2,952 research outputs found
Highly connected manifolds with positive Ricci curvature
We prove the existence of Sasakian metrics with positive Ricci curvature on
certain highly connected odd dimensional manifolds. In particular, we show that
manifolds homeomorphic to the 2k-fold connected sum of S^{2n-1} x S^{2n} admit
Sasakian metrics with positive Ricci curvature for all k. Furthermore, a
formula for computing the diffeomorphism types is given and tables are
presented for dimensions 7 and 11.Comment: This is the version published by Geometry & Topology on 29 November
200
Stability of Sasaki-extremal metrics under complex deformations
We consider the stability of Sasaki-extremal metrics under deformations of
the complex structure on the Reeb foliation. Given such a deformation
preserving the action of a compact subgroup of the automorphism group of a
Sasaki-extremal structure, a sufficient condition is given involving the
nondegeneracy of the relative Futaki invariant for the deformations to contain
Sasaki-extremal structures.
Deformations of Sasaki-Einstein metrics are also considered, where it
suffices that the deformation preserve a maximal torus. As an application, new
families of Sasaki-Einstein and Sasaki-extremal metrics are given on
deformations of well known 3-Sasaki 7-manifolds.Comment: Added the obstruction to the existence of Sasaki structures under
transversal complex deformations. 30 pages and 1 figur
On Sasaki-Einstein manifolds in dimension five
We prove the existence of Sasaki-Einstein metrics on certain simply connected
5-manifolds where until now existence was unknown. All of these manifolds have
non-trivial torsion classes. On several of these we show that there are a
countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde
Bayesian Lower Bounds for Dense or Sparse (Outlier) Noise in the RMT Framework
Robust estimation is an important and timely research subject. In this paper,
we investigate performance lower bounds on the mean-square-error (MSE) of any
estimator for the Bayesian linear model, corrupted by a noise distributed
according to an i.i.d. Student's t-distribution. This class of prior
parametrized by its degree of freedom is relevant to modelize either dense or
sparse (accounting for outliers) noise. Using the hierarchical Normal-Gamma
representation of the Student's t-distribution, the Van Trees' Bayesian
Cram\'er-Rao bound (BCRB) on the amplitude parameters is derived. Furthermore,
the random matrix theory (RMT) framework is assumed, i.e., the number of
measurements and the number of unknown parameters grow jointly to infinity with
an asymptotic finite ratio. Using some powerful results from the RMT,
closed-form expressions of the BCRB are derived and studied. Finally, we
propose a framework to fairly compare two models corrupted by noises with
different degrees of freedom for a fixed common target signal-to-noise ratio
(SNR). In particular, we focus our effort on the comparison of the BCRBs
associated with two models corrupted by a sparse noise promoting outliers and a
dense (Gaussian) noise, respectively
Joint ML calibration and DOA estimation with separated arrays
This paper investigates parametric direction-of-arrival (DOA) estimation in a
particular context: i) each sensor is characterized by an unknown complex gain
and ii) the array consists of a collection of subarrays which are substantially
separated from each other leading to a structured noise covariance matrix. We
propose two iterative algorithms based on the maximum likelihood (ML)
estimation method adapted to the context of joint array calibration and DOA
estimation. Numerical simulations reveal that the two proposed schemes, the
iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint
array calibration and DOA estimation, outperform the state of the art methods
and the MIML algorithm reaches the Cram\'er-Rao bound for a low number of
iterations
Relaxed concentrated MLE for robust calibration of radio interferometers
In this paper, we investigate the calibration of radio interferometers in
which Jones matrices are considered to model the interaction between the
incident electromagnetic field and the antennas of each station. Specifically,
perturbation effects are introduced along the signal path, leading to the
conversion of the plane wave into an electric voltage by the receptor. In order
to design a robust estimator, the noise is assumed to follow a spherically
invariant random process (SIRP). The derived algorithm is based on an iterative
relaxed concentrated maximum likelihood estimator (MLE), for which closed-form
expressions are obtained for most of the unknown parameters
Fast sequential source localization using the projected companion matrix approach
International audienceThe sequential forms of the spectral MUSIC algorithm, such as the Sequential MUSIC (S-MUSIC) and the Recursively Applied and Projected MUSIC (RAP-MUSIC) algorithms, use the previously estimated DOA (Direction Of Arrival) to form an intermediate array gain matrix and project both the array manifold and the signal subspace estimate into its orthogonal complement. By doing this, these methods avoid the delicate search of multiple maxima and yield a more accurate DOA estimation in difficult scenarios. However, these high-resolution algorithms adapted to a general array geometry suffer from a high computational cost. On the other hand, for linear equispaced sensor array, the root- MUSIC algorithm is a fast and accurate high-resolution scheme which also avoids the delicate search of multiple maxima but a sequential scheme based on the root-MUSIC algorithm does not exist. This paper fills this need. Thus, we present a new sequential high-resolution estimation method, called the Projected Companion Matrix MUSIC (PCM-MUSIC) method, in the context of source localisation in the case of linear equispaced sensor array. Remark that the proposed algorithm can be used without modification in the context of spectral analysis
Energy properness and Sasakian-Einstein metrics
In this paper, we show that the existence of Sasakian-Einstein metrics is
closely related to the properness of corresponding energy functionals. Under
the condition that admitting no nontrivial Hamiltonian holomorphic vector
field, we prove that the existence of Sasakian-Einstein metric implies a
Moser-Trudinger type inequality. At the end of this paper, we also obtain a
Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page
Phenylation of aminoindazole derivatives
AbstractThe triphenylbismuth diacetate reacted selectively with different aminoindazole derivatives in presence of copper diacetate to engender a new series of mono phenyl aminoindazole compounds in good to high yields. Moreover, the same reagent with 4-chloro-2-methyl-2H-indazol-7-amine led to a mixture of mono- and N,N-diphenylaminoindazoles. However, its combination with 2H-indazol-4-amine provided only one N,1-diphenylaminoindazole compound
GLRT-Based Framework for the Multidimensional Statistical Resolution Limit
International audienceRecently, a criterion for Multidimensional Statistical Resolution Limit (MSRL) evaluation, which is defined as the minimal separation to resolve two closely spaced signals depending on several parameters, was empirically proposed in [1] but without a statistical analysis. In this paper, we fill this lack by demonstrating that this MSRL criterion is asymptotically equivalent (upon to a translator factor) to a UMP (Uniformly Most Powerful) test among all invariant statistical tests. This result is an extension of a previous work on mono-dimensional SRL (i.e., when the signals only depend on one parameter). As an illustrative example, the 3-D harmonic retrieval case for wireless channel sounding is treated to show the good agreement of the proposed result
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