Search results for "Invariant"

Testing Equality of Multiple Power Spectral Density Matrices

2018

This paper studies the existence of optimal invariant detectors for determining whether P multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i.e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the c…

Locally optimal invariant detector for testing equality of two power spectral densities

2018

This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT do…

The generalized plane piezoelectric problem: Theoretical formulation and application to heterostructure nanowires

2016

We present a systematic methodology for the reformulation of a broad class of three-dimensional (3D) piezoelectric problems into a two-dimensional (2D) mathematical form. The sole underlying hypothesis is that the system geometry and material properties as well as the applied loads (forces and charges) and boundary conditions are translationally invariant along some direction. This class of problems is commonly denoted here as the generalized plane piezoelectric (GPP) problem. The first advantage of the generalized plane problems is that they are more manageable from both analytical and computational points of view. Moreover, they are flexible enough to accommodate any geometric cross secti…

On the role of symmetry in solving maximum lifetime problem in two-dimensional sensor networks

2016

We analyze a continuous and discrete symmetries of the maximum lifetime problem in two dimensional sensor networks. We show, how a symmetry of the network and invariance of the problem under a given transformation group $G$ can be utilized to simplify its solution. We prove, that for a $G$-invariant maximum lifetime problem there exists a $G$-invariant solution. Constrains which follow from the $G$-invariance allow to reduce the problem and its solution to a subset, an optimal fundamental region of the sensor network. We analyze in detail solutions of the maximum lifetime problem invariant under a group of isometry transformations of a two dimensional Euclidean plane.

Intensity-invariant nonlinear filtering for detection in camouflage.

2005

We introduce a method based on an orthonormal vector space basis representation to detect camouflaged targets in natural environments. The method is intensity invariant so that camouflaged targets are detected independently of the illumination conditions. The detection technique does not require one to know the exact camouflage pattern, but only the class of patterns (e.g., foliage, netting, woods). We use nonlinear filtering and the calculation of several correlations. The nonlinearity of the filtering process also allows high discrimination against false targets. Several experiments confirm the target detectability where strong camouflage might delude even human viewers.

Convergence analysis of cubature Kalman filter

2014

This paper investigates the stability analysis of cubature Kalman filter (CKF) for nonlinear systems with linear measurement. The certain conditions to ensure that the estimation error of CKF remains bounded are proved. Then, the effect of process noise covariance is investigated and an adaptive process noise covariance is proposed to deal with large estimation error. Accordingly, a modified CKF (MCKF) is developed to enhance the stability and accuracy of state estimation. The performance of the MCKF is compared to the CKF by two case studies. Simulation results demonstrate that the large estimation error may lead to instability of CKF while the MCKF is successfully able to estimate the sta…

Edge detection insensitive to changes of illumination in the image

2010

In this paper we present new edge detection algorithms which are motivated by recent developments on edge-adapted reconstruction techniques [F. Arandiga, A. Cohen, R. Donat, N. Dyn, B. Matei, Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques, Appl. Comput. Harmon. Anal. 24 (2) (2008) 225-250]. They are based on comparing local quantities rather than on filtering and thresholding. This comparison process is invariant under certain transformations that model light changes in the image, hence we obtain edge detection algorithms which are insensitive to changes in illumination.

Adiabatic invariant change due to separatrix crossing at sweeping through a Feshbach resonance in a nonlinear two-mode system.

2007

Dielectron production in proton-proton and proton-lead collisions at √sNN=5.02TeV

2020

The first measurements of dielectron production at midrapidity (|ηe| < 0.8) in proton–proton and proton–lead collisions at √sNN = 5.02 TeV at the LHC are presented. The dielectron cross section is measured with the ALICE detector as a function of the invariant mass mee and the pair transverse momentum pT, ee in the ranges mee < 3.5 GeV/c2 and pT, ee < 8 GeV/c, in both collision systems. In proton–proton collisions, the charm and beauty cross sections are determined at midrapidity from a fit to the data with two different event generators. This complements the existing dielectron measurements performed at √s = 7 and 13 TeV. The slope of the √s dependence of the three measurements is…

Measurement of CP asymmetries in the decays B0 → K*0 μ+μ- and B+ → K+ μ+μ-

2014

The direct CP asymmetries of the decays B 0 → K *0 μ + μ − and B + → K + μ + μ − are measured using pp collision data corresponding to an integrated luminosity of 3.0 fb−1 collected with the LHCb detector. The respective control modes B 0 → J/ψK *0 and B + → J/ψK + are used to account for detection and production asymmetries. The measurements are made in several intervals of μ + μ − invariant mass squared, with the ϕ(1020) and charmonium resonance regions excluded. Under the hypothesis of zero CP asymmetry in the control modes, the average values of the asymmetries are ACP(B0→K∗0μ+μ−)=−0.035±0.024±0.003,ACP(B+→K+μ+μ−)=0.012±0.017±0.001, where the first uncertainties are statistical and the …