Abstract:
In this paper, we introduce the concept of piecewise pseudo almost periodic functions on a Banach space and establish some composition theorems of piecewise pseudo almost periodic functions. We apply these composition theorems to investigate the existence of piecewise pseudo almost periodic (mild) solutions to abstract impulsive differential equations. In addition, the stability of piecewise pseudo almost periodic solutions is considered.

Abstract:
Based on a combination of $k \cdot p$ theory, band topology analysis and electronic structure calculations, we predict the (111) thin films of the SnTe class of three-dimensional (3D) topological crystalline insulators realize the quantum spin Hall phase in a wide range of thickness. The nontrivial topology originates from the inter-surface coupling of the topological surface states of TCI in the 3D limit. The inter-surface coupling changes sign and gives rise to topological phase transitions as a function of film thickness. Furthermore, this coupling can be strongly affected by an external electric field, hence the quantum spin Hall phase can be effectively tuned under experimentally accessible the electric field. Our results show that (111) thin films of SnTe-class TCI can be an ideal platform to realize the novel applications of quantum spin Hall insulators.

Abstract:
We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we propose a graphical Fermat's principle to regularize the distribution family. Such principle enforces the existence of a distribution-dependent pseudo-metric such that any two nodes have a smaller distance than that of two other nodes who have a geodesic path include these two nodes. Guided by this principle, we show that a greedy strategy is able to recover the true graph. The resulting algorithm only requires a pairwise distance matrix as input and is computationally even more efficient than calculating the minimum spanning tree. We consider graph estimation problems under different settings, including discrete and nonparametric distribution families. Thorough numerical results are provided to illustrate the usefulness of the proposed method.

Abstract:
Plasma’s conductive and dielectric properties have been well known for decades. Plasma antenna is a general terms representing using plasma as a conductive medium to transmit or reflect signals. It has unique properties like low RCS (radar cross section), variable impedance and instant on-off capability. Previous plasma antenna uses RF power to generate the plasma column. We developed AC-biased (alternating current) plasma antenna, which has larger operation frequency scale and lower sustaining power. Signals propagated are coupled into the plasma antenna via capacitive coupling. Impedance of the plasma shifts slightly with the AC current. Radiation pattern of the plasma antenna is less uniform than metal antenna and its gain is related to AC power, from the measuring results of AC-biased plasma antenna we found its advantages compare to the plasma antenna excited by the surface wave.

Carbon nanowire (CNW)-singlewalled carbon
nanotube (SWCNT) networks hybrid films with a large area (~400 mm^{2}) are grown
on molybdenum (Mo) layers by microwave plasma chemical vapour deposition
system. The Mo layers, which were deposited on Al_{2}O_{3} ceramic
substrates through electron beam evaporation deposition, were pretreated by
a laser-grooving (LG) technology. Furthermore, the surface morphology,
micro-structure and field emission properties of these samples are
characterized by scanning electron microscope, Raman spectra, and field emission
I - V measurements. ACNW-SWCNT networks hybrid film was formed in the surface of Mo layer, but the laser etched area (linear pits array
area) the distribution of the CNW-SWCNT networks density is lower than the
un-etched area CNW-SWCNT networks distribution density. The
diameter of the CNWs and SWCNTs, respectively in the 8 - 15 nm and 0.9 - 1.5 nm
range, and the length of CNW-SWCNTs ranges from 1 μm to 4 μm. The growth
mechanisms of the films were discussed. Effects of LG pretreatment on surface
morphologies and microstructure of the hybrid films were investigated. The
field electron emission experimental results shown that the ture on field as low
as 1.6 V/μm, and a current density of 0.15 mA/cm2 at an electric field of 4.3 V/μm
was obtained.

Abstract:
Two-dimensional (2D) topological crystalline insulators (TCIs) were recently predicted in thin films of the SnTe class of IV-VI semiconductors, which can host metallic edge states protected by mirror symmetry. As thickness decreases, quantum confinement effect will increase and surpass the inverted gap below a critical thickness, turning TCIs into normal insulators. Surprisingly, based on first-principles calculations, here we demonstrate that (001) monolayers of rocksalt IV-VI semiconductors XY (X=Ge, Sn, Pb and Y= S, Se, Te) are 2D TCIs with the fundamental band gap as large as 260 meV in monolayer PbTe, providing a materials platform for realizing two-dimensional Dirac fermion systems with tunable band gap. This unexpected nontrivial topological phase stems from the strong {\it crystal field effect} in the monolayer, which lifts the degeneracy between $p_{x,y}$ and $p_z$ orbitals and leads to band inversion between cation $p_z$ and anion $p_{x,y}$ orbitals. This crystal field effect induced topological phase offers a new strategy to find and design other atomically thin 2D topological materials.

Abstract:
We predict a new class of topological crystalline insulators (TCI) in the anti-perovskite material family with the chemical formula A$_3$BX. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a "Dirac octet". Our work suggests that anti-perovskites are a promising new venue for exploring the cooperative interplay between band topology, crystal symmetry and electron correlation.

Abstract:
Topological crystalline insulators (TCI) are new topological phases of matter protected by crystal symmetry of solids. Recently, the first realization of TCI has been predicted and observed in IV-VI semiconductor SnTe and related alloys Pb_{1-x}Sn_{x}(Te, Se). By combining k.p theory and band structure calculation, we present a unified approach to study topological surface states on various crystal surfaces of TCI in IV-VI semiconductors. We explicitly derive k.p Hamiltonian for topological surface states from electronic structure of the bulk, thereby providing a microscopic understanding of bulk-boundary correspondence in TCI. Depending on the surface orientation, we find two types of surface states with qualitatively different properties. In particular, we predict that (111) surface states consist of four Dirac cones centered at time-reversal-invariant momenta {\Gamma} and M, while (110) surface states consist of Dirac cones at non-time-reversal-invariant momenta, similar to (001). Moreover, both (001) and (110) surface states exhibit a Lifshitz transition as a function of Fermi energy, which is accompanied by a Van-Hove singularity in density of states arising from saddle points in the band structure.

Abstract:
We propose a novel class of dynamic nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model we develop statistical tests for presence of edges both locally at a fixed index value and globally over a range of values. The tests are developed for a high-dimensional regime, are robust to model selection mistakes and do not require commonly assumed minimum signal strength. The testing procedures are based on a high dimensional, debiasing-free moment estimator, which uses a novel kernel smoothed Kendall's tau correlation matrix as an input statistic. The estimator consistently estimates the latent inverse Pearson correlation matrix uniformly in both index variable and kernel bandwidth. Its rate of convergence is shown to be minimax optimal. Thorough numerical simulations and an application to a neural imaging dataset support the usefulness of our method.

Abstract:
We propose a novel high dimensional nonparametric model named ATLAS which naturally generlizes the sparse additive model. Given a covariate of interest $X_j$, the ATLAS model assumes the mean function can be locally approximated by a sparse additive function whose sparsity pattern may vary from the global perspective. We propose to infer the marginal influence function $f_j^*(z) = \mathbb{E}[f(X_1,\ldots, X_d) \mid X_j = z]$ using a new kernel-sieve approach that combines the local kernel regression with the B-spline basis approximation. We prove the rate of convergence for estimating $f_j^*$ under the supremum norm. We also propose two types of confidence bands for $f_j^*$ and illustrate their statistical-comptuational tradeoffs. Thorough numerical results on both synthetic data and real-world genomic data are provided to demonstrate the efficacy of the theory.