2,882 research outputs found
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
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
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
Critical Droplets and Phase Transitions in Two Dimensions
In two space dimensions, the percolation point of the pure-site clusters of
the Ising model coincides with the critical point T_c of the thermal transition
and the percolation exponents belong to a special universality class. By
introducing a bond probability p_B<1, the corresponding site-bond clusters keep
on percolating at T_c and the exponents do not change, until
p_B=p_CK=1-exp(-2J/kT): for this special expression of the bond weight the
critical percolation exponents switch to the 2D Ising universality class. We
show here that the result is valid for a wide class of bidimensional models
with a continuous magnetization transition: there is a critical bond
probability p_c such that, for any p_B>=p_c, the onset of percolation of the
site-bond clusters coincides with the critical point of the thermal transition.
The percolation exponents are the same for p_c<p_B<=1 but, for p_B=p_c, they
suddenly change to the thermal exponents, so that the corresponding clusters
are critical droplets of the phase transition. Our result is based on Monte
Carlo simulations of various systems near criticality.Comment: Final version for publication, minor changes, figures adde
Implementation of the Quantum Fourier Transform
The quantum Fourier transform (QFT) has been implemented on a three bit
nuclear magnetic resonance (NMR) quantum computer, providing a first step
towards the realization of Shor's factoring and other quantum algorithms.
Implementation of the QFT is presented with fidelity measures, and state
tomography. Experimentally realizing the QFT is a clear demonstration of NMR's
ability to control quantum systems.Comment: 6 pages, 2 figure
Testing Cluster Structure of Graphs
We study the problem of recognizing the cluster structure of a graph in the
framework of property testing in the bounded degree model. Given a parameter
, a -bounded degree graph is defined to be -clusterable, if it can be partitioned into no more than parts, such
that the (inner) conductance of the induced subgraph on each part is at least
and the (outer) conductance of each part is at most
, where depends only on . Our main
result is a sublinear algorithm with the running time
that takes as
input a graph with maximum degree bounded by , parameters , ,
, and with probability at least , accepts the graph if it
is -clusterable and rejects the graph if it is -far from
-clusterable for , where depends only on . By the lower
bound of on the number of queries needed for testing graph
expansion, which corresponds to in our problem, our algorithm is
asymptotically optimal up to polylogarithmic factors.Comment: Full version of STOC 201
Solution of the Bohr hamiltonian for soft triaxial nuclei
The Bohr-Mottelson model is solved for a generic soft triaxial nucleus,
separating the Bohr hamiltonian exactly and using a number of different
model-potentials: a displaced harmonic oscillator in , which is solved
with an approximated algebraic technique, and Coulomb/Kratzer,
harmonic/Davidson and infinite square well potentials in , which are
solved exactly. In each case we derive analytic expressions for the
eigenenergies which are then used to calculate energy spectra.
Here we study the chain of osmium isotopes and we compare our results with
experimental information and previous calculations.Comment: 13 pages, 9 figure
The macro-behavior of agents' opinion under the influence of an external field
In this paper, a model about the evolution of opinion on small world networks
is proposed. We studied the macro-behavior of the agents' opinion and the
relative change rate as time elapses. The external field was found to play an
important role in making the opinion balance or increase, and without
the influence of the external field, the relative change rate shows
a nonlinear increasing behavior as time runs. What's more, this nonlinear
increasing behavior is independent of the initial condition, the strength of
the external field and the time that we cancel the external field. Maybe the
results can reflect some phenomenon in our society, such as the function of the
macro-control in China or the Mass Media in our society.Comment: 8 pages, 3 figure
Outflow Dynamics in Modeling Oligopoly Markets: The Case of the Mobile Telecommunications Market in Poland
In this paper we introduce two models of opinion dynamics in oligopoly
markets and apply them to a situation, where a new entrant challenges two
incumbents of the same size. The models differ in the way the two forces
influencing consumer choice -- (local) social interactions and (global)
advertising -- interact. We study the general behavior of the models using the
Mean Field Approach and Monte Carlo simulations and calibrate the models to
data from the Polish telecommunications market. For one of the models
criticality is observed -- below a certain critical level of advertising the
market approaches a lock-in situation, where one market leader dominates the
market and all other brands disappear. Interestingly, for both models the best
fits to real data are obtained for conformity level . This
agrees very well with the conformity level found by Solomon Asch in his famous
social experiment
Exploratory topic modeling with distributional semantics
As we continue to collect and store textual data in a multitude of domains,
we are regularly confronted with material whose largely unknown thematic
structure we want to uncover. With unsupervised, exploratory analysis, no prior
knowledge about the content is required and highly open-ended tasks can be
supported. In the past few years, probabilistic topic modeling has emerged as a
popular approach to this problem. Nevertheless, the representation of the
latent topics as aggregations of semi-coherent terms limits their
interpretability and level of detail.
This paper presents an alternative approach to topic modeling that maps
topics as a network for exploration, based on distributional semantics using
learned word vectors. From the granular level of terms and their semantic
similarity relations global topic structures emerge as clustered regions and
gradients of concepts. Moreover, the paper discusses the visual interactive
representation of the topic map, which plays an important role in supporting
its exploration.Comment: Conference: The Fourteenth International Symposium on Intelligent
Data Analysis (IDA 2015
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