The uplift of the Tibetan plateau, an area that is 2,000 km wide, to an altitude of about 5,000 m has been shown to modify global climate and to influence monsoon intensity. Mechanical and thermal models for homogeneous thickening of the lithosphere make specific predictions about uplift rates of the Tibetan plateau, but the precise history of the uplift of the plateau has yet to be confirmed by observations. Here we present well-preserved fossil leaf assemblages from the Namling basin, southern Tibet, dated to approximately 15 Myr ago, which allow us to reconstruct the temperatures within the basin at that time. Using a numerical general circulation model to estimate moist static energy at the location of the fossil leaves, we reconstruct the elevation of the Namling basin 15 Myr ago to be 4,689 +/- 895 m or 4,638 +/- 847 m, depending on the reference data used. This is comparable to the present-day altitude of 4,600 m. We conclude that the elevation of the southern Tibetan plateau probably has remained unchanged for the past 15 Myr.

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Summary Variance estimation is a fundamental problem in statistical modelling. In ultrahigh dimensional linear regression where the dimensionality is much larger than the sample size, traditional variance estimation techniques are not applicable. Recent advances in variable selection in ultrahigh dimensional linear regression make this problem accessible. One of the major problems in ultrahigh dimensional regression is the high spurious correlation between the unobserved realized noise and some of the predictors. As a result, the realized noises are actually predicted when extra irrelevant variables are selected, leading to serious underestimate of the level of noise. We propose a two-stage refitted procedure via a data splitting technique, called refitted cross-validation, to attenuate the influence of irrelevant variables with high spurious correlations. Our asymptotic results show that the resulting procedure performs as well as the oracle estimator, which knows in advance the mean regression function. The simulation studies lend further support to our theoretical claims. The naive two-stage estimator and the plug-in one-stage estimators using the lasso and smoothly clipped absolute deviation are also studied and compared. Their performances can be improved by the reffitted cross-validation method proposed.

Graphical models have attracted increasing attention in recent years, especially in settings involving high dimensional data. In particular Gaussian graphical models are used to model the conditional dependence structure among multiple Gaussian random variables. As a result of its computational efficiency the graphical lasso (glasso) has become one of the most popular approaches for fitting high dimensional graphical models. In this article we extend the graphical models concept to model the conditional * Shaojun Guo was partially supported by National Science Foundation of China (NO. 11771447). significantly outperforms possible competing methods through both simulations and an analysis of a real world EEG data set comparing alcoholic and non-alcoholic patients.Some key words: Functional data; Graphical models; Functional principal component analysis;Block sparse precision matrix, Block coordinate descent algorithm.

Quantum walks are the quantum mechanical analog of classical random walks and an extremely powerful tool in quantum simulations, quantum search algorithms, and even for universal quantum computing. In our work, we have designed and fabricated an 8x8 two-dimensional square superconducting qubit array composed of 62 functional qubits. We used this device to demonstrate high fidelity single and two particle quantum walks. Furthermore, with the high programmability of the quantum processor, we implemented a Mach-Zehnder interferometer where the quantum walker coherently traverses in two paths before interfering and exiting. By tuning the disorders on the evolution paths, we observed interference fringes with single and double walkers. Our work is an essential milestone in the field, brings future larger scale quantum applications closer to realization on these noisy intermediate-scale quantum processors.