Probabilistic learning on manifolds (PLoM) with partition

The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the “small data” limit where the number N of points in the training set is small. Many extensions have since been proposed, making it possible to deal with increasingly complex cases. However, the performance limit has been observed and explained for applications for which N is very small and for which the dimension of the diffusion-map basis is close to N. For these cases, we propose a novel extension based on the introduction of a partition in independent random vectors. We take advantage of this development to present improvements of the PLoM such as a simplified algorithm for constructing the diffusion-map basis and a new mathematical result for quantifying the concentration of the probability measure in terms of a probability upper bound. The analysis of the efficiency of this extension is presented through two applications.     

An invariant subspace‐based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non‐unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal‐based reduced‐order model of the system. Copyright © 2012 John Wiley & Sons, Ltd.     

Quality of dried haskap berries (Lonicera caerulea L.) as affected by prior juice extraction,osmotic treatment,and drying conditions

The effect of juice extraction conditions on the quality of haskap berries (Lonicera caerulea L.) dried at different temperatures (60, 100, and 140°C) was investigated. The conventional juice extraction (process A) consisted of a two-press process, where thawed berries were pressed, and osmotic treatment was applied before pressing again. This was compared with a modified extraction (process B), which applied osmotic treatment during fruit thawing and only one press was used for extraction. The quality parameters investigated included moisture content, pressed berry yield, extraction loss, drying yield, total anthocyanin content (TAC), vitamin C content, and the rehydration characteristics of the final dried berries. Pressing the berries to 70% juice yield resulted in a higher pressed berry yield and better physicochemical quality in the pressed product. The yield was 26.39 and 28.92% in the conventional and modified extraction, with moisture contents of 70.32 and 77.75%, respectively. The TACs of pressed berries from extraction processes A and B were 24.62 and 33.03?mg C-3-G g^?1 DW and the vitamin C contents were 14.14 and 36.18?mg/100?g, respectively. Drying at 60°C until 25% moisture content was better than at higher temperatures, resulting in a better quality dried product. It revealed drying yields of 45.32 and 52.75%, TACs of 4.00 and 4.30?mg C-3-G g^?1 DW, vitamin C contents of 2.97 and 4.91?mg /100?g, and rehydration ratios of 2.22 and 2.37 from processes A and B, respectively. Process B with the one-step extraction is recommended for higher pressed berry yield, higher drying yield, and enhanced quality of the pressed and dried products. It is also a more efficient process, in terms of time, cost, and energy.     

Efficient Monte Carlo computation of Fisher information matrix using prior information

The Fisher information matrix (FIM) is a critical quantity in several aspects of mathematical modeling, including input selection and confidence region calculation. Analytical determination of the FIM in a general setting, especially in nonlinear models, may be difficult or almost impossible due to intractable modeling requirements or/and intractable high-dimensional integration.To circumvent these difficulties, a Monte Carlo simulation based technique, known as resampling algorithm, is usually recommended, in which values of the log-likelihood function or its exact stochastic gradient computed based on a set of pseudo-data vectors are used. The current work proposes an extension of this resampling algorithm in order to enhance the statistical qualities of the estimator of the FIM. This modified resampling algorithm is useful in those cases when some elements of the FIM are analytically known from prior information and the rest of the elements are unknown. The estimator of the FIM resulting from the proposed algorithm simultaneously preserves the analytically known elements and reduces variances of the estimators of the unknown elements. This is achieved by capitalizing on the information contained in the known elements.     

A theoretical physiologically based pharmacokinetic approach for modeling the fate of anthocyanins in vivo

Recent studies on the pharmacokinetics of anthocyanins (ACNs) and their metabolites have uncovered evidence for hitherto unknown physiological effects affecting the fate of these compounds in vivo. In particular, it has been shown that the stomach, in addition to the small intestine, has an important role in absorption. Most studies still use a noncompartmental or one-compartmental approach to determine the pharmacokinetic parameters of ACNs, which does not represent the anatomical and physiological conditions that a compound is subject to in the organism. Thus, the objective of this study was to review the current knowledge of the different processes involved in the metabolism of ACNs once ingested and, based on this information, propose a theoretical physiologically based, multicompartmental pharmacokinetic (PBMK) model to describe their fate in vivo. This is the first study that reports a PBMK model for ACNs; the model provides a more physiologically representative approach for ANC metabolism, which could be used as a basis for experimental designs and interspecies scale-up.     

Tuning a hydrophilic nanobelt’s crystal lattice for interface-tailored nanocompositing with a hydrophobic polymer

Nanoblending hydrophilic nanofillers thoroughly into hydrophobic polymer matrices has long been challenging, especially if involving no pre-functionalization on a 1D ceramic nanomaterial. Here we report a facile approach to fine-tuning of sodium titanate (Na₂Ti₃O₇) nanobelt’s (NB) surface chemistry widely by exchanging the NB’s crystal lattice cations, for successfully nanoblending the low-cost and versatile NBs into the poly(vinyl benzyl chloride) or p(VBC) and the sulfonated form of pVBC’s [or sp(VBC)] matrixes. For the first time, the adjustable nanocompositing showed a long-sought workability in not only in situ radical polymerization of VBC monomer but also ex situ nanoblending of the p(VBC), with the NBs. The resultant nanocomposites possess an unusual surface versatility that can be tailored from being hydrophilic to being hydrophobic by design. This method concludes a generalized and industry-viable approach to mass-producing nanocomposites of many types facilely at low-cost, especially for large scale industries such as packaging materials.     

Activation effect of silver nanoparticles on the photoelectrochemical performance of mesoporous TiO2 nanospheres photoanodes for water oxidation reaction

This work reports the photodeposition of Ag nanoparticles onto mesoporous TiO₂ (m-TiO₂) pre-formed by the evaporation-induced self-assembly method. Photoanodes of Ag/m-TiO₂ assembled by electrophoretic disclose a superior photoelectrochemical (PEC) performance for water oxidation reaction related to m-TiO₂. The photoanodes physicochemical investigations witness the even arrangement of m-TiO₂ nanospheres particles over the substrates. The PEC study displays a steady photocurrent density of 1 mAcm^?2 at ?1.0 V vs SCE was attained for Ag/m-TiO₂ photoanodes in visible light illumination and it is nearly twofold enhancements in comparison with m-TiO₂ photoanodes. The observed superior PEC nature was attributed to the reduced band-gap energy and charge recombination that caused from the incorporation of plasmonic photodeposited Ag nanoparticles on m-TiO₂ nanospheres photoanodes.