Abstract:
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be semiparametric generalized linear models with unspecified base measure functions. Thus, one advantage of our method is that it is unnecessary to specify the type of each node and the method is more convenient to apply in practice. Under the proposed model, we consider both problems of parameter estimation and hypothesis testing in high dimensions. In particular, we propose a symmetric pairwise score test for the presence of a single edge in the graph. Compared to the existing methods for hypothesis tests, our approach takes into account of the symmetry of the parameters, such that the inferential results are invariant with respect to the different parametrizations of the same edge. Thorough numerical simulations and a real data example are provided to back up our results.

Abstract:
In the cognitive radio system, spectrum sensing for detecting the presence of primary users in a licensed spectrum is a fundamental problem. Energy detection is the most popular spectrum sensing scheme used to differentiate the case where the primary user’s signal is present from the case where there is only noise. In fact, the nature of spectrum sensing can be taken as a binary classification problem, and energy detection is a linear classifier. If the signal-to-noise ratio (SNR) of the received signal is low, and the number of received signal samples for sensing is small, the binary classification problem is linearly inseparable. In this situation the performance of energy detection will decrease seriously. In this paper, a novel approach for obtaining a nonlinear threshold based on support vector machine with particle swarm optimization (PSO-SVM) to replace the linear threshold used in traditional energy detection is proposed. Simulations demonstrate that the performance of the proposed algorithm is much better than that of traditional energy detection.

Abstract:
We consider positive solutions of the problem \begin{equation} \left\{\begin{array}{l}-\mbox{div}(x_{n}^{a}\nabla u)=0\qquad \mbox{in}\;\;\mathbb{R}_+^n,\\ \frac{\partial u}{\partial \nu^a}=u^{q} \qquad \mbox{on}\;\;\partial \mathbb{R}_+^n,\\ \end{array} \right. \end{equation} where $a\in (-1,0)\cup(0,1)$, $q>1$ and $\frac{\partial u}{\partial \nu^a}:=-\lim_{x_{n}\rightarrow 0^+}x_{n}^{a}\frac{\partial u}{\partial x_{n}}$. We obtain some qualitative properties of positive axially symmetric solutions in $n\geq3$ for the case $a\in (-1,0)$ under the condition $q\geq\frac{n-a}{n+a-2}$. In particular, we establish the asymptotic expansion of positive axially symmetric solutions.

Abstract:
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an $\ell_1$-regularized least-squares estimator. Unlike classical linear regression, the corresponding optimization problem is nonconvex because of the nonlinearity of $f$. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. In addition, we provide an efficient algorithm that provably converges to a stationary point. We also access the uncertainty of the obtained estimator. Specifically, based on any stationary point of the objective, we construct valid hypothesis tests and confidence intervals for the low dimensional components of the high-dimensional parameter $\beta^*$. Detailed numerical results are provided to back up our theory.

A scheme for chaotic signal generation in a
semiconductor ring laser (SRL) with optical feedback is presented. Part of the
output is returned to the SRL, resulting in chaotic oscillation.

Abstract:
Let $\lambda^{*}>0$ denote the largest possible value of $\lambda$ such that $$ \{{array}{lllllll} \Delta^{2}u=\frac{\lambda}{(1-u)^{p}} & \{in}\ \ B, 01$ and $n$ is the exterior unit normal vector. We show that for $\lambda=\lambda^{*}$ this problem possesses a unique weak solution $u^{*}$, called the extremal solution. We prove that $u^{*}$ is singular when $n\geq 13$ for $p$ large enough and $1-C_{0}r^{\frac{4}{p+1}}\leq u^{*}(x)\leq 1-r^{\frac{4}{p+1}}$ on the unit ball, where $ C_{0}:=(\lambda^{*}/\bar{\lambda})^{\frac{1}{p+1}}$ and $\bar{\lambda}:=\frac{8(p-1)}{(p+1)^{2}}[n-\frac{2(p-1)}{p+1}][n-\frac{4p}{p+1}]$. Our results actually complete part of the open problem which \cite{D} lef

Abstract:
We use density functional plus $U$ methods to study the effects of a tensile or compressive substrate strain on the charge-ordered insulating phase of LuNiO$_3$. The numerical results are analyzed in terms of a Landau energy function, with octahedral rotational distortions of the perovskite structure included as a perturbation. Approximately 4% tensile or compressive strain leads to a first-order transition from an insulating structure with large amplitude breathing mode distortions of the NiO$_6$ octahedra to a metallic state in which breathing mode distortions are absent but Jahn-Teller distortions in which two Ni-O bonds become long and the other four become short are present. Compressive strain produces uniform Jahn-Teller order with the long axis aligned perpendicular to the substrate plane while tensile strain produces a staggered Jahn-Teller order in which the long bond lies in the plane and alternates between two nearly orthogonal in-plane directions forming a checkerboard pattern. In the absence of the breathing mode distortions and octahedral rotations, the tensile strain-induced transition to the staggered Jahn-Teller state would be of second order.

Abstract:
We study the nonequilibrium dynamics of photoexcited electrons in the narrow-gap Mott insulator VO$_2$. The initial stages of relaxation are treated using a quantum Boltzmann equation methodology, which reveals a rapid ($\sim$ femtosecond time scale) relaxation to a pseudothermal state characterized by a few parameters that vary slowly in time. The long-time limit is then studied by a Hartree-Fock methodology, which reveals the possibility of nonequilibrium excitation to a new metastable $M_1$ metal phase that is qualitatively consistent with a recent experiment. The general physical picture of photoexcitation driving a correlated electron system to a new state that is not accessible in equilibrium may be applicable in similar materials.

Abstract:
Cognitive Radio (CR) is an efficient way to solve the problem of the lack of the spectrum resource. In a Cognitive Radio Network the unlicensed users (secondary users) must incessantly monitor the spectrum for the presence of the licensed users (primary users) to avoid the interference to primary users. In this study, a spectrum sensing scheme based on adaptive optimal SVM (support vector machine) is proposed. A prototype system and the simulation experiments show that in low SNR the algorithm can also get a reasonable probability of detection and a low probability of false alarm.

Abstract:
As an important area of reserve land resources, the Yellow River Delta is faced with the problem of soil salinization. Grasping the characteristics of soil salinity as well as its spatial variation patterns is an important foundation of prevention, control and utilization of saline soil. This study selected Kenli County of the Yellow River Delta, obtained soil salinity data through field survey and lab experiment, and used statistical, GIS interpolation and buffer analysis methods to analyze the characteristics of soil salinity and its spatial variation patterns. Our results showed that the general soil salinity in the study area was mainly moderate and there was a significant positive correlation between different soil layers of 0 - 15 cm, 15 - 30 cm and 30 - 45 cm and soil salinity increased with the increase of soil depth. The areas with high soil salinity in each soil layer mainly distributed in the east near the Bo Sea in the county, while the areas with lower soil salinity mainly distributed in the southwest, centre and the two sides of the Yellow River in the northeast. Soil salinity showed a trend of decrease with the increase in distance to the Bo Sea, while stretching from the Yellow River, it showed increase tendency with the increase in distance to the Yellow River. The order from high soil salinity to low of different vegetation types was naked land → suaeda glauca → tamarix → vervain → reed → couch grass → paddy → cotton → winter wheat → maize; the order for different geomorphic types was depression → slightly sloping ground → slow hillock → high flood land. This study preliminary delineated the characteristics of soil salinity as well as its spatial variation patterns in the study area, and provided scientific basis for soil resource sustainable utilization in the Yellow River Delta.