A new approach to variable selection in least squares problems

The title Lasso has been suggested by Tibshirani (1996) as acolourful name for a technique of variable selection which requiresthe minimization of a sum of squares subject to an l₁ bound on the solution. This forces zero components in the minimizingsolution for small values of . Thus this bound can functionas a selection parameter. This paper makes two contributionsto computational problems associated with implementing the Lasso:(1) a compact descent method for solving the constrained problemfor a particular value of is formulated, and (2) a homotopymethod, in which the constraint bound becomes the homotopyparameter, is developed to completely describe the possibleselection regimes. Both algorithms have a finite terminationproperty. It is suggested that modified Gram-Schmidt orthogonalizationapplied to an augmented design matrix provides an effectivebasis for implementing the algorithms.     

Monte Carlo simulation of a film growth with reactive hydrophobic, polar, and aqueous components by a covalent bond fluctuating model

Using a bond fluctuating model (BFM), Monte Carlo simulations are performed to study the film growth in a mixture of reactive hydrophobic (H) and hydrophilic (P) groups in a simultaneous reactive and evaporating aqueous (A) solution on a simple three dimensional lattice. In addition to the excluded volume, short range phenomenological interactions among each constituents and kinetic functionalities are used to capture their major characteristics. The simulation involves thermodynamic equilibration via stochastic movement of each constituent by Metropolis algorithm as well as cross-linking reaction among constituents with evaporating aqueous component. The film thickness (h) and its interface width (W) are examined with a reactive aqueous solvent for a range of temperatures (T). Results are compared with a previous study [Yang et al. Macromol. Theory Simul. 15, 263 (2006)] with an effective bond fluctuation model (EBFM). Simulation data show a much slower power-law growth for h and W with BFM than that with EBFM. With BFM, growth of the film thickness can be described by h proportionaltgamma, with a typical value gamma1 approximately 0.97 in initial time regime followed by gamma2 approximately 0.77 at T=5, for example. Growth of the interface width can also be described by a power law, W proportionaltbeta, with beta1 approximately 0.40 initially and beta2 approximately 0.25 in later stage. Corresponding values of the exponents with EBFM are much higher, i.e., gamma1 approximately 1.84, gamma2 approximately 1.34 and beta1 approximately 1.05, beta2 approximately 0.60 at T=5. Correct restrictions on the bond length with the excluded volume used with BFM are found to have a greater effect on steady-state film thickness (hs) and the interface width (Ws) at low temperatures than that at high temperatures. The relaxation patterns of the interface width with BFM seem to change noticeably from those with EBFM. A better relaxed film with a smoother surface is thus achieved by the improved cross-linking covalent bond fluctuation model which is more realistic in capturing appropriate details of systems such as polyurethane film. The steady-state film thickness increases monotonically with the temperature possibly with two logarithmic dependences. The equilibrium interface width shows a nonmonotonic dependence: on increasing the temperature, Ws seems to increase slowly before it begins to decay Ws=4.12-1.39 ln(T).     

Electrophoretic flow of interacting polymer chains: Effects of temperature,polymer concentration,and porosity

Using a Monte Carlo simulation in three dimensions, we studied the variation of the root-meansquare (rms) displacement (R_rms) of polymer chains with time and the rates of their mass transfer (j) as a function of biased field (B), polymer concentration (p), chain length (L_c), porosity (p_s), and temperature (T). In homogeneous/annealed system, the rms displacement of the chains shows a drift-like behavior, R_rms ∼ t, in the asymptotic time regime preceded by a subdiffusive power-law (R_rms ∼ t^k, with k < 1/2) at high p. The subdiffusive regime expands on increasing L_c and p but reduces on increasing T or B. In quenched porous media, the drift-like behavior of R_rms persists at low barrier concentration (p_b) and high T. However, at high p_b and/or low T, chains relax into a subdrift and/or subdiffusive behavior especially with high p or long L_c. Flow of chains is measured via an effective permeability (σ) using a linear response assumption. In annealed system, σ increases monotonically with B at high T and low p but varies nonmonotonically at low T, high p and high L_c. We find that σ decays with L_c, σ ∼ L, where α depends on B, p and T with a typical value a α ∼ 0.43−0.64 for p = 0.1-0.3 at B = 0.5. Further, σ decays with p, σ ∼ − Cp with a decay rate C sensitive to T and B. In quenched porous media, even at low pb and high T, σ varies nonmonotonically with bias, i.e., the increase of σ is followed by decay on increasing the bias beyond a characteristic value (B_c). This characteristic bias seems to decrease logarithmically with barrier concentration, B_c ∼ −klnp_b. The prefactor k depends on the chain length, k ≈ 0.35 for shorter chains (L_c = 20, 40) and ≈ 0.15 for longer chains (L_c = 60). Scaling dependence of σ on L_c similar to that in annealed system is also observed in porous media with different values of exponent α. The current density shows a nonlinear power-law response, j ∼ B^σ, with a nonuniversal exponent δ ≈ 1.10−1.39 at high temperatures and low barrier concentrations.     

Supramolecular assembly of a biomineralizing antimicrobial peptide in coarse-grained Monte Carlo simulations

Monte Carlo simulations are used to model the self-organizing behavior of the biomineralizing peptide KSL (KKVVFKVKFK) in the presence of phosphate. Originally identified as an antimicrobial peptide, KSL also directs the formation of biosilica through a hypothetical supramolecular template that requires phosphate for assembly. Specificity of each residue and the interactions between the peptide and phosphate are considered in a coarse-grained model. Both local and global physical quantities are calculated as the constituents execute their stochastic motion in the presence and absence of phosphate. Ordered peptide aggregates develop after simulations reach thermodynamic equilibrium, wherein phosphates form bridging ligands with lysines and are found interdigitated between peptide molecules. Results demonstrate that interactions between the lysines and phosphate drive self-organization into lower energy conformations of interconnected peptide scaffolds that resemble the supramolecular structures of polypeptide- and polyamine-mediated silica condensation systems. Furthermore, the specific phosphate-peptide organization appears to mimic the zwitterionic structure of native silaffins (scaffold proteins of diatom shells), suggesting a similar template organization for silica deposition between the in vitro KSL and silaffin systems.     

Enhanced Emission of Silver Nanoclusters Through Quantitative Phase Transfer

Silver nanoclusters composed of only a few metal atoms present appealing properties such as fluorescence. We have previously reported on aqueous solutions of this fluorophore using poly(methacrylic acid) as scaffold and their sensing properties. Here we report on the preparation of organic solutions of fluorescent silver nanoclusters by quantitative transfer from aqueous solution to an immiscible organic solvent. The fluorescent silver nanoclusters in the organic phase present enhanced emission properties and increased purity, which may expand the range of applications of this promising fluorophore.     

Determination of volatile organic sulfur compounds in the air at sewage management areas by thermal desorption and gas chromatography-mass spectrometry

The concentrations of seven volatile organic sulfur compounds (VOSCs) in air samples were determined by active collection on multisorbent tubes followed by two-stage thermal desorption and gas chromatography-mass spectrometry. The compounds studied were ethyl mercaptan (CH(3)CH(2)SH), dimethyl sulfide ((CH(3))(2)S), carbon disulfide (CS(2)), propyl mercaptan (C(3)H(8)S), butyl mercaptan (C(4)H(10)S), dimethyl disulfide ((CH(3))(2)S(2)) and 1-pentanethiol (C(5)H(12)S). Active collection on SilcoSteel multisorbent tubes enabled an air volume of 3000ml to be sampled without observing breakthrough. This study focused on an exhaustive sampling of several process steps or sections from sewage management plants. A wide range of concentrations was observed. Dimethyl sulfide, carbon disulfide and dimethyl disulfide were the most abundant compounds in all samples, the highest concentrations being 608.5microg m(-3), 658.5microg m(-3) and 857.8microg m(-3), respectively. The less appearing compound was ethyl mercaptan, which was only detected in the sludge digestion process at a maximum concentration of 14.8microg m(-3). The remaining compounds were detected and measured in about half the samples. The sections with the maximum values of VOSCs involved sludge processes such as mixing, thickening and digestion. The results were also strongly influenced by the design characteristics of the sampling point, e.g. whether the sample was taken at a confined site or in the open air.     

Relation between s-polarized and p-polarized internal reflection spectra: application for the spectral resolution of perpendicular vibrational modes

The orientation of chemical bonds in thin films is commonly probed with polarized internal reflection Fourier transform infrared spectroscopy. Here we demonstrate how the internal reflection spectra obtained using s-polarized light are related with the corresponding p-polarized spectra. The relation between s- and p-polarized internal reflection spectra is applied to resolve the absorption bands of vibrational modes with components oriented perpendicular to the substrate. This is successfully demonstrated using Langmuir-Blodgett films containing smectite clay minerals and a surfactant deposited on ZnSe and Ge internal reflection elements.