Biconvex sets and optimization with biconvex functions: a survey and extensions

The problem of optimizing a biconvex function over a given (bi)convex or compact set frequently occurs in theory as well as in industrial applications, for example, in the field of multifacility location or medical image registration. Thereby, a function is called biconvex, if f(x,y) is convex in y for fixed x∈X, and f(x,y) is convex in x for fixed y∈Y. This paper presents a survey of existing results concerning the theory of biconvex sets and biconvex functions and gives some extensions. In particular, we focus on biconvex minimization problems and survey methods and algorithms for the constrained as well as for the unconstrained case. Furthermore, we state new theoretical results for the maximum of a biconvex function over biconvex sets. J. Gorski and K. Klamroth were partially supported by a grant of the German Research Foundation (DFG).     

Pincer‐Type Complexes for Catalytic (De)Hydrogenation and Transfer (De)Hydrogenation Reactions: Recent Progress

Pincer complexes are becoming increasingly important for organometallic chemistry and organic synthesis. Since numerous applications for such catalysts have been developed in recent decades, this Minireview covers progress in their use as catalysts for (de)hydrogenation and transfer (de)hydrogenation reactions during the last four years. Aside from noble‐metal‐based pincer complexes, the corresponding base metal complexes are also highlighted and their applications summarized.     

LED‐Illuminated NMR Studies of Flavin‐Catalyzed Photooxidations Reveal Solvent Control of the Electron‐Transfer Mechanism

Mechanistic insights into chemical photocatalysis are mainly the domain of UV/Vis spectroscopy, because NMR spectroscopy has been limited by the type of illumination so far. An improved LED‐based illumination device can be used to obtain NMR reaction profiles of photocatalytic reactions under synthetic conditions and perform both photo‐CIDNP and intermediate studies. Flavin‐catalyzed photooxidations of alcohols show the potential of this setup. After identical initial photoreaction steps the stabilization of a downstream intermediate is the key to the further reaction mechanism and the reactivity. As a chemical photocatalyst flavin can act either as a one‐ or a two‐electron mediator when the stability of the zwitterionic radical pair is moldulated in different solvents. This demonstrates the importance of downstream intermediates and NMR‐accessible complementary information in photocatalytic reactions and suggests the control of photoorganic reactions by solvent effects.     

Direct Ruthenium‐Catalyzed Hydrogenation of Carboxylic Acids to Alcohols

The “green” reduction of carboxylic acids to alcohols is a challenging task in organic chemistry. Herein, we describe a general protocol for generation of alcohols by catalytic hydrogenation of carboxylic acids. Key to success is the use of a combination of Ru(acac)₃, triphos and Lewis acids. The novel method showed broad substrate tolerance and a variety of aliphatic carboxylic acids including biomass‐derived compounds can be smoothly reduced.     

Large-scale similarity search profiling of ChEMBL compound data sets

A large-scale similarity search investigation has been carried out on 266 well-defined compound activity classes extracted from the ChEMBL database. The analysis was performed using two widely applied two-dimensional (2D) fingerprints that mark opposite ends of the current performance spectrum of these types of fingerprints, i.e., MACCS structural keys and the extended connectivity fingerprint with bond diameter four (ECFP4). For each fingerprint, three nearest neighbor search strategies were applied. On the basis of these search calculations, a similarity search profile of the ChEMBL database was generated. Overall, the fingerprint search campaign was surprisingly successful. In 203 of 266 test cases (～76%), a compound recovery rate of at least 50% was observed with at least the better performing fingerprint and one search strategy. The similarity search profile also revealed several general trends. For example, fingerprint searching was often characterized by an early enrichment of active compounds in database selection sets. In addition, compound activity classes have been categorized according to different similarity search performance levels, which helps to put the results of benchmark calculations into perspective. Therefore, a compendium of activity classes falling into different search performance categories is provided. On the basis of our large-scale investigation, the performance range of state-of-the-art 2D fingerprinting has been delineated for compound data sets directed against a wide spectrum of pharmaceutical targets.     

Fourier transform rheology as a universal non-linear mechanical characterization of droplet size and interfacial tension of dilute monodisperse emulsions

A new protocol to gain interfacial tension and droplet size of dilute monodisperse emulsions from Fourier Transform Rheology (FTR), is proposed. Specifically, a universal dimensionless quantity E was found at small strain amplitudes to correlate with the droplet size of the emulsion where E is inversely related to the square of the capillary number Ca and directly proportional to the relative intensities of the fifth and third harmonics, I(5)/I(3). The limiting value E(0) at small strain deformations can be used as a universal parameter to calculate different emulsion properties. Different morphological constitutive models for emulsions were used to establish the universality of the parameter E(0). Preliminary analysis on experimental data confirms the validity of this approach for the characterization of emulsion properties, including the estimation of interfacial tension and droplet radius.     

Sensing carbohydrate-protein interactions at picomolar concentrations using cantilever arrays

Carbohydrates are important mediators of many biological processes that underlie cellular communication and disease mechanisms. Therapeutic agents include carbohydrate-based vaccines and the potent anti-viral protein Cyanovirin-N (CV-N). CV-N acts by specifically binding the carbohydrate structures decorating the cell surface of deadly viruses including human immunodeficiency virus (HI-V) or Ebola. In search for new carbohydrate-binding proteins and the development of sensors that exploit carbohydrate-protein interactions the label-free cantilever array technique can provides a fast, parallel and low-cost approach.