473 research outputs found
A linear theory for control of non-linear stochastic systems
We address the role of noise and the issue of efficient computation in
stochastic optimal control problems. We consider a class of non-linear control
problems that can be formulated as a path integral and where the noise plays
the role of temperature. The path integral displays symmetry breaking and there
exist a critical noise value that separates regimes where optimal control
yields qualitatively different solutions. The path integral can be computed
efficiently by Monte Carlo integration or by Laplace approximation, and can
therefore be used to solve high dimensional stochastic control problems.Comment: 5 pages, 3 figures. Accepted to PR
Path integrals and symmetry breaking for optimal control theory
This paper considers linear-quadratic control of a non-linear dynamical
system subject to arbitrary cost. I show that for this class of stochastic
control problems the non-linear Hamilton-Jacobi-Bellman equation can be
transformed into a linear equation. The transformation is similar to the
transformation used to relate the classical Hamilton-Jacobi equation to the
Schr\"odinger equation. As a result of the linearity, the usual backward
computation can be replaced by a forward diffusion process, that can be
computed by stochastic integration or by the evaluation of a path integral. It
is shown, how in the deterministic limit the PMP formalism is recovered. The
significance of the path integral approach is that it forms the basis for a
number of efficient computational methods, such as MC sampling, the Laplace
approximation and the variational approximation. We show the effectiveness of
the first two methods in number of examples. Examples are given that show the
qualitative difference between stochastic and deterministic control and the
occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA
Survey propagation at finite temperature: application to a Sourlas code as a toy model
In this paper we investigate a finite temperature generalization of survey
propagation, by applying it to the problem of finite temperature decoding of a
biased finite connectivity Sourlas code for temperatures lower than the
Nishimori temperature. We observe that the result is a shift of the location of
the dynamical critical channel noise to larger values than the corresponding
dynamical transition for belief propagation, as suggested recently by
Migliorini and Saad for LDPC codes. We show how the finite temperature 1-RSB SP
gives accurate results in the regime where competing approaches fail to
converge or fail to recover the retrieval state
Summer activity patterns of antarctic and high alpine lichen-dominated biological soil crusts-similar but different?
Replica symmetry breaking in the `small world' spin glass
We apply the cavity method to a spin glass model on a `small world' lattice,
a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. We
show the correspondence with a replicated transfer matrix approach, up to the
level of one step replica symmetry breaking (1RSB). Using the scheme developed
by M\'ezard & Parisi for the Bethe lattice, we evaluate observables for a model
with fixed connectivity and long range bonds. Our results agree with
numerical simulations significantly better than the replica symmetric (RS)
theory.Comment: 21 pages, 3 figure
The Supersymmetric Particle Spectrum
We examine the spectrum of supersymmetric particles predicted by grand
unified theoretical (GUT) models where the electroweak symmetry breaking is
accomplished radiatively. We evolve the soft supersymmetry breaking parameters
according to the renormalization group equations (RGE). The minimization of the
Higgs potential is conveniently described by means of tadpole diagrams. We
present complete one-loop expressions for these minimization conditions,
including contributions from the matter and the gauge sectors. We concentrate
on the low fixed point region (that provides a natural explanation
of a large top quark mass) for which we find solutions to the RGE satisfying
both experimental bounds and fine-tuning criteria. We also find that the
constraint from the consideration of the lightest supersymmetric particle as
the dark matter of the universe is accommodated in much of parameter space
where the lightest neutralino is predominantly gaugino. The supersymmetric mass
spectrum displays correlations that are model-independent over much of the GUT
parameter space.Comment: 62 pages + 10 PS figures included (uuencoded), MAD/PH/80
Effect of coupling asymmetry on mean-field solutions of direct and inverse Sherrington-Kirkpatrick model
We study how the degree of symmetry in the couplings influences the
performance of three mean field methods used for solving the direct and inverse
problems for generalized Sherrington-Kirkpatrick models. In this context, the
direct problem is predicting the potentially time-varying magnetizations. The
three theories include the first and second order Plefka expansions, referred
to as naive mean field (nMF) and TAP, respectively, and a mean field theory
which is exact for fully asymmetric couplings. We call the last of these simply
MF theory. We show that for the direct problem, nMF performs worse than the
other two approximations, TAP outperforms MF when the coupling matrix is nearly
symmetric, while MF works better when it is strongly asymmetric. For the
inverse problem, MF performs better than both TAP and nMF, although an ad hoc
adjustment of TAP can make it comparable to MF. For high temperatures the
performance of TAP and MF approach each other
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
extende
Optimal control as a graphical model inference problem
We reformulate a class of non-linear stochastic optimal control problems
introduced by Todorov (2007) as a Kullback-Leibler (KL) minimization problem.
As a result, the optimal control computation reduces to an inference
computation and approximate inference methods can be applied to efficiently
compute approximate optimal controls. We show how this KL control theory
contains the path integral control method as a special case. We provide an
example of a block stacking task and a multi-agent cooperative game where we
demonstrate how approximate inference can be successfully applied to instances
that are too complex for exact computation. We discuss the relation of the KL
control approach to other inference approaches to control.Comment: 26 pages, 12 Figures; Machine Learning Journal (2012
The future of sovereignty in multilevel governance Europe: a constructivist reading
Multilevel governance presents a depiction of contemporary structures in EU Europe as consisting of overlapping authorities and competing competencies. By focusing on emerging non-anarchical structures in the international system, hence moving beyond the conventional hierarchy/anarchy dichotomy to distinguish domestic and international arenas, this seems a radical transformation of the familiar Westphalian system and to undermine state sovereignty. Paradoxically, however, the principle of sovereignty proves to be resilient despite its alleged empirical decline. This article argues that social constructivism can explain the paradox, by considering sovereign statehood as a process-dependent institutional fact, and by showing that multilevel governance can feed into this process
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