Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme.

A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers T G V 2 and N s T G V 2 . Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging data is proved by Γ -convergence under a conditional uniform bound on the trace constant of the operators and a finite-null-space condition. Some first examples and numerical results are given.

Advanced Chemophenetic Analysis of Essential Oil from Leaves of Piper gaudichaudianum Kunth (Piperaceae) Using a New Reduction-Oxidation Index to Explore Seasonal and Circadian Rhythms.

The aromatic species Piper gaudichaudianum Kunth (Piperaceae) is widely used in Brazil for medicinal and ritualistic applications. In the current study, chemophenetic patterns were realized across season and circadian rhythm based on the chemical profile of essential oils (EOs) from leaves. Hydrodistilled essential oils were analyzed by GC-MS and GC-FID, and a new calculation of metabolite oxidation level, averaged for each individual molecule component of the EO, was used to explore the patterns of metabolism/biosynthesis. This new index used an intermediate calculation, the 'weighted average redox standard' (SRO), to enable a value for mixtures of metabolites to be generated, the 'general mixture redox index' (GMOR). The indices were subjected to a proof-of-concept approach by making comparison to outcomes from multivariate analyses, i.e., PCA and HCA. Chemical analysis demonstrated that the essential oils were dominated by sesquiterpenes, constructed of 15 classes of compound (C-skeletons), and 4 C-skeletons were recognized in the monoterpene group, giving a total of 19. The variation of chemical profiles was distinct at different phenological stages, but stronger chemical variation was evident between day and night as compared to season. Furthermore, due to comprehensive sampling across different regions, nine chemotypes were recognized, including those previously reported. The SRO and GMRO indices demonstrate that phenological variation of chemistry is mainly an outcome of redox fluctuations in terpene biosynthesis, changing from day to night. These indices also corroborate that chemical diversity is increased with oxidative metabolism. Lastly, the current study demonstrates pronounced phenotypic plasticity in P. gaudichaudianum, which makes it a suitable candidate to help further our understanding of chemophenetics and chemical ecology.

Topics in the mathematical design of materials.

We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phase-transforming and shape-morphing materials, (ii) epitaxy as an approach of central importance in the design of advanced semiconductor materials, (iii) selected design problems in soft matter, (iv) mathematical problems in magnetic materials, (v) some open problems in liquid crystals and soft materials and (vi) mathematical problems on liquid crystal colloids. The presentation combines topics from soft and hard condensed matter, with specific focus on those design themes where mathematical approaches could possibly lead to exciting progress. This article is part of the theme issue 'Topics in mathematical design of complex materials'.