Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models

AbstractConsider the independent Wishart matrices S1W(Σ + λΘ,q1) and S2W(Σ, q2) where Σ is an unknown positive definite (p.d.) matrix, Θ is an unknown nonnegative definite (n.n.d.) matrix, and λ is a known positive scalar. For the estimation of Θ, a class of estimators of the form Θ̂(c,ϵ) = (c/λ){S1/q1 − ϵ(S2/q2)} (c ≥ 0, ϵ ≤ 1), uniformly better than the unbiased estimator Θ̂U = (1/λ){S1/q1 − S2/q2}, is derived (for the squared error loss function). Necessary and sufficient conditions are obtained For the existence of an n.n.d. estimator of the form Θ̂(c,ϵ) uniformly better than ΘU. It turns out that such an n.n.d. estimator exists only under restrictive conditions. However, for a suitable choice of c > 0, ϵ > 0, the estimator obtained by taking the positive part of Θ̂(c, ϵ) results in an n.n.d. estimator, say Θ̂(c, ϵ) +, that is uniformly better than Θ̂U. Numerical results indicate that in terms of mean squared error, Θ̂(c, ϵ) + performs much better than both Θ̂U and the restricted maximum likelihood estimator Θ̂REML of Θ. Similar results are also obtained for the nonnegative estimation of tr Θ and a′Θa, where a is an arbitrary nonzero vector. For estimating Σ, we have derived estimators that are claimed to be uniformly better than the unbiased estimator Σ̂U = S2/q2 under the squared error loss function and the entropy loss function. We have been able to establish the claim only in the bivariate case. Numerical results are reported showing the risk improvement of our proposed estimators of Σ

Annexes of fourth year evaluation of the IDRC / CIDA co-financed BAIF Research Foundation Rural Research Project

Contents: Fourth year evaluation of women in development aspects; Fourth year evaluation of information aspects; Fourth year evaluation of animal science aspects; Fourth year evaluation of training aspect

Lockin to Weak Ferromagnetism in TbNi2B2C and ErNi2B2C

This article describes a model in which ferromagnetism necessarily accompanies a spin-density-wave lockin transition in the borocarbide structure provided the commensurate phase wave vector satisfies Q = (m/n)a* with m even and n odd. The results account for the magnetic properties of TbNi2B2C, and are also possibly relevant also for those of ErNi2B2C.Comment: 4 page

Space-time evolution of ultra-relativistic heavy ion collisions and hadronic spectra

The space-time evolution of the hot and dense matter formed after the collisions of heavy nuclei at ultra-relativistic energies is investigated using (3+1) dimensional hydrodynamical models. The effects of the spectral shift of the hadronic properties are incorporated in the equation of state (EOS) of the evolving matter. In-medium shift of hadronic properties are considered for Quantum Hadrodynamics (QHD) and universal scaling scenarios. It is found that the EOS for the hadronic matter for universal scaling of hadronic masses (except pseudoscalar mesons) is similar to the recent lattice results. We observe that the space-time volume of the hadronic matter at the freeze-out is considerably different from the one when medium effects on the hadrons are ignored. The sensitivity of the results on the initial radial velocity profile is investigated. The transverse mass spectra of pions and protons of NA49 collaboration are analyzed.Comment: Total 17 pages with 18 figure

Magnetic Phase Diagram of GdNi2B2C: Two-ion Magnetoelasticity and Anisotropic Exchange Couplings

Extensive magnetization and magnetostriction measurements were carried out on a single crystal of GdNi2B2C along the main tetragonal axes. Within the paramagnetic phase, the magnetic and strain susceptibilities revealed a weak anisotropy in the exchange couplings and two-ion tetragonal-preserving alpha-strain modes. Within the ordered phase, magnetization and magnetostriction revealed a relatively strong orthorhombic distortion mode and rich field-temperature phase diagrams. For H//(100) phase diagram, three field-induced transformations were observed, namely, at: Hd(T), related to the domain alignment; Hr(T), associated with reorientation of the moment towards the c-axis; and Hs(T), defining the saturation process wherein the exchange field is completely counterbalanced. On the other hand, For H//(001) phase diagram, only two field-induced transformations were observed, namely at: Hr(T) and Hs(T). For both phase diagrams, Hs(T) follows the relation Hs[1-(T/Tn)^2]^(1/2)kOe with Hs(T-->0)=128.5(5) kOe and Tn(H=0)=19.5 K. In contrast, the thermal evolution of Hr(T) along the c-axis (much simpler than along the a-axis) follows the relation Hr[1-T/Tr]^(1/3) kOe where Hr(T-->0)=33.5(5) kOe and Tr(H=0)=13.5 K. It is emphasized that the magnetoelastic interaction and the anisotropic exchange coupling are important perturbations and therefore should be explicitly considered if a complete analysis of the magnetic properties of the borocarbides is desired

Photon interferometry and size of the hot zone in relativistic heavy ion collisions

The parameters obtained from the theoretical analysis of the single photon spectra observed by the WA98 collaboration at SPS energies have been used to evaluate the two photon correlation functions. The single photon spectra and the two photon correlations at RHIC energies have also been evaluated, taking into account the effects of the possible spectral change of hadrons in a thermal bath. We find that the ratio $R_{side}/R_{out} \sim 1$ for SPS and $R_{side}/R_{out} <1$ for RHIC energy.Comment: text changed, figures adde

Particle density fluctuations

Event-by-event fluctuations in the multiplicities of charged particles and photons at SPS energies are discussed. Fluctuations are studied by controlling the centrality of the reaction and rapidity acceptance of the detectors. Results are also presented on the event-by-event study of correlations between the multiplicity of charged particles and photons to search for DCC-like signals.Comment: Talk presented at Quark Matter 2002, Nantes, Franc

Search for DCC in 158A GeV Pb+Pb Collisions

A detailed analysis of the phase space distributions of charged particles and photons have been carried out using two independent methods. The results indicate the presence of nonstatistical fluctuations in localized regions of phase space.Comment: Talk at the PANIC99 Conference, June 9-16, 199

Pion Freeze-Out Time in Pb+Pb Collisions at 158 A GeV/c Studied via pi-/pi+ and K-/K+ Ratios

The effect of the final state Coulomb interaction on particles produced in Pb+Pb collisions at 158 A GeV/c has been investigated in the WA98 experiment through the study of the pi-/pi+ and K-/K+ ratios measured as a function of transverse mass. While the ratio for kaons shows no significant transverse mass dependence, the pi-/pi+ ratio is enhanced at small transverse mass values with an enhancement that increases with centrality. A silicon pad detector located near the target is used to estimate the contribution of hyperon decays to the pi-/pi+ ratio. The comparison of results with predictions of the RQMD model in which the Coulomb interaction has been incorporated allows to place constraints on the time of the pion freeze-out.Comment: 9 pages, 12 figure

Present Status and Future of DCC Analysis

Disoriented Chiral Condensates (DCC) have been predicted to form in high energy heavy ion collisions where the approximate chiral symmetry of QCD has been restored. This leads to large imbalances in the production of charged to neutral pions. Sophisticated analysis methods are being developed to disentangle DCC events out of the large background of events with conventionally produced particles. We present a short review of current analysis methods and future prospects.Comment: 12 pages, 5 figures. Invited talk presented at the 13th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 97), Tsukuba, Japan, 1-5 Dec 199