Effect of W, LR, and LM Tests on the Performance of Preliminary Test Ridge Regression Estimators

This paper combines the idea of preliminary test and ridge regression methodology, when it is suspected that the regression coefficients may be restricted to a subspace. The preliminary test ridge regression estimators (PTRRE) based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are considered. The bias and the mean square errors (MSE) of the proposed estimators are derived under both null and alternative hypotheses. By studying the MSE criterion, the regions of optimality of the estimators are determined. Under the null hypothesis, the PTRRE based on LM test has the smallest risk followed by the estimators based on LR and W tests. However, the PTRRE based on W test performs the best followed by the LR and LM based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimator for both ridge parameter k and departure parameter (triangle symbol) are provided. Some graphical representations have been presented which support the findings of the paper. Some tables for maximum and minimum guaranteed relative efficiency of the proposed estimators have been provided. These tables allow us to determine the optimum level of significance corresponding to the optimum estimators among proposed estimators. Finally, we concluded that the optimum choice of the level of significance becomes the traditional choice by using the W test for all non-negative ridge parameter, k.Dominance; Lagrangian Multiplier; Likelihood Ratio Test; MSE; Non-central Chisquare and F; Ridge Regression; Superiority; Wald Test.

Role of entanglement in two-photon imaging

The use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever the strength of the correlations between the two photons. We consider a two-photon imaging system in which one photon is used to probe a remote (transmissive or scattering) object, while the other serves as a reference. We discuss the role of entanglement versus correlation in such a setting, and demonstrate that entanglement is a prerequisite for achieving distributed quantum imaging.Comment: 15 pages, 2 figure

Synthesis of Supported Catalysts by Dry Impregnation in Fluidized Bed

The synthesis of catalytic or not composite materials by dry impregnation in fluidized bed is described. This process can be carried out under mild conditions from solutions of organometallic precursors or colloidal solutions of preformed nanoparticles giving rise to reproducible metallic nanoparticles containing composite materials with a high reproducibility. The adequate choice of the reaction conditions makes possible to deposit uniformly the metal precursor within the porous matrix or on the support surface. When the ratio between the drying time and the capillary penetration time (tsec/tcap) is higher than 10, the impregnation under soft drying conditions leads to a homogeneous deposit inside the pores of the particles of support. The efficiency of the metal deposition is close to 100%, and the size of the formed metal nanoparticles is controlled by the pores diameter. Finally, some of the presented composite materials have been tested as catalysts: iron-based materials were used in carbon-nanotubes synthesis, while Pd and Rh composite materials have been investigated in hydrogenation reactions

Non-diffracting Optical Beams in a Three-level Raman System

Diffractionless propagation of optical beams through atomic vapors is investigated. The atoms in the vapor are operated in a three-level Raman configuration. A suitably chosen control beam couples to one of the transitions, and thereby creates a spatially varying index of refraction modulation in the warm atomic vapor for a probe beam which couples to the other transition in the atoms. We show that a Laguerre-Gaussian control beam allows to propagate single Gaussian probe field modes as well as multi-Gaussian modes and non-Gaussian modes over macroscopic distances without diffraction. This opens perspectives for the propagation of arbitrary images through warm atomic vapors.Comment: 8 pages, 7 figure

Performance of Photon-Pair Quantum Key Distribution Systems

We analyze the quantitative improvement in performance provided by a novel quantum key distribution (QKD) system that employs a correlated photon source (CPS) and a photon-number resolving detector (PNR). Our calculations suggest that given current technology, the CPR implementation offers an improvement of several orders of magnitude in secure bit rate over previously described implementations

Generation of Entangled Photon Holes using Quantum Interference

In addition to photon pairs entangled in polarization or other variables, quantum mechanics also allows optical beams that are entangled through the absence of the photons themselves. These correlated absences, or ``entangled photon holes'', can lead to counter-intuitive nonlocal effects analogous to those of the more familiar entangled photon pairs. Here we report an experimental observation of photon holes generated using quantum interference effects to suppress the probability that two photons in a weak laser pulse will separate at an optical beam splitter.Comment: 4 pages, color figures, submitted to Phys. Rev.

Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection

We consider the problem of distinguishing, with minimum probability of error, two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over M signal and M' idler mode pairs of which the signal modes are bounced off the beam splitter while the idler modes are retained losslessly. We obtain a lower bound on the output state fidelity valid for any pure input state. We define number-diagonal signal (NDS) states to be input states whose density operator in the signal modes is diagonal in the multimode number basis. For such input states, we derive series formulas for the optimal error probability, the output state fidelity, and the Chernoff-type upper bounds on the error probability. For the special cases of quantum reading of a classical digital memory and target detection (for which the reflectivities are real valued), we show that for a given input signal photon probability distribution, the fidelity is minimized by the NDS states with that distribution and that for a given average total signal energy N_s, the fidelity is minimized by any multimode Fock state with N_s total signal photons. For reading of an ideal memory, it is shown that Fock state inputs minimize the Chernoff bound. For target detection under high-loss conditions, a no-go result showing the lack of appreciable quantum advantage over coherent state transmitters is derived. A comparison of the error probability performance for quantum reading of number state and two-mode squeezed vacuum state (or EPR state) transmitters relative to coherent state transmitters is presented for various values of the reflectances. While the nonclassical states in general perform better than the coherent state, the quantitative performance gains differ depending on the values of the reflectances.Comment: 12 pages, 7 figures. This closely approximates the published version. The major change from v2 is that Section IV has been re-organized, with a no-go result for target detection under high loss conditions highlighted. The last sentence of the abstract has been deleted to conform to the arXiv word limit. Please see the PDF for the full abstrac

PHYLOGENETIC RELATIONSHIPS AMONGST 10 Durio SPECIES BASED ON PCR-RFLP ANALYSIS OF TWO CHLOROPLAST GENES

Twenty seven species of Durio have been identified in Sabah and Sarawak, Malaysia, but their relationships have not been studied. This study was conducted to analyse phylogenetic relationships amongst 10 Durio species in Malaysia using PCR-RFLP on two chloroplast DNA genes, i.e. ndhC-trnV and rbcL. DNAs were extracted from young leaves of 11 accessions from 10 Durio species collected from the Tenom Agriculture Research Station, Sabah, and University Agriculture Park, Universiti Putra Malaysia. Two pairs of oligonucleotide primers, N1-N2 and rbcL1-rbcL2, were used to flank the target regions ndhC-trnV and rbcL. Eight restriction enzymes, HindIII, BsuRI, PstI, TaqI, MspI, SmaI, BshNI, and EcoR130I, were used to digest the amplicons. Based on the results of PCR-RFLP on ndhC-trnV gene, the 10 Durio species were grouped into five distinct clusters, and the accessions generally showed high variations. However, based on the results of PCR-RFLP on the rbcL gene, the species were grouped into three distinct clusters, and generally showed low variations. This means that ndhC-trnV gene is more reliable for phylogenetic analysis in lower taxonomic level of Durio species or for diversity analysis, while rbcL gene is reliable marker for phylogenetic analysis at higher taxonomic level. PCR-RFLP on the ndhC-trnV and rbcL genes could therefore be considered as useful markers to phylogenetic analysis amongst Durio species. These finding might be used for further molecular marker assisted in Durio breeding program

Finite Mirror Effects in Advanced Interferometric Gravitational Wave Detectors

Thermal noise is expected to be the dominant source of noise in the most sensitive frequency band of second generation ground based gravitational wave detectors. Reshaping the beam to a flatter wider profile which probes more of the mirror surface reduces this noise. The "Mesa" beam shape has been proposed for this purpose and was subsequently generalized to a family of hyperboloidal beams with two parameters: twist angle alpha and beam width D. Varying alpha allows a continuous transition from the nearly-flat to the nearly-concentric Mesa beam configurations. We analytically prove that in the limit of infinite D hyperboloidal beams become Gaussians. The Advanced LIGO diffraction loss design constraint is 1 ppm per bounce. In the past the diffraction loss has often been calculated using the clipping approximation that, in general, underestimates the diffraction loss. We develop a code using pseudo-spectral methods to compute the diffraction loss directly from the propagator. We find that the diffraction loss is not a strictly monotonic function of beam width, but has local minima that occur due to finite mirror effects and leads to natural choices of D. For the Mesa beam a local minimum occurs at D = 10.67 cm and leads to a diffraction loss of 1.4 ppm. We find that if one requires a diffraction loss of strictly 1 ppm, the alpha = 0.91 pi hyperboloidal beam is optimal, leading to the coating thermal noise being lower by about 10% than for a Mesa beam while other types of thermal noise decrease as well. We then develop an iterative process that reconstructs the mirror to specifically account for finite mirror effects. This allows us to increase the D parameter and lower the coating noise by about 30% compared to the original Mesa configuration.Comment: 13 pages, 12 figures, 4 tables. Referee input included and typos fixed. Accepted by Phys. Rev.