12,571 research outputs found
Systematic Topology Analysis and Generation Using Degree Correlations
We present a new, systematic approach for analyzing network topologies. We
first introduce the dK-series of probability distributions specifying all
degree correlations within d-sized subgraphs of a given graph G. Increasing
values of d capture progressively more properties of G at the cost of more
complex representation of the probability distribution. Using this series, we
can quantitatively measure the distance between two graphs and construct random
graphs that accurately reproduce virtually all metrics proposed in the
literature. The nature of the dK-series implies that it will also capture any
future metrics that may be proposed. Using our approach, we construct graphs
for d=0,1,2,3 and demonstrate that these graphs reproduce, with increasing
accuracy, important properties of measured and modeled Internet topologies. We
find that the d=2 case is sufficient for most practical purposes, while d=3
essentially reconstructs the Internet AS- and router-level topologies exactly.
We hope that a systematic method to analyze and synthesize topologies offers a
significant improvement to the set of tools available to network topology and
protocol researchers.Comment: Final versio
Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty
Motivated by the massive deployment of power-hungry data centers for service
provisioning, we examine the problem of routing in optical networks with the
aim of minimizing traffic-driven power consumption. To tackle this issue,
routing must take into account energy efficiency as well as capacity
considerations; moreover, in rapidly-varying network environments, this must be
accomplished in a real-time, distributed manner that remains robust in the
presence of random disturbances and noise. In view of this, we derive a pricing
scheme whose Nash equilibria coincide with the network's socially optimum
states, and we propose a distributed learning method based on the Boltzmann
distribution of statistical mechanics. Using tools from stochastic calculus, we
show that the resulting Boltzmann routing scheme exhibits remarkable
convergence properties under uncertainty: specifically, the long-term average
of the network's power consumption converges within of its
minimum value in time which is at most ,
irrespective of the fluctuations' magnitude; additionally, if the network
admits a strict, non-mixing optimum state, the algorithm converges to it -
again, no matter the noise level. Our analysis is supplemented by extensive
numerical simulations which show that Boltzmann routing can lead to a
significant decrease in power consumption over basic, shortest-path routing
schemes in realistic network conditions.Comment: 24 pages, 4 figure
Preferential attachment during the evolution of a potential energy landscape
It has previously been shown that the network of connected minima on a
potential energy landscape is scale-free, and that this reflects a power-law
distribution for the areas of the basins of attraction surrounding the minima.
Here, we set out to understand more about the physical origins of these
puzzling properties by examining how the potential energy landscape of a
13-atom cluster evolves with the range of the potential. In particular, on
decreasing the range of the potential the number of stationary points increases
and thus the landscape becomes rougher and the network gets larger. Thus, we
are able to follow the evolution of the potential energy landscape from one
with just a single minimum to a complex landscape with many minima and a
scale-free pattern of connections. We find that during this growth process, new
edges in the network of connected minima preferentially attach to more
highly-connected minima, thus leading to the scale-free character. Furthermore,
minima that appear when the range of the potential is shorter and the network
is larger have smaller basins of attraction. As there are many of these smaller
basins because the network grows exponentially, the observed growth process
thus also gives rise to a power-law distribution for the hyperareas of the
basins.Comment: 10 pages, 10 figure
Agent-based mapping of credit risk for sustainable microfinance
Inspired by recent ideas on how the analysis of complex financial risks can
benefit from analogies with independent research areas, we propose an
unorthodox framework for mapping microfinance credit risk---a major obstacle to
the sustainability of lenders outreaching to the poor. Specifically, using the
elements of network theory, we constructed an agent-based model that obeys the
stylised rules of microfinance industry. We found that in a deteriorating
economic environment confounded with adverse selection, a form of latent moral
hazard may cause a regime shift from a high to a low loan repayment
probability. An after-the-fact recovery, when possible, required the economic
environment to improve beyond that which led to the shift in the first place.
These findings suggest a small set of measurable quantities for mapping
microfinance credit risk and, consequently, for balancing the requirements to
reasonably price loans and to operate on a fully self-financed basis. We
illustrate how the proposed mapping works using a 10-year monthly data set from
one of the best-known microfinance representatives, Grameen Bank in Bangladesh.
Finally, we discuss an entirely new perspective for managing microfinance
credit risk based on enticing spontaneous cooperation by building social
capital.Comment: 9 pages, 5 figure
Generating constrained random graphs using multiple edge switches
The generation of random graphs using edge swaps provides a reliable method
to draw uniformly random samples of sets of graphs respecting some simple
constraints, e.g. degree distributions. However, in general, it is not
necessarily possible to access all graphs obeying some given con- straints
through a classical switching procedure calling on pairs of edges. We therefore
propose to get round this issue by generalizing this classical approach through
the use of higher-order edge switches. This method, which we denote by "k-edge
switching", makes it possible to progres- sively improve the covered portion of
a set of constrained graphs, thereby providing an increasing, asymptotically
certain confidence on the statistical representativeness of the obtained
sample.Comment: 15 page
Coevolutionary games - a mini review
Prevalence of cooperation within groups of selfish individuals is puzzling in
that it contradicts with the basic premise of natural selection. Favoring
players with higher fitness, the latter is key for understanding the challenges
faced by cooperators when competing with defectors. Evolutionary game theory
provides a competent theoretical framework for addressing the subtleties of
cooperation in such situations, which are known as social dilemmas. Recent
advances point towards the fact that the evolution of strategies alone may be
insufficient to fully exploit the benefits offered by cooperative behavior.
Indeed, while spatial structure and heterogeneity, for example, have been
recognized as potent promoters of cooperation, coevolutionary rules can extend
the potentials of such entities further, and even more importantly, lead to the
understanding of their emergence. The introduction of coevolutionary rules to
evolutionary games implies, that besides the evolution of strategies, another
property may simultaneously be subject to evolution as well. Coevolutionary
rules may affect the interaction network, the reproduction capability of
players, their reputation, mobility or age. Here we review recent works on
evolutionary games incorporating coevolutionary rules, as well as give a
didactic description of potential pitfalls and misconceptions associated with
the subject. In addition, we briefly outline directions for future research
that we feel are promising, thereby particularly focusing on dynamical effects
of coevolutionary rules on the evolution of cooperation, which are still widely
open to research and thus hold promise of exciting new discoveries.Comment: 24 two-column pages, 10 figures; accepted for publication in
BioSystem
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