132 research outputs found
The Weak-Coupling Limit of 3D Simplicial Quantum Gravity
We investigate the weak-coupling limit, kappa going to infinity, of 3D
simplicial gravity using Monte Carlo simulations and a Strong Coupling
Expansion. With a suitable modification of the measure we observe a transition
from a branched polymer to a crinkled phase. However, the intrinsic geometry of
the latter appears similar to that of non-generic branched polymer, probable
excluding the existence of a sensible continuum limit in this phase.Comment: 3 pages 4 figs. LATTICE99(Gravity
Networks and Our Limited Information Horizon
In this paper we quantify our limited information horizon, by measuring the
information necessary to locate specific nodes in a network. To investigate
different ways to overcome this horizon, and the interplay between
communication and topology in social networks, we let agents communicate in a
model society. Thereby they build a perception of the network that they can use
to create strategic links to improve their standing in the network. We observe
a narrow distribution of links when the communication is low and a network with
a broad distribution of links when the communication is high.Comment: 5 pages and 5 figure
Simulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations
We extend a model of four-dimensional simplicial quantum gravity to include
degenerate triangulations in addition to combinatorial triangulations
traditionally used. Relaxing the constraint that every 4-simplex is uniquely
defined by a set of five distinct vertexes, we allow triangulations containing
multiply connected simplexes and distinct simplexes defined by the same set of
vertexes. We demonstrate numerically that including degenerated triangulations
substantially reduces the finite-size effects in the model. In particular, we
provide a strong numerical evidence for an exponential bound on the entropic
growth of the ensemble of degenerate triangulations, and show that a
discontinuous crumpling transition is already observed on triangulations of
volume N_4 ~= 4000.Comment: Latex, 8 pages, 4 eps-figure
The Weak-Coupling Limit of Simplicial Quantum Gravity
In the weak-coupling limit, kappa_0 going to infinity, the partition function
of simplicial quantum gravity is dominated by an ensemble of triangulations
with the ratio N_0/N_D close to the upper kinematic limit. For a combinatorial
triangulation of the D--sphere this limit is 1/D. Defining an ensemble of
maximal triangulations, i.e. triangulations that have the maximal possible
number of vertices for a given volume, we investigate the properties of this
ensemble in three dimensions using both Monte Carlo simulations and a
strong-coupling expansion of the partition function, both for pure simplicial
gravity and a with a suitable modified measure. For the latter we observe a
continuous phase transition to a crinkled phase and we investigate the fractal
properties of this phase.Comment: 32 pages, latex2e + 17 eps file
Focusing on the Fixed Point of 4D Simplicial Gravity
Our earlier renormalization group analysis of simplicial gravity is extended.
A high statistics study of the volume and coupling constant dependence of the
cumulants of the node distribution is carried out. It appears that the phase
transition of the theory is of first order, contrary to what is generally
believed.Comment: Latex, 20 pages, 6 postscript figures, published versio
Towards a Non-Perturbative Renormalization of Euclidean Quantum Gravity
A real space renormalization group technique, based on the hierarchical
baby-universe structure of a typical dynamically triangulated manifold, is used
to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the
-function is defined and calculated numerically. An evidence for the
existence of an ultraviolet stable fixed point of the theory is presentedComment: 12 pages Latex + 1 PS fi
Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership
Detecting community structure in social networks is a fundamental problem
empowering us to identify groups of actors with similar interests. There have
been extensive works focusing on finding communities in static networks,
however, in reality, due to dynamic nature of social networks, they are
evolving continuously. Ignoring the dynamic aspect of social networks, neither
allows us to capture evolutionary behavior of the network nor to predict the
future status of individuals. Aside from being dynamic, another significant
characteristic of real-world social networks is the presence of leaders, i.e.
nodes with high degree centrality having a high attraction to absorb other
members and hence to form a local community. In this paper, we devised an
efficient method to incrementally detect communities in highly dynamic social
networks using the intuitive idea of importance and persistence of community
leaders over time. Our proposed method is able to find new communities based on
the previous structure of the network without recomputing them from scratch.
This unique feature, enables us to efficiently detect and track communities
over time rapidly. Experimental results on the synthetic and real-world social
networks demonstrate that our method is both effective and efficient in
discovering communities in dynamic social networks
Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results
We review some recent attempts to extract information about the nature of
quantum gravity, with and without matter, by quantum field theoretical methods.
More specifically, we work within a covariant lattice approach where the
individual space-time geometries are constructed from fundamental simplicial
building blocks, and the path integral over geometries is approximated by
summing over a class of piece-wise linear geometries. This method of
``dynamical triangulations'' is very powerful in 2d, where the regularized
theory can be solved explicitly, and gives us more insights into the quantum
nature of 2d space-time than continuum methods are presently able to provide.
It also allows us to establish an explicit relation between the Lorentzian- and
Euclidean-signature quantum theories. Analogous regularized gravitational
models can be set up in higher dimensions. Some analytic tools exist to study
their state sums, but, unlike in 2d, no complete analytic solutions have yet
been constructed. However, a great advantage of our approach is the fact that
it is well-suited for numerical simulations. In the second part of this review
we describe the relevant Monte Carlo techniques, as well as some of the
physical results that have been obtained from the simulations of Euclidean
gravity. We also explain why the Lorentzian version of dynamical triangulations
is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde
Discrete approaches to quantum gravity in four dimensions
The construction of a consistent theory of quantum gravity is a problem in
theoretical physics that has so far defied all attempts at resolution. One
ansatz to try to obtain a non-trivial quantum theory proceeds via a
discretization of space-time and the Einstein action. I review here three major
areas of research: gauge-theoretic approaches, both in a path-integral and a
Hamiltonian formulation, quantum Regge calculus, and the method of dynamical
triangulations, confining attention to work that is strictly four-dimensional,
strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the
author welcomes any comments and suggestion
Statistical mechanics of complex networks
Complex networks describe a wide range of systems in nature and society, much
quoted examples including the cell, a network of chemicals linked by chemical
reactions, or the Internet, a network of routers and computers connected by
physical links. While traditionally these systems were modeled as random
graphs, it is increasingly recognized that the topology and evolution of real
networks is governed by robust organizing principles. Here we review the recent
advances in the field of complex networks, focusing on the statistical
mechanics of network topology and dynamics. After reviewing the empirical data
that motivated the recent interest in networks, we discuss the main models and
analytical tools, covering random graphs, small-world and scale-free networks,
as well as the interplay between topology and the network's robustness against
failures and attacks.Comment: 54 pages, submitted to Reviews of Modern Physic
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