A Two-Stage Penalized Least Squares Method for Constructing Large Systems of Structural Equations

We propose a two-stage penalized least squares method to build large systems of structural equations based on the instrumental variables view of the classical two-stage least squares method. We show that, with large numbers of endogenous and exogenous variables, the system can be constructed via consistent estimation of a set of conditional expectations at the first stage, and consistent selection of regulatory effects at the second stage. While the consistent estimation at the first stage can be obtained via the ridge regression, the adaptive lasso is employed at the second stage to achieve the consistent selection. The resultant estimates of regulatory effects enjoy the oracle properties. This method is computationally fast and allows for parallel implementation. We demonstrate its effectiveness via simulation studies and real data analysis

Eigenfunctions for quasi-laplacian

To study the regularity of heat flow, Lin-Wang[1] introduced the quasi-harmonic sphere, which is a harmonic map from $M=(\mathbb{R}^m,e^{-\frac{|x|^2}{2(m-2)}}ds_0^2)$ to $N$ with finite energy. Here $ds_0^2$ is Euclidean metric in $\mathbb{R}^m$. Ding-Zhao [2] showed that if the target is a sphere, any equivariant quasi-harmonic spheres is discontinuous at infinity. The metric $g=e^{-\frac{|x|^2}{2(m-2)}}ds_0^2$ is quite singular at infinity and it is not complete. In this paper , we mainly study the eigenfunction of Quasi-Laplacian $\Delta_g=e^{\frac{|x|^2}{2(m-2)}} ( \Delta_{g_0} - \nabla_{g_0}h\cdot \nabla_{g_0}) =e^{\frac{|x|^2}{2(m-2)}} \Delta_h$ for $h=\frac{|x|^2}{4}$. In particular, we show that non-constant eigenfunctions of $\Delta_g$ must be discontinuous at infinity and non-constant eigenfunctions of drifted Laplacian $\Delta_h=\Delta_{g_0} - \nabla_{g_0} h\cdot \nabla_{g_0}$ is also discontinuous at infinity

Constructing Nonabelian (1,0) Hypermultiplet Theories in Six Dimensions

We construct a class of nonabelian superconformal (1,0) hypermultiplet theories in six dimensions by introducing an abelian auxiliary field. The gauge fields of this class of theories are non-dynamical, and this class of theories can be viewed as Chern-Simons-matter theories in 6D.Comment: 5 pages, minor changes, reference adde

Steady-state bifurcation analysis of a strong nonlinear atmospheric vorticity equation

The quasi-geostrophic equation or the Euler equation with dissipation studied in the present paper is a simplified form of the atmospheric circulation model introduced by Charney and DeVore [J. Atmos. Sci. 36(1979), 1205-1216] on the existence of multiple steady states to the understanding of the persistence of atmospheric blocking. The fluid motion defined by the equation is driven by a zonal thermal forcing and an Ekman friction forcing measured by $\kappa>0$. It is proved that the steady-state solution is unique for $\kappa >1$ while multiple steady-state solutions exist for $\kappa<\kappa_{crit}$ with respect to critical value $\kappa_{crit}<1$. Without involvement of viscosity, the equation has strong nonlinearity as its nonlinear part contains the highest order derivative term. Steady-state bifurcation analysis is essentially based on the compactness, which can be simply obtained for semi-linear equations such as the Navier-Stokes equations but is not available for the quasi-geostrophic equation in the Euler formulation. Therefore the Lagrangian formulation of the equation is employed to gain the required compactness.Comment: 20 pages, 0 figures, 30 reference

Ill-posedness of waterline integral of time domain free surface Green function for surface piercing body advancing at dynamic speed

In the linear time domain computation of a floating body advancing at a dynamic speed, the source formulation for the velocity potential of the hydrodynamic problem is commonly used so that the velocity potential is expressed as the integral of time domain free surface sources distributed on the two-dimensional wetted body surface and the one-dimensional waterline, which is the intersection of the wetted body surface and the mean free water surface. A time domain free surface source is corresponding to the time domain free surface Green function associated with a suitable source strength, which is to be solved from body boundary condition and normal velocity boundary integral equation of the source formulation. The normal velocity boundary integral equation contains an integral of the normal derivative of the time domain free surface Green function on the waterline. It is shown that the waterline integral is ill-posed. Thus the source strength of velocity potential is not obtainable

Unifying quantum heat transfer and superradiant signature in a nonequilibrium collective-qubit system: a polaron-transformed Redfield approach

We investigate full counting statistics of quantum heat transfer in a collective-qubit system, constructed by multi-qubits interacting with two thermal baths. The nonequilibrium polaron-transformed Redfield approach embedded with an auxiliary counting field is applied to obtain the steady state heat current and fluctuations, which enables us to study the impact of the qubit-bath interaction in a wide regime. The heat current, current noise and skewness are all found to clearly unify the limiting results in the weak and strong couplings, respectively. Moreover, the superradiant heat transfer is clarified as a system-size-dependent effect, and large number of qubits dramatically suppresses the nonequilibrium superradiant signature.Comment: 12pages, 3figs, accepted by Chin. Phys.

OSp(4|4) superconformal currents in three-dimensional N=4 Chern-Simons quiver gauge theories

We prove explicitly that the general D=3, N=4 Chern-Simons-matter (CSM) theory has a complete OSp(4|4) superconformal symmetry, and construct the corresponding conserved currents. We re-derive the OSp(5|4) superconformal currents in the general N=5 theory as special cases of the OSp(4|4) currents by enhancing the supersymmetry from N=4 to N=5. The closure of the full OSp(4|4) superconformal algebra is verified explicitly.Comment: 23 pages, published in PR

New formulation of the finite depth free surface Green function

For a pulsating free surface source in a three-dimensional finite depth fluid domain, the Green function of the source presented by John [F. John, On the motion of floating bodies II. Simple harmonic motions, Communs. Pure Appl. Math. 3 (1950) 45-101] is superposed as the Rankine source potential, an image source potential and a wave integral in the infinite domain $(0, \infty)$. When the source point together with a field point is on the free surface, John's integral and its gradient are not convergent since the integration $\int^\infty_\kappa$ of the corresponding integrands does not tend to zero in a uniform manner as $\kappa$ tends to $\infty$. Thus evaluation of the Green function is not based on direct integration of the wave integral but is obtained by approximation expansions in earlier investigations. In the present study, five images of the source with respect to the free surface mirror and the water bed mirror in relation to the image method are employed to reformulate the wave integral. Therefore the free surface Green function of the source is decomposed into the Rankine potential, the five image source potentials and a new wave integral, of which the integrand is approximated by a smooth and rapidly decaying function. The gradient of the Green function is further formulated so that the same integration stability with the wave integral is demonstrated. The significance of the present research is that the improved wave integration of the Green function and its gradient becomes convergent. Therefore evaluation of the Green function is obtained through the integration of the integrand in a straightforward manner. The application of the scheme to a floating body or a submerged body motion in regular waves shows that the approximation is sufficiently accurate to compute linear wave loads in practice.Comment: 24 pages, 7 figure

Instability of the Kolmogorov flow in a wall-bounded domain

In the magnetohydrodynamics (MHD) experiment performed by Bondarenko and his co-workers in 1979, the Kolmogorov flow loses stability and transits into a secondary steady state flow at the Reynolds number $R=O(10^3)$. This problem is modelled as a MHD flow bounded between lateral walls under slip wall boundary condition. The existence of the secondary steady state flow is now proved. The theoretical solution has a very good agreement with the flow measured in laboratory experiment at $R=O(10^3)$. Further transition of the secondary flow is observed numerically. Especially, well developed turbulence arises at $R=O(10^4)$

OSp(5|4) Superconformal Symmetry of N=5 Chern-Simons Theory

We demonstrate that the general D=3, N=5 Chern-Simons matter theory possesses a full OSp(5|4) superconformal symmetry, and construct the corresponding superconformal currents. The closure of the superconformal algebra is verified in detail. We also show that the conserved OSp(6|4) superconformal currents in the general N=6 theory can be obtained as special cases of the OSp(5|4) currents by enhancing the R-symmetry of the N=5 theory from USp(4) to SU(4).Comment: 24 pages, minor changes, version published in Nucl.Phys.