An efficiency upper bound for inverse covariance estimation

We derive an upper bound for the efficiency of estimating entries in the inverse covariance matrix of a high dimensional distribution. We show that in order to approximate an off-diagonal entry of the density matrix of a $d$-dimensional Gaussian random vector, one needs at least a number of samples proportional to $d$. Furthermore, we show that with $n \ll d$ samples, the hypothesis that two given coordinates are fully correlated, when all other coordinates are conditioned to be zero, cannot be told apart from the hypothesis that the two are uncorrelated.Comment: 7 Page

Aerothermodynamic Characteristics of Boundary Layer Transition and Trip Effectiveness of the HIFiRE Flight 5 Vehicle

An experimental wind tunnel test was conducted in the NASA Langley Research Center s 20-Inch Mach 6 Tunnel in support of the Hypersonic International Flight Research Experimentation Program. The information in this report is focused on the Flight 5 configuration, one in a series of flight experiments. This report documents experimental measurements made over a range of Reynolds numbers and angles of attack on several scaled ceramic heat transfer models of the Flight 5 vehicle. The heat transfer rate was measured using global phosphor thermography and the resulting images and heat transfer rate distributions were used to infer the state of the boundary layer on the windside, leeside and side surfaces. Boundary layer trips were used to force the boundary layer turbulent, and a study was conducted to determine the effectiveness of the trips with various heights. The experimental data highlighted in this test report were used determine the allowable roughness height for both the windside and side surfaces of the vehicle as well as provide for future tunnel-to-tunnel comparisons

Muon Catalyzed Fusion in 3 K Solid Deuterium

Muon catalyzed fusion in deuterium has traditionally been studied in gaseous and liquid targets. The TRIUMF solid-hydrogen-layer target system has been used to study the fusion reaction rates in the solid phase of D_2 at a target temperature of 3 K. Products of two distinct branches of the reaction were observed; neutrons by a liquid organic scintillator, and protons by a silicon detector located inside the target system. The effective molecular formation rate from the upper hyperfine state of $\mu d$ and the hyperfine transition rate have been measured: $\tilde{\lambda}_(3/2)=2.71(7)_{stat.}(32)_{syst.} \mu/s$, and $\tilde{\lambda}_{(3/2)(1/2)} =34.2(8)_{stat.}(1)_{syst.} \mu /s$. The molecular formation rate is consistent with other recent measurements, but not with the theory for isolated molecules. The discrepancy may be due to incomplete thermalization, an effect which was investigated by Monte Carlo calculations. Information on branching ratio parameters for the s and p wave d+d nuclear interaction has been extracted.Comment: 19 pages, 11 figures, submitted to PRA Feb 20, 199

Measurement of the Resonant dμtd\mu t Molecular Formation Rate in Solid HD

Measurements of muon-catalyzed dt fusion ($d\mu t \to ^4He+n+\mu^-$) in solid HD have been performed. The theory describing the energy dependent resonant molecular formation rate for the reaction $\mu t$ + HD $\to [(d\mu t)pee]^*$ is compared to experimental results in a pure solid HD target. Constraints on the rates are inferred through the use of a Monte Carlo model developed specifically for the experiment. From the time-of- flight analysis of fusion events in 16 and 37 $\mu g\cdot cm^{-2}$ targets, an average formation rate consistent with 0.897$\pm$(0.046)$_{stat}\pm$ (0.166)$_{syst}$ times the theoretical prediction was obtained.Comment: 4 pages, 5 figure

Chandra grating spectroscopy of three hot white dwarfs

High-resolution soft X-ray spectroscopic observations of single hot white dwarfs are scarce. With the Chandra Low-Energy Transmission Grating, we have observed two white dwarfs, one is of spectral type DA (LB 1919) and the other is a non-DA of spectral type PG1159 (PG 1520+525). The spectra of both stars are analyzed, together with an archival Chandra spectrum of another DA white dwarf (GD 246). The soft X-ray spectra of the two DA white dwarfs are investigated in order to study the effect of gravitational settling and radiative levitation of metals in their photospheres. LB 1919 is of interest because it has a significantly lower metallicity than DAs with otherwise similar atmospheric parameters. GD 246 is the only white dwarf known that shows identifiable individual iron lines in the soft X-ray range. For the PG1159 star, a precise effective temperature determination is performed in order to confine the position of the blue edge of the GW Vir instability region in the HRD. (abridged)Comment: A&A, in pres

Discrete-time quantum walks on one-dimensional lattices

In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the return probability, which shows scaling behavior $P(0,t)\sim t^{-1}$ and does not depends on the initial states of the walk. In the long-time limit, the probability distribution shows various patterns, depending on the initial states, coin parameters and the lattice size. The average mixing time $M_{\epsilon}$ closes to the limiting probability in linear $N$ (size of the lattice) for large values of thresholds $\epsilon$. Finally, we introduce another kind of quantum walk on infinite or even-numbered size of lattices, and show that the walk is equivalent to the traditional quantum walk with symmetrical initial state and coin parameter.Comment: 17 pages research not