Confidence intervals of prediction accuracy measures for multivariable prediction models based on the bootstrap-based optimism correction methods

In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction accuracy measures are corrected by adequate bootstrap-based correction methods, but their confidence intervals are not corrected, e.g., the DeLong's confidence interval is usually used for assessing the C-statistic. These naive methods do not adjust for the optimism bias and do not account for statistical variability in the estimation of parameters in the prediction models. Therefore, their coverage probabilities of the true value of the prediction accuracy measure can be seriously below the nominal level (e.g., 95%). In this article, we provide two generic bootstrap methods, namely (1) location-shifted bootstrap confidence intervals and (2) two-stage bootstrap confidence intervals, that can be generally applied to the bootstrap-based optimism correction methods, i.e., the Harrell's bias correction, 0.632, and 0.632+ methods. In addition, they can be widely applied to various methods for prediction model development involving modern shrinkage methods such as the ridge and lasso regressions. Through numerical evaluations by simulations, the proposed confidence intervals showed favourable coverage performances. Besides, the current standard practices based on the optimism-uncorrected methods showed serious undercoverage properties. To avoid erroneous results, the optimism-uncorrected confidence intervals should not be used in practice, and the adjusted methods are recommended instead. We also developed the R package predboot for implementing these methods (https://github.com/nomahi/predboot). The effectiveness of the proposed methods are illustrated via applications to the GUSTO-I clinical trial

From multimode to monomode guided atom lasers: an entropic analysis

We have experimentally demonstrated a high level of control of the mode populations of guided atom lasers (GALs) by showing that the entropy per particle of an optically GAL, and the one of the trapped Bose Einstein condensate (BEC) from which it has been produced are the same. The BEC is prepared in a crossed beam optical dipole trap. We have achieved isentropic outcoupling for both magnetic and optical schemes. We can prepare GAL in a nearly pure monomode regime (85 % in the ground state). Furthermore, optical outcoupling enables the production of spinor guided atom lasers and opens the possibility to tailor their polarization

Ultra-discrete Optimal Velocity Model: a Cellular-Automaton Model for Traffic Flow and Linear Instability of High-Flux Traffic

In this paper, we propose the ultra-discrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultra-discrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the mKdV equation, a soliton equation. Meanwhile, the ultra-discrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations, and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.Comment: 9 pages, 6 figure

Multiorbital analysis of the effects of uniaxial and hydrostatic pressure on TcT_c in the single-layered cuprate superconductors

The origin of uniaxial and hydrostatic pressure effects on $T_c$ in the single-layered cuprate superconductors is theoretically explored. A two-orbital model, derived from first principles and analyzed with the fluctuation exchange approximation gives axial-dependent pressure coefficients, $\partial T_c/\partial P_a>0$, $\partial T_c/\partial P_c<0$, with a hydrostatic response $\partial T_c/\partial P>0$ for both La214 and Hg1201 cuprates, in qualitative agreement with experiments. Physically, this is shown to come from a unified picture in which higher $T_c$ is achieved with an "orbital distillation", namely, the less the $d_{x^2-y^2}$ main band is hybridized with the $d_{z^2}$ and $4s$ orbitals higher the $T_c$. Some implications for obtaining higher $T_c$ materials are discussed.Comment: 6pages, 4 figure

Chaos and its quantization in dynamical Jahn-Teller systems

We investigate the $E_g \otimes e_g$ Jahn-Teller system for the purpose to reveal the nature of quantum chaos in crystals. This system simulates the interaction between the nuclear vibrational modes and the electronic motion in non-Kramers doublets for multiplets of transition-metal ions. Inclusion of the anharmonic potential due to the trigonal symmetry in crystals makes the system nonintegrable and chaotic. Besides the quantal analysis of the transition from Poisson to Wigner level statistics with increasing the strength of anharmonicity, we study the effect of chaos on the electronic orbital angular momentum and explore the magnetic $g$-factor as a function of the system's energy. The regular oscillation of this factor changes to a rapidly-decaying irregular oscillation by increasing the anharmonicity (chaoticity).Comment: 8 pages, 6 figure

Frustrated quantum-spin system on a triangle coupled with ege_g lattice vibrations - Correspondence to Longuet-Higgins et al.'s Jahn-Teller model -

We investigate the quantum three spin model $({\bf S_1},{\bf S_2},{\bf S_3})$ of spin$=1/2$ on a triangle, in which spins are coupled with lattice-vibrational modes through the exchange interaction depending on distances between spin sites. The present model corresponds to the dynamic Jahn-Teller system $E_g\otimes e_g$ proposed by Longuet-Higgins {\it et al.}, Proc.R.Soc.A.{\bf 244},1(1958). This correspondence is revealed by using the transformation to Nakamura-Bishop's bases proposed in Phys.Rev.Lett.{\bf 54},861(1985). Furthermore, we elucidate the relationship between the behavior of a chiral order parameter ${\hat \chi}={\bf S_1\cdot(S_2\times S_3)}$ and that of the electronic orbital angular momentum ${\hat \ell_z}$ in $E_g\otimes e_g$ vibronic model: The regular oscillatory behavior of the expectation value $$for vibronic structures with increasing energy can also be found in that of$$. The increase of the additional anharmonicity(chaoticity) is found to yield a rapidly decaying irregular oscillation of $$