5,752 research outputs found
Asymptotic properties of maximum likelihood estimators in models with multiple change points
Models with multiple change points are used in many fields; however, the
theoretical properties of maximum likelihood estimators of such models have
received relatively little attention. The goal of this paper is to establish
the asymptotic properties of maximum likelihood estimators of the parameters of
a multiple change-point model for a general class of models in which the form
of the distribution can change from segment to segment and in which, possibly,
there are parameters that are common to all segments. Consistency of the
maximum likelihood estimators of the change points is established and the rate
of convergence is determined; the asymptotic distribution of the maximum
likelihood estimators of the parameters of the within-segment distributions is
also derived. Since the approach used in single change-point models is not
easily extended to multiple change-point models, these results require the
introduction of those tools for analyzing the likelihood function in a multiple
change-point model.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ232 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors
The main objective of this paper is to derive the efficiency bounds for estimating certain linear functionals of an unknown structural function when the latter is not itself a conditional expectation.
Regular quantum graphs
We introduce the concept of regular quantum graphs and construct connected
quantum graphs with discrete symmetries. The method is based on a decomposition
of the quantum propagator in terms of permutation matrices which control the
way incoming and outgoing channels at vertex scattering processes are
connected. Symmetry properties of the quantum graph as well as its spectral
statistics depend on the particular choice of permutation matrices, also called
connectivity matrices, and can now be easily controlled. The method may find
applications in the study of quantum random walks networks and may also prove
to be useful in analysing universality in spectral statistics.Comment: 12 pages, 3 figure
Linking the Quasi-Normal and Natural Modes of an open cavity
The present paper proposes a comparison between the extinction theorem and
the Sturm-Liouville theory approaches for calculating the e.m. field inside an
optical cavity. We discuss for the first time to the best of our knowledge, in
the framework of classical electrodynamics, a simple link between the Quasi
Normal Modes (QNMs) and the Natural Modes (NMs) for one-dimensional (1D),
two-sided, open cavities. The QNM eigenfrequencies and eigenfunctions are
calculated for a linear Fabry-Perot (FP) cavity. The first-order Born
approximation is applied to the same cavity in order to compare the first-order
Born approximated and the actual QNM eigenfunctions of the cavity. We
demonstrate that the first-order Born approximation for an FP cavity introduces
symmetry breaking: in fact, each Born approximated QNM eigenfunction produces
values below or above the actual QNM eigenfunction value on the terminal
surfaces of the same cavity. Consequently, the two error-functions for an
approximated QNM are not equal in proximity to the two terminal surfaces of the
cavity.Comment: 38 pages, 3 figures; Earth-prints, http://hdl.handle.net/2122/5993
(2009
Perturbation theory in a pure exchange non-equilibrium economy
We develop a formalism to study linearized perturbations around the
equilibria of a pure exchange economy. With the use of mean field theory
techniques, we derive equations for the flow of products in an economy driven
by heterogeneous preferences and probabilistic interaction between agents. We
are able to show that if the economic agents have static preferences, which are
also homogeneous in any of the steady states, the final wealth distribution is
independent of the dynamics of the non-equilibrium theory. In particular, it is
completely determined in terms of the initial conditions, and it is independent
of the probability, and the network of interaction between agents. We show that
the main effect of the network is to determine the relaxation time via the
usual eigenvalue gap as in random walks on graphs.Comment: 7 pages, 2 figure
On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback
© 1963-2012 IEEE. We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions
Lorentz Beams
A new kind of tridimensional scalar optical beams is introduced. These beams
are called Lorentz beams because the form of their transverse pattern in the
source plane is the product of two independent Lorentz functions. Closed-form
expression of free-space propagation under paraxial limit is derived and pseudo
non-diffracting features pointed out. Moreover, as the slowly varying part of
these fields fulfils the scalar paraxial wave equation, it follows that there
exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original
Lorentz beam to a Gaussian apodization function. Although the existence of
Lorentz-Gauss beams can be shown by using two different and independent ways
obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega
et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different
approach, which makes use of Lie's group theory, and which possesses the merit
to put into evidence the symmetries present in paraxial Optics.Comment: 11 pages, 1 figure, submitted to Journal of Optics
HIDDEN ENTANGLEMENT AND UNITARITY AT THE PLANCK SCALE
Attempts to go beyond the framework of local quantum field theory include scenarios in which the action of external symmetries on the quantum fields Hilbert space is deformed. We show how the Fock spaces of such theories exhibit a richer structure in their multi-particle sectors. When the deformation scale is proportional to the Planck energy, such new structure leads to the emergence of a "planckian" mode-entanglement, invisible to an observer that cannot probe the Planck scale. To the same observer, certain unitary processes would appear non-unitary. We show how entanglement transfer to the additional degrees of freedom can provide a potential way out of the black hole information paradox
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