A globally linearly convergent method for pointwise quadratically supportable convex–concave saddle point problems

We study the Proximal Alternating Predictor–Corrector (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle [8] to solve nonsmooth structured convex–concave saddle point problems consisting of the sum of a smooth convex function, a finite collection of nonsmooth convex functions and bilinear terms. We introduce the notion of pointwise quadratic supportability, which is a relaxation of a standard strong convexity assumption and allows us to show that the primal sequence is R-linearly convergent to an optimal solution and the primal-dual sequence is globally Q-linearly convergent. We illustrate the proposed method on total variation denoising problems and on locally adaptive estimation in signal/image deconvolution and denoising with multiresolution statistical constraints.     

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

Polyhydroxyalkanoates (PHAs) are considered promising “green” alternatives to synthetic polymers because they are bio-derived, biodegradable and biocompatible. The properties of bacterial PHA copolymers depend on their microstructures, which can be modified with the use of different fermentation processes and feed materials. Thus, it is desirable to have an improved testing method for the determination of PHA microstructures. In this work, a detailed NMR analysis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) microstructure was made. Previously only two of the hydroxyvalerate ¹³C NMR peaks have been assigned at the triad level. In this work, three of the ¹³C hydroxyvalerate peaks and two of the hydroxybutyrate peaks were found to be split into four peaks each due to comonomer sequence effects. Using eight copolymer samples with a wide compositional range, we were able to assign all these peaks to B-centered and V-centered triad sequences. Through curve deconvolution, the triad intensities were determined. These triad sequence intensities can then be analyzed via both the first-order Markovian and two-component Bernoullian models to obtain more in-depth information on copolymer composition and comonomer reactivities.     

Decolorization and mineralization of yellow 5 (E102) by UV/Fe2+/H2O2 process. Optimization of the operational conditions by response surface methodology

In this study, the optimization and implementation of a homogeneous photo-Fenton process for the decolorization and mineralization of a wastewater containing highly concentrated yellow 5 (E102) dye, resulting from an industry placed in the suburbs of Medellin (Colombia), is presented. Response surface methodology was applied as a tool for the optimization of operational conditions such as initial dyestuff concentration, H₂O₂ concentration, and UV-radiation power (number of lamps). The decolorization, degradation and mineralization efficiencies were used as response variables. The following conditions were found to be optimal for decolorization and mineralization of yellow 5: UV radiation of 365 nm (4 W, one lamp), dye concentration of 200 mg/L, Fe²⁺ concentration of 1.0 mM, H₂O₂ concentration of 1.75 mL/L, treatment time of 180 min, Fe²⁺ concentration of 1 mM and pH = 3. Under these conditions (180 min), the photo-Fenton process allowed us to reach ca. 100% of color dye degradation, 99% of COD degradation, and 85% of mineralization (TOC). The scavenging effect of the Cl^– anion on the photodegradation process was also confirmed.     

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

Experimental and theoretical study of thermodynamic properties of levoglucosan

The heat capacity of levoglucosan was measured over the temperature range (5 to 370) K by adiabatic calorimetry. The temperatures and enthalpies of a solid-phase transition and fusion for the compound were found by DSC. The obtained results allowed us to calculate thermodynamic properties of crystalline levoglucosan in the temperature range (0 to 384) K. The enthalpy of sublimation for the low-temperature crystal phase was found from the temperature-dependent saturated vapor pressures determined by the Knudsen effusion method. The thermodynamic properties of gaseous levoglucosan were calculated by methods of statistical thermodynamics using the molecular parameters from quantum chemical calculations. The enthalpy of formation of the crystalline compound was found from the experiments in a combustion calorimeter. The gas-phase enthalpy of formation was also obtained at the G4 level of theory. The thermodynamic analysis of equilibria of levoglucosan formation from cellulose, starch, and glucose was conducted.     

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows

The Lagrangian–Eulerian (LE) approach is used in many computational methods to simulate two-way coupled dispersed two-phase flows. These include averaged equation solvers, as well as direct numerical simulations (DNS) and large-eddy simulations (LES) that approximate the dispersed-phase particles (or droplets or bubbles) as point sources. Accurate calculation of the interphase momentum transfer term in LE simulations is crucial for predicting qualitatively correct physical behavior, as well as for quantitative comparison with experiments. Numerical error in the interphase momentum transfer calculation arises from both forward interpolation/approximation of fluid velocity at grid nodes to particle locations, and from backward estimation of the interphase momentum transfer term at particle locations to grid nodes. A novel test that admits an analytical form for the interphase momentum transfer term is devised to test the accuracy of the following numerical schemes: (1) fourth-order Lagrange Polynomial Interpolation (LPI-4), (3) Piecewise Cubic Approximation (PCA), (3) second-order Lagrange Polynomial Interpolation (LPI-2) which is basically linear interpolation, and (4) a Two-Stage Estimation algorithm (TSE). A number of tests are performed to systematically characterize the effects of varying the particle velocity variance, the distribution of particle positions, and fluid velocity field spectrum on estimation of the mean interphase momentum transfer term. Numerical error resulting from backward estimation is decomposed into statistical and deterministic (bias and discretization) components, and their convergence with number of particles and grid resolution is characterized. It is found that when the interphase momentum transfer is computed using values for these numerical parameters typically encountered in the literature, it can incur errors as high as 80% for the LPI-4 scheme, whereas TSE incurs a maximum error of 20%. The tests reveal that using multiple independent simulations and higher number of particles per cell are required for accurate estimation using current algorithms. The study motivates further testing of LE numerical methods, and the development of better algorithms for computing interphase transfer terms.     

A mesh simplification strategy for a spatial regression analysis over the cortical surface of the brain

We present a new mesh simplification technique developed for a statistical analysis of a large data set distributed on a generic complex surface, topologically equivalent to a sphere. In particular, we focus on an application to cortical surface thickness data. The aim of this approach is to produce a simplified mesh which does not distort the original data distribution so that the statistical estimates computed over the new mesh exhibit good inferential properties. To do this, we propose an iterative technique that, for each iteration, contracts the edge of the mesh with the lowest value of a cost function. This cost function takes into account both the geometry of the surface and the distribution of the data on it. After the data are associated with the simplified mesh, they are analyzed via a spatial regression model for non-planar domains. In particular, we resort to a penalized regression method that first conformally maps the simplified cortical surface mesh into a planar region. Then, existing planar spatial smoothing techniques are extended to non-planar domains by suitably including the flattening phase. The effectiveness of the entire process is numerically demonstrated via a simulation study and an application to cortical surface thickness data.     

A stochastic-structurally based three dimensional finite-strain damage model for fibrous soft tissue

A fully three dimensional finite-strain damage model for fibrous soft tissue is developed. The model assumes uncoupled contributions for the matrix and collagen fibers, and uncoupled bulk and deviatoric response over any range of deformations. A simple isotropic damage mechanism within the framework of continuum damage mechanics has been used to describe the softening behavior under deformation for the matrix. On the other hand, statistical aspects related to the length distribution of the reinforcing fibers lead to a damage model for the reinforcing material. As a result, a general theoretical framework for constitutive modeling of biological soft tissue with continuum damage is obtained. A theoretical example consisting of a biaxial test of a soft tissue reinforced with two families of collagen fibers has been considered to demonstrate the capabilities of the proposed model and to study the sensitivity to changes in the statistical parameters associated with the reinforcing material. Also, a preliminary numerical example is included to demonstrate the model on a inhomogeneous boundary value problem. Results show that the model is able to capture the typical stress-strain behavior observed in fibrous soft tissue and seems to confirm the soundness of the proposed formulation.