13,625 research outputs found
Learning and innovative elements of strategy adoption rules expand cooperative network topologies
Cooperation plays a key role in the evolution of complex systems. However,
the level of cooperation extensively varies with the topology of agent networks
in the widely used models of repeated games. Here we show that cooperation
remains rather stable by applying the reinforcement learning strategy adoption
rule, Q-learning on a variety of random, regular, small-word, scale-free and
modular network models in repeated, multi-agent Prisoners Dilemma and Hawk-Dove
games. Furthermore, we found that using the above model systems other long-term
learning strategy adoption rules also promote cooperation, while introducing a
low level of noise (as a model of innovation) to the strategy adoption rules
makes the level of cooperation less dependent on the actual network topology.
Our results demonstrate that long-term learning and random elements in the
strategy adoption rules, when acting together, extend the range of network
topologies enabling the development of cooperation at a wider range of costs
and temptations. These results suggest that a balanced duo of learning and
innovation may help to preserve cooperation during the re-organization of
real-world networks, and may play a prominent role in the evolution of
self-organizing, complex systems.Comment: 14 pages, 3 Figures + a Supplementary Material with 25 pages, 3
Tables, 12 Figures and 116 reference
The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant
We extend here the canonical treatment of spherically symmetric (quantum)
gravity to the most simple matter coupling, namely spherically symmetric
Maxwell theory with or without a cosmological constant. The quantization is
based on the reduced phase space which is coordinatized by the mass and the
electric charge as well as their canonically conjugate momenta, whose
geometrical interpretation is explored. The dimension of the reduced phase
space depends on the topology chosen, quite similar to the case of pure (2+1)
gravity. We investigate several conceptual and technical details that might be
of interest for full (3+1) gravity. We use the new canonical variables
introduced by Ashtekar, which simplifies the analysis tremendously.Comment: 37p, LATE
Statistical thermodynamics for choice models on graphs
Formalism based on equilibrium statistical thermodynamics is applied to
communication networks of decision making individuals. It is shown that in
statistical ensembles for choice models, properly defined disutility can play
the same role as energy in statistical mechanics. We demonstrate additivity and
extensivity of disutility and build three types of equilibrium statistical
ensembles: the canonical, the grand canonical and the super-canonical. Using
Boltzmann-like probability measure one reproduce the logit choice model. We
also propose using q-distributions for temperature evolution of moments of
stochastic variables. The formalism is applied to three network topologies of
different degrees of symmetry, for which in many cases analytic results are
obtained and numerical simulations are performed for all of them. Possible
applications of the model to airline networks and its usefulness for practical
support of economic decisions is pointed out.Comment: 17 pages, 13 figure
Sensitivity and stability: A signal propagation sweet spot in a sheet of recurrent centre crossing neurons
In this paper we demonstrate that signal propagation across a laminar sheet of recurrent neurons is maximised when two conditions are met. First, neurons must be in the so-called centre crossing configuration. Second, the network’s topology and weights must be such that the network comprises strongly coupled nodes, yet lies within the weakly coupled regime. We develop tools from linear stability analysis with which to describe this regime, and use them to examine the apparent tension between the sensitivity and instability of centre crossing networks
Three-loop mixed QCD-electroweak corrections to Higgs boson gluon fusion
We compute the contribution of three-loop mixed QCD-electroweak corrections
() to the scattering amplitude. We employ the
method of differential equations to compute the relevant integrals and express
them in terms of Goncharov polylogarithms.Comment: 21 pages, associated ancillary files distributed with the paper or
available from external repository. Correct typos and reference
Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions
Kernel mean embeddings have recently attracted the attention of the machine
learning community. They map measures from some set to functions in a
reproducing kernel Hilbert space (RKHS) with kernel . The RKHS distance of
two mapped measures is a semi-metric over . We study three questions.
(I) For a given kernel, what sets can be embedded? (II) When is the
embedding injective over (in which case is a metric)? (III) How does
the -induced topology compare to other topologies on ? The existing
machine learning literature has addressed these questions in cases where is
(a subset of) the finite regular Borel measures. We unify, improve and
generalise those results. Our approach naturally leads to continuous and
possibly even injective embeddings of (Schwartz-) distributions, i.e.,
generalised measures, but the reader is free to focus on measures only. In
particular, we systemise and extend various (partly known) equivalences between
different notions of universal, characteristic and strictly positive definite
kernels, and show that on an underlying locally compact Hausdorff space,
metrises the weak convergence of probability measures if and only if is
continuous and characteristic.Comment: Old and longer version of the JMLR paper with same title (published
2018). Please start with the JMLR version. 55 pages (33 pages main text, 22
pages appendix), 2 tables, 1 figure (in appendix
The multiregional core-periphery model: the role of the spatial topology
We use the multiregional core-periphery model of the new economic geography to
analyze and compare the agglomeration and dispersion forces shaping the location of
economic activity for a continuum of network topologies characterized by their degree
of centrality, and comprised between two extremes represented by the homogenous
(ring) and the heterogeneous (star) configurations. Resorting to graph theory, we
systematically extend the analytical tools and graphical representations of the
coreperiphery model for alternative spatial configurations, and study the stability of
the alternative equilibria in terms of the sustain and break points. We study new
phenomena such as the absence of any stable distribution of economic activity for some
range of transport costs, and the infeasibility of the dispersed equilibrium in the
heterogeneous space, resulting in the introduction of the concept pseudo flat-earth as a
long run-equilibrium corresponding to an uneven distribution of economic activity
between region
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