3,364 research outputs found
The Wiener maximum quadratic assignment problem
We investigate a special case of the maximum quadratic assignment problem
where one matrix is a product matrix and the other matrix is the distance
matrix of a one-dimensional point set. We show that this special case, which we
call the Wiener maximum quadratic assignment problem, is NP-hard in the
ordinary sense and solvable in pseudo-polynomial time. Our approach also yields
a polynomial time solution for the following problem from chemical graph
theory: Find a tree that maximizes the Wiener index among all trees with a
prescribed degree sequence. This settles an open problem from the literature.Comment: 11 pages, no figure
Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
We address the inverse problem of cosmic large-scale structure reconstruction
from a Bayesian perspective. For a linear data model, a number of known and
novel reconstruction schemes, which differ in terms of the underlying signal
prior, data likelihood, and numerical inverse extra-regularization schemes are
derived and classified. The Bayesian methodology presented in this paper tries
to unify and extend the following methods: Wiener-filtering, Tikhonov
regularization, Ridge regression, Maximum Entropy, and inverse regularization
techniques. The inverse techniques considered here are the asymptotic
regularization, the Jacobi, Steepest Descent, Newton-Raphson,
Landweber-Fridman, and both linear and non-linear Krylov methods based on
Fletcher-Reeves, Polak-Ribiere, and Hestenes-Stiefel Conjugate Gradients. The
structures of the up-to-date highest-performing algorithms are presented, based
on an operator scheme, which permits one to exploit the power of fast Fourier
transforms. Using such an implementation of the generalized Wiener-filter in
the novel ARGO-software package, the different numerical schemes are
benchmarked with 1-, 2-, and 3-dimensional problems including structured white
and Poissonian noise, data windowing and blurring effects. A novel numerical
Krylov scheme is shown to be superior in terms of performance and fidelity.
These fast inverse methods ultimately will enable the application of sampling
techniques to explore complex joint posterior distributions. We outline how the
space of the dark-matter density field, the peculiar velocity field, and the
power spectrum can jointly be investigated by a Gibbs-sampling process. Such a
method can be applied for the redshift distortions correction of the observed
galaxies and for time-reversal reconstructions of the initial density field.Comment: 40 pages, 11 figure
Towards an Optimal Reconstruction of Baryon Oscillations
The Baryon Acoustic Oscillations (BAO) in the large-scale structure of the
universe leave a distinct peak in the two-point correlation function of the
matter distribution. That acoustic peak is smeared and shifted by bulk flows
and non-linear evolution. However, it has been shown that it is still possible
to sharpen the peak and remove its shift by undoing the effects of the bulk
flows. We propose an improvement to the standard acoustic peak reconstruction.
Contrary to the standard approach, the new scheme has no free parameters,
treats the large-scale modes consistently, and uses optimal filters to extract
the BAO information. At redshift of zero, the reconstructed linear matter power
spectrum leads to a markedly improved sharpening of the reconstructed acoustic
peak compared to standard reconstruction.Comment: 20 pages, 5 figures; footnote adde
The Onsager--Machlup functional for data assimilation
When taking the model error into account in data assimilation, one needs to
evaluate the prior distribution represented by the Onsager--Machlup functional.
Through numerical experiments, this study clarifies how the prior distribution
should be incorporated into cost functions for discrete-time estimation
problems. Consistent with previous theoretical studies, the divergence of the
drift term is essential in weak-constraint 4D-Var (w4D-Var), but it is not nec
essary in Markov chain Monte Carlo with the Euler scheme. Although the former
property may cause difficulties when implementing w4D-Var in large systems,
this paper proposes a new technique for estimating the divergence term and its
derivative.Comment: Reprint from Nonlin. Processes Geophys. (ver.5). 12 pages, 5 figure
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
Foreground separation methods for satellite observations of the cosmic microwave background
A maximum entropy method (MEM) is presented for separating the emission due
to different foreground components from simulated satellite observations of the
cosmic microwave background radiation (CMBR). In particular, the method is
applied to simulated observations by the proposed Planck Surveyor satellite.
The simulations, performed by Bouchet and Gispert (1998), include emission from
the CMBR, the kinetic and thermal Sunyaev-Zel'dovich (SZ) effects from galaxy
clusters, as well as Galactic dust, free-free and synchrotron emission. We find
that the MEM technique performs well and produces faithful reconstructions of
the main input components. The method is also compared with traditional Wiener
filtering and is shown to produce consistently better results, particularly in
the recovery of the thermal SZ effect.Comment: 31 pages, 19 figures (bitmapped), accpeted for publication in MNRA
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