Ridge Estimation of Inverse Covariance Matrices from High-Dimensional Data

We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do not coincide with common ridge penalties. Subsequently, starting from a common ridge penalty, analytic expressions are derived for two alternative ridge estimators of the precision matrix. The alternative estimators are compared to the archetypes with regard to eigenvalue shrinkage and risk. The alternatives are also compared to the graphical lasso within the context of graphical modeling. The comparisons may give reason to prefer the proposed alternative estimators

Technological learning for innovating towards sustainable cultivation practices: the Vietnamese smallholder rose sector

Deregulation and globalisation has altered the views of public involvement in development and led to strategies focusing on private sector participation. An implicit assumption seems to be that these linkages will enhance the technological capacity of smallholder producers by way of more cost-efficient technologies trickling down through the value chain or by quality requirements inducing best practices. The argument put forward in this paper is that sustainable non traditional agricultural chain development requires more purposeful actions and institutional transitions, both in the public and private spheres, targeting improved upstream innovative capacities. Empirical findings from a Dutch-Vietnamese partnership on sustainable floriculture development are used. Research revealed that the pest and disease control solutions applied by smallholder rose growers were incremental adaptations of experiences obtained in former food crop cultivation practices. Floriculture however may require more drastic changes in cultivation practices to make the sector more environmentally benign. In the case of smallholder Vietnamese flower producers, this implies adaptation of knowledge and skills currently not present. An important hindrance in promoting this knowledge and skills appears to be the weak vertical linkages between flower growers and public and private research and development organizations

Exciton trapping in magnetic wire structures

The lateral magnetic confinement of quasi two-dimensional excitons into wire like structures is studied. Spin effects are take into account and two different magnetic field profiles are considered, which experimentally can be created by the deposition of a ferromagnetic stripe on a semiconductor quantum well with magnetization parallel or perpendicular to the grown direction of the well. We find that it is possible to confine excitons into one-dimensional (1D) traps. We show that the dependence of the confinement energy on the exciton wave vector, which is related to its free direction of motion along the wire direction, is very small. Through the application of a background magnetic field it is possible to move the position of the trapping region towards the edge of the ferromagnetic stripe or even underneath the stripe. The exact position of this 1D exciton channel depends on the strength of the background magnetic field and on the magnetic polarisation direction of the ferromagnetic film.Comment: 10 pages, 7 figures, to be published in J. Phys: Condens. Matte

Confined magnetic guiding orbit states

We show how snake-orbit states which run along a magnetic edge can be confined electrically. We consider a two-dimensional electron gas (2DEG) confined into a quantum wire, subjected to a strong perpendicular and steplike magnetic field $B/-B$. Close to this magnetic step new, spatially confined bound states arise as a result of the lateral confinement and the magnetic field step. The number of states, with energy below the first Landau level, increases as $B$ becomes stronger or as the wire width becomes larger. These bound states can be understood as an interference between two counter-propagating one-dimensional snake-orbit states.Comment: 4 pages, 4 figure

An efficient finite-difference scheme for computation of electron states in free-standing and core-shell quantum wires

The electron states in axially symmetric quantum wires are computed by means of the effective-mass Schroedinger equation, which is written in cylindrical coordinates phi, rho, and z. We show that a direct discretization of the Schroedinger equation by central finite differences leads to a non-symmetric Hamiltonian matrix. Because diagonalization of such matrices is more complex it is advantageous to transform it in a symmetric form. This can be done by the Liouville-like transformation proposed by Rizea et al. (Comp. Phys. Comm. 179 (2008) 466-478), which replaces the wave function psi(rho) with the function F(rho)=psi(rho)sqrt(rho) and transforms the Hamiltonian accordingly. Even though a symmetric Hamiltonian matrix is produced by this procedure, the computed wave functions are found to be inaccurate near the origin, and the accuracy of the energy levels is not very high. In order to improve on this, we devised a finite-difference scheme which discretizes the Schroedinger equation in the first step, and then applies the Liouville-like transformation to the difference equation. Such a procedure gives a symmetric Hamiltonian matrix, resulting in an accuracy comparable to the one obtained with the finite element method. The superior efficiency of the new finite-difference (FDM) scheme is demonstrated for a few rho-dependent one-dimensional potentials which are usually employed to model the electron states in free-standing and core-shell quantum wires. The new scheme is compared with the other FDM schemes for solving the effective-mass Schroedinger equation, and is found to deliver energy levels with much smaller numerical error for all the analyzed potentials. Moreover, the PT symmetry is invoked to explain similarities and differences between the considered FDM schemes

Spin- and valley-dependent transport through arrays of ferromagnetic silicene junctions

We study ballistic transport of Dirac fermions in silicene through arrays of barriers, of width $d$, in the presence of an exchange field $M$ and a tunable potential of height $U$ or depth $-U$. The spin- and valley-resolved conductances as functions of $U$ or $M$, exhibit resonances away from the Dirac point (DP) and close to it a pronounced dip that becomes a gap when a critical electric field $E_z$ is applied. This gap widens by increasing the number of barriers and can be used to realize electric field-controlled switching of the current. The spin $p_s$ and valley $p_v$ polarizations of the current near the DP increase with $E_z$ or $M$ and can reach 100\% for certain of their values. These field ranges widen significantly by increasing the number of barriers. Also, $p_s$ and $p_v$ oscillate nearly periodically with the separation between barriers or wells and can be inverted by reversing $M$.Comment: 9 pages, 43 figures, to appear in PRB, figure resolutions reduced for siz

Polaron effects in electron channels on a helium film

Using the Feynman path-integral formalism we study the polaron effects in quantum wires above a liquid helium film. The electron interacts with two-dimensional (2D) surface phonons, i.e. ripplons, and is confined in one dimension (1D) by an harmonic potential. The obtained results are valid for arbitrary temperature ($T$), electron-phonon coupling strength ($\alpha$), and lateral confinement ($\omega_{0}$). Analytical and numerical results are obtained for limiting cases of $T$, $\alpha$, and $\omega_{0}$. We found the surprising result that reducing the electron motion from 2D to quasi-1D makes the self-trapping transition more continuous.Comment: 6 pages, 7 figures, submitted to Phys. Rev.