Tensor Decomposition With Generalized Lasso Penalties

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multiway data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our approach presents many nontrivial challenges at the intersection of modeling and computation, which are studied in detail. An efficient coordinate-wise optimization algorithm for PTD is presented, and its convergence properties are characterized. The method is applied both to simulated data and real data on flu hospitalizations in Texas and motion-capture data from video cameras. These results show that our penalized tensor decomposition can offer major improvements on existing methods for analyzing multiway data that exhibit smooth spatial or temporal features.     

Geometric approach to global asymptotic stability for the SEIRS models in epidemiology

In this paper, we present a more general criterion for the global asymptotic stability of equilibria for nonlinear autonomous differential equations based on the geometric criterion developed by Li and Muldowney. By applying this criterion, we obtain some results for the global asymptotic stability of SEIRS models with constant recruitment and varying total population size. Based on these results, we give a complete affirmative answer to Liu–Hethcote–Levin conjecture. Furthermore, an affirmative answer to Li–Graef–Wang–Karsai’s problem for SEIR model with permanent immunity and varying total population size is given.     

Quadratic cone cutting surfaces for quadratic programs with on–off constraints

We study the convex hull of a set arising as a relaxation of difficult convex mixed integer quadratic programs (MIQP). We characterize the extreme points of the convex hull of the set and the extreme points of its continuous relaxation. We derive four quadratic cutting surfaces that improve the strength of the continuous relaxation. Each of the cutting surfaces is second-order-cone representable. Via a shooting experiment, we provide empirical evidence as to the importance of each inequality type in improving the relaxation. Computational results that employ the new cutting surfaces to strengthen the relaxation for MIQPs arising from portfolio optimization applications are promising.     

A complete characterization of disjunctive conic cuts for mixed integer second order cone optimization

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique, we show that one can extend our previous results to the case in which that intersection is unbounded. We provide a complete characterization in closed form of the conic inequalities required to describe the convex hull when the hyperplanes defining the disjunction are parallel.     

Comparative Studies of Selected Criteria Enabling Optimization of the Extraction of Polar Biologically Active Compounds from Alfalfa with Supercritical Carbon Dioxide

The aim of this research was to provide crucial and useful data about the selection of the optimization criteria of supercritical carbon dioxide extraction of alfalfa at a quarter-technical plant. The correlation between more general output, including total phenolics and flavonoids content, and a more specified composition of polar constituents was extensively studied. In all alfalfa extracts, polar bioactive constituents were analyzed by both spectrometric (general output) and chromatographic (detailed output) analyses. Eight specific phenolic acids and nine flavonoids were determined. The most dominant were salicylic acid (221.41 µg g⁻¹), ferulic acid (119.73 µg g⁻¹), quercetin (2.23 µg g⁻¹), and apigenin (2.60 µg g⁻¹). For all seventeen analyzed compounds, response surface methodology and analysis of variance were used to provide the optimal conditions of supercritical fluid extraction for each individual constituent. The obtained data have shown that eight of those compounds have a similar range of optimal process parameters, being significantly analogous for optimization based on total flavonoid content.     

Optimization of Vacuum-Microwave-Assisted Extraction of Natural Polyphenols and Flavonoids from Raw Solid Waste of the Orange Juice Producing Industry at Industrial Scale

Orange pomace (OP) is a solid waste produced in bulk as a byproduct of the orange juice industry and accounts for approximately 50% of the quantity of the fruits processed into juice. In numerous literature references there is information about diverse uses of orange pomace for the production of high-added-value products including production of natural antioxidant and antimicrobial extracts rich in polyphenols and flavonoids which can substitute the hazardous chemical antioxidants/antimicrobials used in agro-food and cosmetics sectors. In this work and for the first time, according to our knowledge, the eco-friendly aqueous vacuum microwave assisted extraction of orange pomace was investigated and optimized at real industrial scale in order to produce aqueous antioxidant/antimicrobial extracts. A Response Surface Optimization methodology with a multipoint historical data experimental design was employed to obtain the optimal values of the process parameters in order to achieve the maximum rates of extraction of OP total polyphenols and/or total flavonoids for economically optimum production at industrial scale. The three factors used for the optimization were: (a) microwave power (b) water to raw pomace ratio and (c) extraction time. Moreover, the effectiveness and statistical soundness of the derived cubic polynomial predictive models were verified by ANOVA.