Shape-Constrained Estimation Using Nonnegative Splines

We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.     

Zero-Divisor Graphs for Group Rings

Let R be a commutative ring with 1 ≠ 0, G be a nontrivial finite group, and let Z(R) be the set of zero divisors of R. The zero-divisor graph of R is defined as the graph Γ(R) whose vertex set is Z(R)* = Z(R)?{0} and two distinct vertices a and b are adjacent if and only if ab = 0. In this paper, we investigate the interplay between the ring-theoretic properties of group rings RG and the graph-theoretic properties of Γ(RG). We characterize finite commutative group rings RG for which either diam(Γ(RG)) ≤2 or gr(Γ(RG)) ≥4. Also, we investigate the isomorphism problem for zero-divisor graphs of group rings. First, we show that the rank and the cardinality of a finite abelian p-group are determined by the zero-divisor graph of its modular group ring. With the notion of zero-divisor graphs extended to noncommutative rings, it is also shown that two finite semisimple group rings are isomorphic if and only if their zero-divisor graphs are isomorphic. Finally, we show that finite noncommutative reversible group rings are determined by their zero-divisor graphs.     

Instant controlled pressure drop technology and ultrasound assisted extraction for sequential extraction of essential oil and antioxidants

The instant controlled pressure drop (DIC) technology enabled both the extraction of essential oil and the expansion of the matrix itself which improved solvent extraction. The sequential use of DIC and Ultrasound Assisted Extraction (UAE) triggered complementary actions materialized by supplementary effects. We visualized these combination impacts by comparing them to standard techniques: Hydrodistillation (HD) and Solvent Extraction (SE). First, the extraction of orange peel Essential Oils (EO) was achieved by HD during 4 h and DIC process (after optimization) during 2 min; EO yields was 1.97 mg/g dry material (dm) with HD compared to 16.57 mg/g dm with DIC. Second, the solid residue was recovered to extract antioxidant compounds (naringin and hesperidin) by SE and UAE. Scanning electron microscope showed that after HD the recovered solid shriveled as opposite to DIC treatment which expanded the product structure. HPLC analyses showed that the best kinetics and yields of naringin and hesperidin extraction was when DIC and UAE are combined. Indeed, after 1 h of extraction, DIC treated orange peels with UAE were 0.825 ± 1.6 × 10^?2 g/g of dry material (dm) for hesperidin and 6.45 × 10^?2 ± 2.3 × 10^?4 g/g dm for naringin compared to 0.64 ± 2.7 × 10^?2 g/g of dry material (dm) and 5.7 × 10^?2 ± 1.6 × 10^?3 g/g dm, respectively with SE. By combining DIC to UAE, it was possible to enhance kinetics and yields of antioxidant extraction.     

Green ultrasound-assisted extraction of carotenoids based on the bio-refinery concept using sunflower oil as an alternative solvent

A green, inexpensive and easy-to-use method for carotenoids extraction from fresh carrots assisted by ultrasound was designed in this work. Sunflower oil was applied as a substitute to organic solvents in this green ultrasound-assisted extraction (UAE): a process which is in line with green extraction and bio-refinery concepts. The processing procedure of this original UAE was first compared with conventional solvent extraction (CSE) using hexane as solvent. Moreover, the UAE optimal conditions for the subsequent comparison were optimized using response surface methodology (RSM) and ultra performance liquid chromatography – diode array detector – mass spectroscopy (UPLC–DAD–MS). The results showed that the UAE using sunflower as solvent has obtained its highest β-carotene yield (334.75 mg/l) in 20 min only, while CSE using hexane as solvent obtained a similar yield (321.35 mg/l) in 60 min. The green UAE performed under optimal extraction conditions (carrot to oil ratio of 2:10, ultrasonic intensity of 22.5 W cm^?2, temperature of 40 °C and sonication time of 20 min) gave the best yield of β-carotene.     

Investigation of magnetic field effect on surface and finite-site free energy in one-dimensional Ising model of nanosystems

We investigate a one-dimensional (1-D) Ising model for finite-site systems. The finite-site free energy and the surface free energy are calculated via the transfer matrix method. We show that, at high magnetic fields, the surface free energy has an asymptotic limit. The absolute surface energy increases when the value of f (the ratio of magnetic field to nearest-neighbor interactions) increases, and for f?≥?10 approaches a constant value. For the values of f?≥?0.2, the finite-site free energy also increases, but slowly. The thermodynamic limit in which physical properties approach the bulk value is also explored.     

Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.     

On the eigenvalues of quaternion matrices

This article is a continuation of the article [F. Zhang, Ger?gorin type theorems for quaternionic matrices, Linear Algebra Appl. 424 (2007), pp. 139–153] on the study of the eigenvalues of quaternion matrices. Profound differences in the eigenvalue problems for complex and quaternion matrices are discussed. We show that Brauer's theorem for the inclusion of the eigenvalues of complex matrices cannot be extended to the right eigenvalues of quaternion matrices. We also provide necessary and sufficient conditions for a complex square matrix to have infinitely many left eigenvalues, and analyse the roots of the characteristic polynomials for 2?×?2 matrices. We establish a characterisation for the set of left eigenvalues to intersect or be part of the boundary of the quaternion balls of Ger?gorin.     

Radiation synthesis of starch-acrylic acid–vinyl sulfonic acid/multiwalled carbon nanotubes composite for the removal of 134Cs and 152+154Eu from aqueous solutions

Starch-acrylic acid-co-vinyl sulfonic acid/multiwalled carbon nanotubes (starch-AA-VSA/f-MWCNTs) bionanocomposite was successfully synthesized using gamma radiation for initiate the grafting of AA/VSA on starch in the presence of f-MWCNTs by template polymerization technique. The structural characteristics were confirmed by FTIR, SEM, and TGA. The adsorption behaviors of bionanocomposite toward Eu(III) and Cs(I) were examined using the batch adsorption experiments. Langmuir and Freundlich’s models were used to fit the experimental data of the adsorption isotherms. Kinetic studies showed that the adsorption data followed the pseudo-second-order model. Thermodynamic studies indicated that the reaction was favorable at high temperature and endothermic process.

     

Effect of Microalgae Polysaccharides on Biochemical and Metabolomics Pathways Related to Plant Defense in Solanum lycopersicum

Applied Biochemistry and Biotechnology - Microalgae are photosynthetic microorganisms that produce several bioactive molecules that have received considerable attention in scientific and industrial...