3,070 research outputs found
Scale-free network growth by ranking
Network growth is currently explained through mechanisms that rely on node
prestige measures, such as degree or fitness. In many real networks those who
create and connect nodes do not know the prestige values of existing nodes, but
only their ranking by prestige. We propose a criterion of network growth that
explicitly relies on the ranking of the nodes according to any prestige
measure, be it topological or not. The resulting network has a scale-free
degree distribution when the probability to link a target node is any power law
function of its rank, even when one has only partial information of node ranks.
Our criterion may explain the frequency and robustness of scale-free degree
distributions in real networks, as illustrated by the special case of the Web
graph.Comment: 4 pages, 2 figures. We extended the model to account for ranking by
arbitrarily distributed fitness. Final version to appear on Physical Review
Letter
Information filtering in complex weighted networks
Many systems in nature, society and technology can be described as networks,
where the vertices are the system's elements and edges between vertices
indicate the interactions between the corresponding elements. Edges may be
weighted if the interaction strength is measurable. However, the full network
information is often redundant because tools and techniques from network
analysis do not work or become very inefficient if the network is too dense and
some weights may just reflect measurement errors, and shall be discarded.
Moreover, since weight distributions in many complex weighted networks are
broad, most of the weight is concentrated among a small fraction of all edges.
It is then crucial to properly detect relevant edges. Simple thresholding would
leave only the largest weights, disrupting the multiscale structure of the
system, which is at the basis of the structure of complex networks, and ought
to be kept. In this paper we propose a weight filtering technique based on a
global null model (GloSS filter), keeping both the weight distribution and the
full topological structure of the network. The method correctly quantifies the
statistical significance of weights assigned independently to the edges from a
given distribution. Applications to real networks reveal that the GloSS filter
is indeed able to identify relevantconnections between vertices.Comment: 9 pages, 7 figures, 1 Table. The GloSS filter is implemented in a
freely downloadable software (http://filrad.homelinux.org/resources
Stable and Efficient Structures for the Content Production and Consumption in Information Communities
Real-world information communities exhibit inherent structures that
characterize a system that is stable and efficient for content production and
consumption. In this paper, we study such structures through mathematical
modelling and analysis. We formulate a generic model of a community in which
each member decides how they allocate their time between content production and
consumption with the objective of maximizing their individual reward. We define
the community system as "stable and efficient" when a Nash equilibrium is
reached while the social welfare of the community is maximized. We investigate
the conditions for forming a stable and efficient community under two
variations of the model representing different internal relational structures
of the community. Our analysis results show that the structure with "a small
core of celebrity producers" is the optimally stable and efficient for a
community. These analysis results provide possible explanations to the
sociological observations such as "the Law of the Few" and also provide
insights into how to effectively build and maintain the structure of
information communities.Comment: 21 page
Center clusters in the Yang-Mills vacuum
Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory
at finite temperature are analyzed. We show that spatial clusters can be
identified where the local Polyakov loops have values close to the same center
element. For a suitable definition of these clusters the deconfinement
transition can be characterized by the onset of percolation in one of the
center sectors. The analysis is repeated for different resolution scales of the
lattice and we argue that the center clusters have a continuum limit.Comment: Table added. Final version to appear in JHE
Continuum discretized BCS approach for weakly bound nuclei
The Bardeen-Cooper-Schrieffer (BCS) formalism is extended by including the
single-particle continuum in order to analyse the evolution of pairing in an
isotopic chain from stability up to the drip line. We propose a continuum
discretized generalized BCS based on single-particle pseudostates (PS). These
PS are generated from the diagonalization of the single-particle Hamiltonian
within a Transformed Harmonic Oscillator (THO) basis. The consistency of the
results versus the size of the basis is studied. The method is applied to
neutron rich Oxygen and Carbon isotopes and compared with similar previous
works and available experimental data. We make use of the flexibility of the
proposed model in order to study the evolution of the occupation of the
low-energy continuum when the system becomes weakly bound. We find a larger
influence of the non-resonant continuum as long as the Fermi level approaches
zero.Comment: 20 pages, 16 figures, to be submitte
Lingle v. Norge Division of Magic Chef, Inc.: Revolutionizing the Application of Substantive State Labor Law to Unionized Employees
Distributed Graph Clustering using Modularity and Map Equation
We study large-scale, distributed graph clustering. Given an undirected
graph, our objective is to partition the nodes into disjoint sets called
clusters. A cluster should contain many internal edges while being sparsely
connected to other clusters. In the context of a social network, a cluster
could be a group of friends. Modularity and map equation are established
formalizations of this internally-dense-externally-sparse principle. We present
two versions of a simple distributed algorithm to optimize both measures. They
are based on Thrill, a distributed big data processing framework that
implements an extended MapReduce model. The algorithms for the two measures,
DSLM-Mod and DSLM-Map, differ only slightly. Adapting them for similar quality
measures is straight-forward. We conduct an extensive experimental study on
real-world graphs and on synthetic benchmark graphs with up to 68 billion
edges. Our algorithms are fast while detecting clusterings similar to those
detected by other sequential, parallel and distributed clustering algorithms.
Compared to the distributed GossipMap algorithm, DSLM-Map needs less memory, is
up to an order of magnitude faster and achieves better quality.Comment: 14 pages, 3 figures; v3: Camera ready for Euro-Par 2018, more
details, more results; v2: extended experiments to include comparison with
competing algorithms, shortened for submission to Euro-Par 201
Lingle v. Norge Division of Magic Chef, Inc.: Revolutionizing the Application of Substantive State Labor Law to Unionized Employees
Modularity functions maximization with nonnegative relaxation facilitates community detection in networks
We show here that the problem of maximizing a family of quantitative
functions, encompassing both the modularity (Q-measure) and modularity density
(D-measure), for community detection can be uniformly understood as a
combinatoric optimization involving the trace of a matrix called modularity
Laplacian. Instead of using traditional spectral relaxation, we apply
additional nonnegative constraint into this graph clustering problem and design
efficient algorithms to optimize the new objective. With the explicit
nonnegative constraint, our solutions are very close to the ideal community
indicator matrix and can directly assign nodes into communities. The
near-orthogonal columns of the solution can be reformulated as the posterior
probability of corresponding node belonging to each community. Therefore, the
proposed method can be exploited to identify the fuzzy or overlapping
communities and thus facilitates the understanding of the intrinsic structure
of networks. Experimental results show that our new algorithm consistently,
sometimes significantly, outperforms the traditional spectral relaxation
approaches
- …