ST‐PLS: a multi‐directional nearest shrunken centroid type classifier via PLS

The nearest shrunken centroid (NSC) Classifier is successfully applied for class prediction in a wide range of studies based on microarray data. The contribution from seemingly irrelevant variables to the classifier is minimized by the so‐called soft‐thresholding property of the approach. In this paper, we first show that for the two‐class prediction problem, the NSC Classifier is similar to a one‐component discriminant partial least squares (PLS) model with soft‐shrinkage of the loading weights. Then we introduce the soft‐threshold‐PLS (ST‐PLS) as a general discriminant‐PLS model with soft‐thresholding of the loading weights of multiple latent components. This method is especially suited for classification and variable selection when the number of variables is large compared to the number of samples, which is typical for gene expression data. A characteristic feature of ST‐PLS is the ability to identify important variables in multiple directions in the variable space. Both the ST‐PLS and the NSC classifiers are applied to four real data sets. The results indicate that ST‐PLS performs better than the shrunken centroid approach if there are several directions in the variable space which are important for classification, and there are strong dependencies between subsets of variables. Copyright © 2007 John Wiley & Sons, Ltd.     

Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts

Optical rectification of ultrashort near-IR laser pulses with tilted pulse fronts and pulse energies of a few J in Mg-doped stoichiometric LiNbO₃ cooled to low temperature is a powerful technique for efficient generation of THz pulses. The pulse energy critically depends on the Mg doping (necessary for preventing photorefractive damage) and can be easily increased by a factor of three if the MgO content is reduced. Pulse energies up to 400 pJ at repetition rates of 200 kHz and 3.4% quantum conversion efficiency are achieved at 77 K. At 10 K, changing the tilt angle of the pump pulse front results in continuous tuning of the frequency across the 1.0–4.4 THz range. The temporal pulse shapes measured by electro-optic sampling are in good agreement with the signal calculated by a simple theory. This model predicts tunability on a considerably broader range and narrower spectra even at room temperature if GaSe is used instead of LiNbO₃. The advantages of the velocity matching technique utilizing tilted pulse fronts are analyzed in comparison with quasi-phase-matching in periodically poled LiNbO₃ crystals. The first method provides a ten times higher pulse energy conversion efficiency. PACS 42.65.Ky; 42.70.Mp; 42.72.Ai     

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.     

Insights into the dynamics of evaporation and proton migration in protonated water clusters from Large‐scale Born–Oppenheimer direct dynamics

Large‐scale on‐the‐fly Born–Oppenheimer molecular dynamics simulations using recent advances in linear scaling electronic structure theory and trajectory integration techniques have been performed for protonated water clusters around the magic number (H₂O)_nH⁺, for n = 20 and 21. Besides demonstrating the feasibility and efficiency of the computational approach, the calculations reveal interesting dynamical details. Elimination of water molecules is found to be fast for both cluster sizes but rather insensitive to the initial geometry. The water molecules released acquire velocities compatible with thermal energies. The proton solvation shell changes between the well‐known Eigen and Zundel motifs and is characterized by specific low‐frequency vibrational modes, which have been quantified. The proton transfer mechanism largely resembles that of bulk water but one interesting variation was observed. © 2012 Wiley Periodicals, Inc.     

Linear-scaling implementation of molecular electronic self-consistent field theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.     

Surface spin-glass-like behavior of monodispersed superparamagnetic Mn0.5Zn0.5Fe2O4 magnetic fluid

Zero field cooled dc-magnetization measurements of monodispersed Mn_0.5Zn_0.5Fe₂O₄ nanoparticles dispersed in kerosene exhibit two transitions at low temperatures. These transitions correspond to (i) the superparamagnetic to blocked superparamagnetic and (ii) the blocked superparamagnetic to surface spin-glass like/quantum superparamagnetic state upon lowering the temperature. The existence of a disorder surface is confirmed by recording small-angle neutron scattering data below and above the Curie temperature. Magnetic relaxation analysis shows a plateau at low temperature (below 5 K) with a slight minimum at 3 K, which is a characteristic of the surface spin-glass-like state. This is analyzed considering the energy distribution n(E)∼1/E. The existence of surface disorder dominates at low temperature and mimics the transition from superparamagnetic to quantum superparamagnetic states.     

Small-angle neutron scattering study of the mesostructure of bioactive coatings for stone materials based on nanodiamond-modified epoxy siloxane sols

The structure formation of sol-gel-derived epoxy siloxane compositions with different ratios of the main precursors (R _{TEOS/EPONEX 1510} = 16/38, 27/27, 38/16 wt %) and with different concentrations of detonation synthesis nanodiamonds (c _DND = 0.05, 0.10, 0.20 wt %) has been investigated using small-angle neutron scattering (SANS). Based on the SANS data, it has been revealed that the synthesized epoxy siloxane xerogels are systems with a two-level fractal structure, in the formation of which the siloxane component plays a dominant role. It has been found that the fractal dimension D _m2 and the radius of gyration R _g2 of clusters in the epoxy siloxane compositions decrease with an increase in the content of the siloxane component. It has been established that the introduction of small additions of detonation synthesis nanodiamonds (less than 1 wt %) into the epoxy siloxane composition with an equal ratio of the main precursors R _{TEOS/EPONEX 1510} = 27/27 wt % leads to a transition from the two-level to three-level structure organization and affects the fractal dimension D _m and the radius of gyration R _g of the formed clusters.