Size and power of pretest procedures

A pre-test procedure consists of a preliminary test on a nuisance parameter, investigating whether it equals a given value or not, followed by the main testing problem on the parameter of interest. In case of acceptance of the preliminary test, the main test is applied in the restricted family with the given value of the nuisance parameter, while otherwise the test is performed in the complete family, including the nuisance parameter. For locally most powerful tests an attractive expression for the size and power of the pre-test procedure is derived using second order asymptotics. From this expression considerable insight can be obtained in a qualitative and quantitative sense. The results can be applied easily as is illustrated by a number of practical examples, where also the accuracy of the approximations is seen from comparison with numerical results

Power gain by pre-testing?

The aim of this paper is to study whether it is possible to gain power by pre-testing, and to give insight in when this occurs, to what extent, and, at which price. A pre-test procedure consists of a preliminary test which tests a particular property of a given restricted model, followed by a main test for the main hypothesis regarding the parameter of interest. After acceptance by the preliminary test, a basic main test is used in the restricted model. After rejection by the preliminary test, a more general main test is used which does not use prior information about the underlying distribution. The procedure is analyzed in the model against which the preliminary test protects. For classes of tests including the standard first-order optimal tests, a transparent expression is given for the power and size difference of the pre-test procedure compared to the power and (correct) size of the second main test. This expression is based on second-order asymptotics and gives qualitative and quantitative insight in the behaviour of the procedure. It shows that substantial power gain, not merely due to size violation, is possible if the second main test really differs from the basic main test. The smaller the correlation between the two main tests, the larger the power gain

Adaptive control of space based robot manipulators

For space based robots in which the base is free to move, motion planning and control is complicated by uncertainties in the inertial properties of the manipulator and its load. A new adaptive control method is presented for space based robots which achieves globally stable trajectory tracking in the presence of uncertainties in the inertial parameters of the system. A partition is made of the fifteen degree of freedom system dynamics into two parts: a nine degree of freedom invertible portion and a six degree of freedom noninvertible portion. The controller is then designed to achieve trajectory tracking of the invertible portion of the system. This portion consist of the manipulator joint positions and the orientation of the base. The motion of the noninvertible portion is bounded, but unpredictable. This portion consist of the position of the robot's base and the position of the reaction wheel

Glass transition of hard spheres in high dimensions

We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions $d\to \infty$ in the framework of mode-coupling theory. The numerical results for the critical collective and self nonergodicity parameters $f_{c}(k;d)$ and $f_{c}^{(s)}(k;d)$ exhibit non-Gaussian $k$ -dependence even up to $d=800$. $f_{c}^{(s)}(k;d)$ and $f_{c}(k;d)$ differ for $k\sim d^{1/2}$, but become identical on a scale $k\sim d$, which is proven analytically. The critical packing fraction $\phi_{c}(d) \sim d^{2}2^{-d}$ is above the corresponding Kauzmann packing fraction $\phi_{K}(d)$ derived by a small cage expansion. Its quadratic pre-exponential factor is different from the linear one found earlier. The numerical values for the exponent parameter and therefore the critical exponents $a$ and $b$ depend on $d$, even for the largest values of $d$.Comment: 11 pages, 8 figures, Phys. Rev. E (in print

Subglacial drainage processes at a High Arctic polythermal valley glacier

Peer reviewedPublisher PD

State detection using coherent Raman repumping and two-color Raman transfers

We demonstrate state detection based on coherent Raman repumping and a two-color Raman state transfer. The Raman coupling during detection selectively eliminates unwanted dark states in the fluorescence cycle without compromising the immunity of the desired dark state to off-resonant scattering. We demonstrate this technique using $^{137}\mathrm{Ba}^+$ where a combination of Raman coupling and optical pumping leaves the $D_{3/2}$ $\ket{F"=3,m_F"=3}$ metastable state optically dark and immune to off-resonant scattering. All other states are strongly coupled to the upper $P_{1/2}$ levels. We achieve a single shot state-detection efficiency of $89.6(3)$ in a $1\mathrm{ms}$ integration time, limited almost entirely by technical imperfections. Shelving to the $\ket{F"=3,m_F"=3}$ state before detection is performed via a two-color Raman transfer with a fidelity of $1.00(3)$