2,183 research outputs found
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
Curious multisection identities by index factorization
This manuscript introduces a general multisection identity expressed
equivalently in terms of infinite double products and/or infinite double
series, from which several new product or summation identities involving
special functions including Gamma, hyperbolic trigonometric, polygamma, zeta
and Jacobi theta functions, are derived. It is shown that a parameterized
version of this multisection identity exists, a specialization of which
coincides with the standard multisection identity
Quantum computing of delocalization in small-world networks
We study a quantum small-world network with disorder and show that the system
exhibits a delocalization transition. A quantum algorithm is built up which
simulates the evolution operator of the model in a polynomial number of gates
for exponential number of vertices in the network. The total computational gain
is shown to depend on the parameters of the network and a larger than quadratic
speed-up can be reached.
We also investigate the robustness of the algorithm in presence of
imperfections.Comment: 4 pages, 5 figures, research done at
http://www.quantware.ups-tlse.fr
The role of clustering and gridlike ordering in epidemic spreading
The spreading of an epidemic is determined by the connectiviy patterns which
underlie the population. While it has been noted that a virus spreads more
easily on a network in which global distances are small, it remains a great
challenge to find approaches that unravel the precise role of local
interconnectedness. Such topological properties enter very naturally in the
framework of our two-timestep description, also providing a novel approach to
tract a probabilistic system. The method is elaborated for SIS-type epidemic
processes, leading to a quantitative interpretation of the role of loops up to
length 4 in the onset of an epidemic.Comment: Submitted to Phys. Rev. E; 15 pages, 11 figures, 5 table
CONTEST : a Controllable Test Matrix Toolbox for MATLAB
Large, sparse networks that describe complex interactions are a common feature across a number of disciplines, giving rise to many challenging matrix computational tasks. Several random graph models have been proposed that capture key properties of real-life networks. These models provide realistic, parametrized matrices for testing linear system and eigenvalue solvers. CONTEST (CONtrollable TEST matrices) is a random network toolbox for MATLAB that implements nine models. The models produce unweighted directed or undirected graphs; that is, symmetric or unsymmetric matrices with elements equal to zero or one. They have one or more parameters that affect features such as sparsity and characteristic pathlength and all can be of arbitrary dimension. Utility functions are supplied for rewiring, adding extra shortcuts and subsampling in order to create further classes of networks. Other utilities convert the adjacency matrices into real-valued coefficient matrices for naturally arising computational tasks that reduce to sparse linear system and eigenvalue problems
Epidemics and percolation in small-world networks
We study some simple models of disease transmission on small-world networks,
in which either the probability of infection by a disease or the probability of
its transmission is varied, or both. The resulting models display epidemic
behavior when the infection or transmission probability rises above the
threshold for site or bond percolation on the network, and we give exact
solutions for the position of this threshold in a variety of cases. We confirm
our analytic results by numerical simulation.Comment: 6 pages, including 3 postscript figure
Ethical Aspects of Animal Experimentation
If inquiries are made of people regarding their attitudes towards animal experimentation, there will no doubt be various answers corresponding to the different ethical attitudes today. Three principle points of view are imaginable. The two extremes are: an unrestricted support of all animal experiments; and a radical rejection of any such experiment. These two positions, in all likelihood, are taken by only a minority of the population. The majority will approve of animal experimentation in principle, however, only insofar as it is really necessary to preserve human life. So, the point of controversy arises from the question: When is an animal experiment necessary and indispensable
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