970 research outputs found
Modeling self-organization of communication and topology in social networks
This paper introduces a model of self-organization between communication and
topology in social networks, with a feedback between different communication
habits and the topology. To study this feedback, we let agents communicate to
build a perception of a network and use this information to create strategic
links. We observe a narrow distribution of links when the communication is low
and a system with a broad distribution of links when the communication is high.
We also analyze the outcome of chatting, cheating, and lying, as strategies to
get better access to information in the network. Chatting, although only
adopted by a few agents, gives a global gain in the system. Contrary, a global
loss is inevitable in a system with too many liarsComment: 6 pages 7 figures, Java simulation available at
http://cmol.nbi.dk/models/inforew/inforew.htm
Exact solutions for models of evolving networks with addition and deletion of nodes
There has been considerable recent interest in the properties of networks,
such as citation networks and the worldwide web, that grow by the addition of
vertices, and a number of simple solvable models of network growth have been
studied. In the real world, however, many networks, including the web, not only
add vertices but also lose them. Here we formulate models of the time evolution
of such networks and give exact solutions for a number of cases of particular
interest. For the case of net growth and so-called preferential attachment --
in which newly appearing vertices attach to previously existing ones in
proportion to vertex degree -- we show that the resulting networks have
power-law degree distributions, but with an exponent that diverges as the
growth rate vanishes. We conjecture that the low exponent values observed in
real-world networks are thus the result of vigorous growth in which the rate of
addition of vertices far exceeds the rate of removal. Were growth to slow in
the future, for instance in a more mature future version of the web, we would
expect to see exponents increase, potentially without bound.Comment: 9 pages, 3 figure
Solution for the properties of a clustered network
We study Strauss's model of a network with clustering and present an analytic
mean-field solution which is exact in the limit of large network size. Previous
computer simulations have revealed a degenerate region in the model's parameter
space in which triangles of adjacent edges clump together to form
unrealistically dense subgraphs, and perturbation calculations have been found
to break down in this region at all orders. Our analytic solution shows that
this region corresponds to a classic symmetry-broken phase and that the onset
of the degeneracy corresponds to a first-order phase transition in the density
of the network.Comment: 5 pages, 2 figure
The statistical mechanics of networks
We study the family of network models derived by requiring the expected
properties of a graph ensemble to match a given set of measurements of a
real-world network, while maximizing the entropy of the ensemble. Models of
this type play the same role in the study of networks as is played by the
Boltzmann distribution in classical statistical mechanics; they offer the best
prediction of network properties subject to the constraints imposed by a given
set of observations. We give exact solutions of models within this class that
incorporate arbitrary degree distributions and arbitrary but independent edge
probabilities. We also discuss some more complex examples with correlated edges
that can be solved approximately or exactly by adapting various familiar
methods, including mean-field theory, perturbation theory, and saddle-point
expansions.Comment: 15 pages, 4 figure
Greedy Connectivity of Geographically Embedded Graphs
We introduce a measure of {\em greedy connectivity} for geographical networks
(graphs embedded in space) and where the search for connecting paths relies
only on local information, such as a node's location and that of its neighbors.
Constraints of this type are common in everyday life applications. Greedy
connectivity accounts also for imperfect transmission across established links
and is larger the higher the proportion of nodes that can be reached from other
nodes with a high probability. Greedy connectivity can be used as a criterion
for optimal network design
Fairness-Aware Ranking in Search & Recommendation Systems with Application to LinkedIn Talent Search
We present a framework for quantifying and mitigating algorithmic bias in
mechanisms designed for ranking individuals, typically used as part of
web-scale search and recommendation systems. We first propose complementary
measures to quantify bias with respect to protected attributes such as gender
and age. We then present algorithms for computing fairness-aware re-ranking of
results. For a given search or recommendation task, our algorithms seek to
achieve a desired distribution of top ranked results with respect to one or
more protected attributes. We show that such a framework can be tailored to
achieve fairness criteria such as equality of opportunity and demographic
parity depending on the choice of the desired distribution. We evaluate the
proposed algorithms via extensive simulations over different parameter choices,
and study the effect of fairness-aware ranking on both bias and utility
measures. We finally present the online A/B testing results from applying our
framework towards representative ranking in LinkedIn Talent Search, and discuss
the lessons learned in practice. Our approach resulted in tremendous
improvement in the fairness metrics (nearly three fold increase in the number
of search queries with representative results) without affecting the business
metrics, which paved the way for deployment to 100% of LinkedIn Recruiter users
worldwide. Ours is the first large-scale deployed framework for ensuring
fairness in the hiring domain, with the potential positive impact for more than
630M LinkedIn members.Comment: This paper has been accepted for publication at ACM KDD 201
Identifying communities by influence dynamics in social networks
Communities are not static; they evolve, split and merge, appear and
disappear, i.e. they are product of dynamical processes that govern the
evolution of the network. A good algorithm for community detection should not
only quantify the topology of the network, but incorporate the dynamical
processes that take place on the network. We present a novel algorithm for
community detection that combines network structure with processes that support
creation and/or evolution of communities. The algorithm does not embrace the
universal approach but instead tries to focus on social networks and model
dynamic social interactions that occur on those networks. It identifies
leaders, and communities that form around those leaders. It naturally supports
overlapping communities by associating each node with a membership vector that
describes node's involvement in each community. This way, in addition to
overlapping communities, we can identify nodes that are good followers to their
leader, and also nodes with no clear community involvement that serve as a
proxy between several communities and are equally as important. We run the
algorithm for several real social networks which we believe represent a good
fraction of the wide body of social networks and discuss the results including
other possible applications.Comment: 10 pages, 6 figure
Constrained Non-Monotone Submodular Maximization: Offline and Secretary Algorithms
Constrained submodular maximization problems have long been studied, with
near-optimal results known under a variety of constraints when the submodular
function is monotone. The case of non-monotone submodular maximization is less
understood: the first approximation algorithms even for the unconstrainted
setting were given by Feige et al. (FOCS '07). More recently, Lee et al. (STOC
'09, APPROX '09) show how to approximately maximize non-monotone submodular
functions when the constraints are given by the intersection of p matroid
constraints; their algorithm is based on local-search procedures that consider
p-swaps, and hence the running time may be n^Omega(p), implying their algorithm
is polynomial-time only for constantly many matroids. In this paper, we give
algorithms that work for p-independence systems (which generalize constraints
given by the intersection of p matroids), where the running time is poly(n,p).
Our algorithm essentially reduces the non-monotone maximization problem to
multiple runs of the greedy algorithm previously used in the monotone case.
Our idea of using existing algorithms for monotone functions to solve the
non-monotone case also works for maximizing a submodular function with respect
to a knapsack constraint: we get a simple greedy-based constant-factor
approximation for this problem.
With these simpler algorithms, we are able to adapt our approach to
constrained non-monotone submodular maximization to the (online) secretary
setting, where elements arrive one at a time in random order, and the algorithm
must make irrevocable decisions about whether or not to select each element as
it arrives. We give constant approximations in this secretary setting when the
algorithm is constrained subject to a uniform matroid or a partition matroid,
and give an O(log k) approximation when it is constrained by a general matroid
of rank k.Comment: In the Proceedings of WINE 201
Thermodynamics of protein folding: a random matrix formulation
The process of protein folding from an unfolded state to a biologically
active, folded conformation is governed by many parameters e.g the sequence of
amino acids, intermolecular interactions, the solvent, temperature and chaperon
molecules. Our study, based on random matrix modeling of the interactions,
shows however that the evolution of the statistical measures e.g Gibbs free
energy, heat capacity, entropy is single parametric. The information can
explain the selection of specific folding pathways from an infinite number of
possible ways as well as other folding characteristics observed in computer
simulation studies.Comment: 21 Pages, no figure
Functional Liftings of Vectorial Variational Problems with Laplacian Regularization
We propose a functional lifting-based convex relaxation of variational
problems with Laplacian-based second-order regularization. The approach rests
on ideas from the calibration method as well as from sublabel-accurate
continuous multilabeling approaches, and makes these approaches amenable for
variational problems with vectorial data and higher-order regularization, as is
common in image processing applications. We motivate the approach in the
function space setting and prove that, in the special case of absolute
Laplacian regularization, it encompasses the discretization-first
sublabel-accurate continuous multilabeling approach as a special case. We
present a mathematical connection between the lifted and original functional
and discuss possible interpretations of minimizers in the lifted function
space. Finally, we exemplarily apply the proposed approach to 2D image
registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and
Variational Methods" in Hofgeismar, Germany 201
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