49,648 research outputs found
Distributed estimation from relative measurements of heterogeneous and uncertain quality
This paper studies the problem of estimation from relative measurements in a
graph, in which a vector indexed over the nodes has to be reconstructed from
pairwise measurements of differences between its components associated to nodes
connected by an edge. In order to model heterogeneity and uncertainty of the
measurements, we assume them to be affected by additive noise distributed
according to a Gaussian mixture. In this original setup, we formulate the
problem of computing the Maximum-Likelihood (ML) estimates and we design two
novel algorithms, based on Least Squares regression and
Expectation-Maximization (EM). The first algorithm (LS- EM) is centralized and
performs the estimation from relative measurements, the soft classification of
the measurements, and the estimation of the noise parameters. The second
algorithm (Distributed LS-EM) is distributed and performs estimation and soft
classification of the measurements, but requires the knowledge of the noise
parameters. We provide rigorous proofs of convergence of both algorithms and we
present numerical experiments to evaluate and compare their performance with
classical solutions. The experiments show the robustness of the proposed
methods against different kinds of noise and, for the Distributed LS-EM,
against errors in the knowledge of noise parameters.Comment: Submitted to IEEE transaction
What is the Brillouin Zone of an Anisotropic Photonic Crystal?
The concept of the Brillouin zone (BZ) in relation to a photonic crystal
fabricated in an optically anisotropic material is explored both experimentally
and theoretically. In experiment, we used femtosecond laser pulses to excite
THz polaritons and image their propagation in lithium niobate and lithium
tantalate photonic crystal (PhC) slabs. We directly measured the dispersion
relation inside PhCs and observed that the lowest bandgap expected to form at
the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our
analysis shows that in an anisotropic material the BZ - defined as the
Wigner-Seitz cell in the reciprocal lattice - is no longer bounded by Bragg
planes and thus does not conform to the original definition of the BZ by
Brillouin. We construct an alternative Brillouin zone defined by Bragg planes
and show its utility in identifying features of the dispersion bands. We show
that for an anisotropic 2D PhC without dispersion, the Bragg plane BZ can be
constructed by applying the Wigner-Seitz method to a stretched or compressed
reciprocal lattice. We also show that in the presence of the dispersion in the
underlying material or in a slab waveguide, the Bragg planes are generally
represented by curved surfaces rather than planes. The concept of constructing
a BZ with Bragg planes should prove useful in understanding the formation of
dispersion bands in anisotropic PhCs and in selectively tailoring their optical
properties.Comment: 9 pages, 6 figure
A model metal potential exhibiting polytetrahedral clusters
Putative global minima have been located for clusters interacting with an
aluminium glue potential for N<190. Virtually all the clusters have
polytetrahedral structures, which for larger sizes involve an ordered array of
disclinations that are similar to those in the Z, H and sigma Frank-Kasper
phases. Comparisons of sequences of larger clusters suggest that the majority
of the global minima will adopt the bulk face-centred-cubic structure beyond
N=500.Comment: 14 pages, 7 figure
A Physical Theory of the Competition that Allows HIV to Escape from the Immune System
Competition within the immune system may degrade immune control of viral
infections. We formalize the evolution that occurs in both HIV-1 and the immune
system quasispecies. Inclusion of competition in the immune system leads to a
novel balance between the immune response and HIV-1, in which the eventual
outcome is HIV-1 escape rather than control. The analytical model reproduces
the three stages of HIV-1 infection. We propose a vaccine regimen that may be
able to reduce competition between T cells, potentially eliminating the third
stage of HIV-1.Comment: 5 pages, 2 figures, to appear in Phys. Rev. Let
Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in 2D : A study using deposition-evaporation kinetics
Deposition and evaporation of infinitely thin hard rods (needles) is studied
in two dimensions using Monte Carlo simulations. The ratio of deposition to
evaporation rates controls the equilibrium density of rods, and increasing it
leads to an entropy-driven transition to a nematic phase in which both static
and dynamical orientational correlation functions decay as power laws, with
exponents varying continuously with deposition-evaporation rate ratio. Our
results for the onset of the power-law phase agree with those for a conserved
number of rods. At a coarse-grained level, the dynamics of the non-conserved
angle field is described by the Edwards-Wilkinson equation. Predicted relations
between the exponents of the quadrupolar and octupolar correlation functions
are borne out by our numerical results. We explore the effects of spatial
inhomogeneity in the deposition-evaporation ratio by simulations, entropy-based
arguments and a study of the new terms introduced in the free energy. The
primary effect is that needles tend to align along the local spatial gradient
of the ratio. A uniform gradient thus induces a uniformly aligned state, as
does a gradient which varies randomly in magnitude and sign, but acts only in
one direction. Random variations of deposition-evaporation rates in both
directions induce frustration, resulting in a state with glassy
characteristics.Comment: modified version, Accepted for publication in Physical Review
Mapping the magic numbers in binary Lennard-Jones clusters
Using a global optimization approach that directly searches for the
composition of greatest stability, we have been able to find the particularly
stable structures for binary Lennard-Jones clusters with up to 100 atoms for a
range of Lennard-Jones parameters. In particular, we have shown that just
having atoms of different size leads to a remarkable stabilization of
polytetrahedral structures, including both polyicosahedral clusters and at
larger sizes structures with disclination lines.Comment: 5 pages, 5 figure
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