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We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training a deep neural network (DNN) model for the unknown system using its trajectory data. A key feature is that the unknown dynamical system contains system parameters that are completely hidden, in the sense that no information about the parameters is available through either the measurement trajectory data or our prior knowledge of the system. We demonstrate that by training a DNN using the trajectory data with sufficient time history, the resulting DNN model can accurately model the unknown dynamical system. For new initial conditions associated with new, and unknown, system parameters, the DNN model can produce accurate system predictions over longer time.

We present a general numerical approach for constructing governing equations for unknown dynamical systems when only data on a subset of the state variables are available. The unknown equations for these observed variables are thus a reduced system of the complete set of state variables. Reduced systems possess memory integrals, based on the well known Mori-Zwanzig (MZ) formulism. Our numerical strategy to recover the reduced system starts by formulating a discrete approximation of the memory integral in the MZ formulation. The resulting unknown approximate MZ equations are of finite dimensional, in the sense that a finite number of past history data are involved. We then present a deep neural network structure that directly incorporates the history terms to produce memory in the network. The approach is suitable for any practical systems with finite memory length. We then use a set of numerical examples to demonstrate the effectiveness of our method.

The development of next generation sequencing (NGS) technology and genotype imputation methods enabled researchers to measure both common and rare variants in genome-wide association studies (GWAS). Statistical methods have been proposed to test a set of genomic variants together to detect if any of them is associated with the phenotype or disease. In practice, within the set of variants, there is an unknown proportion of variants truly causal or associated with the disease. Because most developed methods are sensitive to either the dense scenario, where a large proportion of the variants are associated, or the sparse scenario, where only a small proportion of the variants are associated, there is a demand of statistical methods with high power in both scenarios. In this paper, we propose a new association test (weighted Adaptive Fisher, wAF) that can adapt to both the dense and sparse scenario by adding weights to the Adaptive Fisher (AF) method we developed before. Using both simulation and the Genetic Analysis Workshop 16 (GAW16) data, we have shown that the new method enjoys comparable or better power to popular methods such as sequence kernel association test (SKAT and SKAT-O) and adaptive SPU (aSPU) test.

In recent years, various doping methods for epitaxial graphene have been demonstrated through atom substitution and adsorption. Here we observe by angle-resolved photoemission spectroscopy (ARPES) a coupling-induced Dirac cone renormalization when depositing small amounts of Ti onto epitaxial graphene on SiC. We obtain a remarkably high doping efficiency and a readily tunable carrier velocity simply by changing the amount of deposited Ti. First-principles theoretical calculations show that a strong lateral (non-vertical) orbital coupling leads to an efficient doping of graphene by hybridizing the 2pz orbital of graphene and the 3d orbitals of the Ti adsorbate, which attached on graphene without creating any trap/scattering states. This Ti-induced hybridization is adsorbate-specific and has major consequences for efficient doping as well as applications towards adsorbate-induced modification of carrier transport in graphene., Comment: 24 pages, 4 figures

We report semiconducting behavior of monolayer graphene enabled through plasma activation of substrate surfaces. The graphene devices are fabricated by mechanical exfoliation onto pre-processed SiO2/Si substrates. Contrary to pristine graphene, these graphene samples exhibit a transport gap as well as nonlinear transfer characteristics, a large on/off ratio of 600 at cryogenic temperatures, and an insulating-like temperature dependence. Raman spectroscopic characterization shows evidence of sp3 hybridization of C atoms in the samples of graphene on activated SiO2/Si substrates. We analyze the hopping transport at low temperatures, and weak localization observed from magnetotransport measurements, suggesting a correlation between carrier localization and the sp3-type defects in the functionalized graphene. The present study demonstrates the functionalization of graphene using a novel substrate surface-activation method for future graphene-based applications.