1,346 research outputs found
Discrete and continuum third quantization of Gravity
We give a brief introduction to matrix models and the group field theory
(GFT) formalism as realizations of the idea of a third quantization of gravity,
and present in some more detail the idea and basic features of a continuum
third quantization formalism in terms of a field theory on the space of
connections, building up on the results of loop quantum gravity that allow to
make the idea slightly more concrete. We explore to what extent one can
rigorously define such a field theory. Concrete examples are given for the
simple case of Riemannian GR in 3 spacetime dimensions. We discuss the relation
between GFT and this formal continuum third quantized gravity, and what it can
teach us about the continuum limit of GFTs.Comment: 21 pages, 5 eps figures; submitted as a contribution to the
proceedings of the conference "Quantum Field Theory and Gravity Conference
Regensburg 2010" (28 September - 1 October 2010, Regensburg/Bavaria); v2:
preprint number include
Simulation of networks of spiking neurons: A review of tools and strategies
We review different aspects of the simulation of spiking neural networks. We
start by reviewing the different types of simulation strategies and algorithms
that are currently implemented. We next review the precision of those
simulation strategies, in particular in cases where plasticity depends on the
exact timing of the spikes. We overview different simulators and simulation
environments presently available (restricted to those freely available, open
source and documented). For each simulation tool, its advantages and pitfalls
are reviewed, with an aim to allow the reader to identify which simulator is
appropriate for a given task. Finally, we provide a series of benchmark
simulations of different types of networks of spiking neurons, including
Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based
or conductance-based synapses, using clock-driven or event-driven integration
strategies. The same set of models are implemented on the different simulators,
and the codes are made available. The ultimate goal of this review is to
provide a resource to facilitate identifying the appropriate integration
strategy and simulation tool to use for a given modeling problem related to
spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of
Computational Neuroscience, in press (2007
Order in glassy systems
A directly measurable correlation length may be defined for systems having a
two-step relaxation, based on the geometric properties of density profile that
remains after averaging out the fast motion. We argue that the length diverges
if and when the slow timescale diverges, whatever the microscopic mechanism at
the origin of the slowing down. Measuring the length amounts to determining
explicitly the complexity from the observed particle configurations. One may
compute in the same way the Renyi complexities K_q, their relative behavior for
different q characterizes the mechanism underlying the transition. In
particular, the 'Random First Order' scenario predicts that in the glass phase
K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis
of a nonequilibrium effective temperature may also be directly tested directly
from configurations.Comment: Typos corrected, clarifications adde
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