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Which quantile is the most informative? Maximum likelihood, maximum entropy and quantile regression
This paper studies the connections among quantile regression, the asymmetric Laplace distribution, maximum likelihood and maximum entropy. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment constraints given by the joint consideration of the mean and median. Using the resulting score functions we propose an estimator based on the joint estimating equations. This approach delivers estimates for the slope parameters together with the associated “most probable” quantile. Similarly, this method can be seen as a penalized quantile regression estimator, where the penalty is given by deviations from the median regression. We derive the asymptotic properties of this estimator by showing consistency and asymptotic normality under certain regularity conditions. Finally, we illustrate the use of the estimator with a simple application to the U.S. wage data to evaluate the effect of training on wages
Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
We study analytically and numerically the dynamics of the generalized
Rosenzweig-Porter model, which is known to possess three distinct phases:
ergodic, multifractal and localized phases. Our focus is on the survival
probability , the probability of finding the initial state after time
. In particular, if the system is initially prepared in a highly-excited
non-stationary state (wave packet) confined in space and containing a fixed
fraction of all eigenstates, we show that can be used as a dynamical
indicator to distinguish these three phases. Three main aspects are identified
in different phases. The ergodic phase is characterized by the standard
power-law decay of with periodic oscillations in time, surviving in the
thermodynamic limit, with frequency equals to the energy bandwidth of the wave
packet. In multifractal extended phase the survival probability shows an
exponential decay but the decay rate vanishes in the thermodynamic limit in a
non-trivial manner determined by the fractal dimension of wave functions.
Localized phase is characterized by the saturation value of ,
finite in the thermodynamic limit , which approaches
in this limit.Comment: 21 pages, 12 figures, 61 reference
Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control
We report the emergence of coexisting synchronous and asynchronous
subpopulations of oscillators in one dimensional arrays of identical
oscillators by applying a self-feedback control. When a self-feedback is
applied to a subpopulation of the array, similar to chimera states, it splits
into two/more sub-subpopulations coexisting in coherent and incoherent states
for a range of self-feedback strength. By tuning the coupling between the
nearest neighbors and the amount of self-feedback in the perturbed
subpopulation, the size of the coherent and the incoherent sub-subpopulations
in the array can be controlled, although the exact size of them is
unpredictable. We present numerical evidence using the Landau-Stuart (LS)
system and the Kuramoto-Sakaguchi (KS) phase model.Comment: 13 pages, 13 figures, accepted for publication in CHAOS (July 2017
Methodologies of Application of Sol-Gel Based Solution onto Substrate: A Review
Just as the diverse as the various substrates that can be coated is the choice of several coating methods by which the coating can be applied to these pretreated surfaces. They include the manual methods, where great skills and experience is needed, on the other hand there are automated and robotics coating control methods where coating can be applied with more precise manner. Sol-gel process is one of the promising bottom up nano-coating technologies to develop thin film over various metallic substrates. The property and characteristic of the resulting film is strongly influenced by the various parameters and reaction conditions of the sol-gel process and of course on the deposition techniques. In this review, we have thrown some lights on different coating application processes covering theoretical principle, advantages, disadvantages, and special various parameters controlling the final film quality
Molecules in clusters: the case of planar LiBeBCNOF built from a triangular form LiOB and a linear four-center species FBeCN
Krueger some years ago proposed a cluster LiBeBCNOF, now called periodane.
His ground-state isomer proposal has recently been refined by Bera et al. using
DFT. Here, we take the approach of molecules in such a cluster as starting
point. We first study therefore the triangular molecule LiOB by coupled cluster
theory (CCSD) and thereby specify accurately its equilibrium geometry in free
space. The second fragment we consider is FBeCN, but treated now by restricted
Hartree-Fock (RHF) theory. This four-center species is found to be linear, and
the bond lengths are obtained from both RHF and CCSD calculations. Finally, we
bring these two entities together and find that while LiOB remains largely
intact, FBeCN becomes bent by the interaction with LiOB. Hartree-Fock and CCSD
theories then predict precisely the same lowest isomer found by Bera et al.
solely on the basis of DFT.Comment: to appear in Phys. Lett.
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