomon Islands case.
Our results demonstrate the importance of the topology of the network, and the
rewiring mechanism in the process of language change
Hidden geometric correlations in real multiplex networks
Real networks often form interacting parts of larger and more complex
systems. Examples can be found in different domains, ranging from the Internet
to structural and functional brain networks. Here, we show that these multiplex
systems are not random combinations of single network layers. Instead, they are
organized in specific ways dictated by hidden geometric correlations between
the individual layers. We find that these correlations are strong in different
real multiplexes, and form a key framework for answering many important
questions. Specifically, we show that these geometric correlations facilitate:
(i) the definition and detection of multidimensional communities, which are
sets of nodes that are simultaneously similar in multiple layers; (ii) accurate
trans-layer link prediction, where connections in one layer can be predicted by
observing the hidden geometric space of another layer; and (iii) efficient
targeted navigation in the multilayer system using only local knowledge, which
outperforms navigation in the single layers only if the geometric correlations
are sufficiently strong. Our findings uncover fundamental organizing principles
behind real multiplexes and can have important applications in diverse domains.Comment: Supplementary Materials available at
http://www.nature.com/nphys/journal/v12/n11/extref/nphys3812-s1.pd
Collective emotions online and their influence on community life
E-communities, social groups interacting online, have recently become an
object of interdisciplinary research. As with face-to-face meetings, Internet
exchanges may not only include factual information but also emotional
information - how participants feel about the subject discussed or other group
members. Emotions are known to be important in affecting interaction partners
in offline communication in many ways. Could emotions in Internet exchanges
affect others and systematically influence quantitative and qualitative aspects
of the trajectory of e-communities? The development of automatic sentiment
analysis has made large scale emotion detection and analysis possible using
text messages collected from the web. It is not clear if emotions in
e-communities primarily derive from individual group members' personalities or
if they result from intra-group interactions, and whether they influence group
activities. We show the collective character of affective phenomena on a large
scale as observed in 4 million posts downloaded from Blogs, Digg and BBC
forums. To test whether the emotions of a community member may influence the
emotions of others, posts were grouped into clusters of messages with similar
emotional valences. The frequency of long clusters was much higher than it
would be if emotions occurred at random. Distributions for cluster lengths can
be explained by preferential processes because conditional probabilities for
consecutive messages grow as a power law with cluster length. For BBC forum
threads, average discussion lengths were higher for larger values of absolute
average emotional valence in the first ten comments and the average amount of
emotion in messages fell during discussions. Our results prove that collective
emotional states can be created and modulated via Internet communication and
that emotional expressiveness is the fuel that sustains some e-communities.Comment: 23 pages including Supporting Information, accepted to PLoS ON
Characterization of Transcription Start Sites of Putative Non-coding RNAs by Multifaceted Use of Massively Paralleled Sequencer
On the basis of integrated transcriptome analysis, we show that not all transcriptional start site clusters (TSCs) in the intergenic regions (iTSCs) have the same properties; thus, it is possible to discriminate the iTSCs that are likely to have biological relevance from the other noise-level iTSCs. We used a total of 251 933 381 short-read sequence tags generated from various types of transcriptome analyses in order to characterize 6039 iTSCs, which have significant expression levels. We analyzed and found that 23% of these iTSCs were located in the proximal regions of the RefSeq genes. These RefSeq-linked iTSCs showed similar expression patterns with the neighboring RefSeq genes, had widely fluctuating transcription start sites and lacked ordered nucleosome positioning. These iTSCs seemed not to form independent transcriptional units, simply representing the by-products of the neighboring RefSeq genes, in spite of their significant expression levels. Similar features were also observed for the TSCs located in the antisense regions of the RefSeq genes. Furthermore, for the remaining iTSCs that were not associated with any RefSeq genes, we demonstrate that integrative interpretation of the transcriptome data provides essential information to specify their biological functions in the hypoxic responses of the cells
Dynamics of Opinion Forming in Structurally Balanced Social Networks
A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends
Evidence for a Conserved Quantity in Human Mobility
Recent seminal works on human mobility have shown that individuals constantly exploit a small set of repeatedly visited locations. A concurrent study has emphasized the explorative nature of human behaviour, showing that the number of visited places grows steadily over time. How to reconcile these seemingly contradicting facts remains an open question. Here, we analyse high-resolution multi-year traces of ~40,000 individuals from 4 datasets and show that this tension vanishes when the long-term evolution of mobility patterns is considered. We reveal that mobility patterns evolve significantly yet smoothly, and that the number of familiar locations an individual visits at any point is a conserved quantity with a typical size of ~25. We use this finding to improve state-of-the-art modelling of human mobility. Furthermore, shifting the attention from aggregated quantities to individual behaviour, we show that the size of an individual’s set of preferred locations correlates with their number of social interactions. This result suggests a connection between the conserved quantity we identify, which as we show cannot be understood purely on the basis of time constraints, and the ‘Dunbar number’ describing a cognitive upper limit to an individual’s number of social relations. We anticipate that our work will spark further research linking the study of human mobility and the cognitive and behavioural sciences
Effects of temporal correlations in social multiplex networks
Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure and function has not been investigated in much detail so far. Here we study the temporal correlations between layers exhibited by real social multiplex networks. At a basic level, the presence of such correlations implies a certain degree of predictability in the contact pattern, as we quantify by an extension of the entropy and mutual information analyses proposed for the single-layer case. At a different level, we demonstrate that temporal correlations are a signature of a ‘multitasking’ behavior of network agents, characterized by a higher level of switching between different social activities than expected in a uncorrelated pattern. Moreover, temporal correlations significantly affect the dynamics of coupled epidemic processes unfolding on the network. Our work opens the way for the systematic study of temporal multiplex networks and we anticipate it will be of interest to researchers in a broad array of fields
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